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In this work we investigate the presence of integrable hidden structures in the dynamics of perturbed non-rotating black holes (BHs). This can also be considered as a first step in a wider program of an effective identification of ``slow'' and ``fast'' degrees of freedom (DoFs) in the (binary) BH dynamics, following a wave-mean flow perspective. The slow DoFs would be associated with a nonlinear integrable dynamics, on which the fast ones propagate following an effective linear dynamics. BH perturbation theory offers a natural ground to test these properties. Indeed, the decoupling of Einstein equations into wave master equations with a potential provides an instance of such splitting into (frozen) slow DoFs (background potential) over which the linear dynamics of the fast ones (perturbation master functions) evolve. It has been recently shown that these wave equations possess an infinite number of symmetries that correspond to the flow of the infinite hierarchy of Korteweg-de Vries (KdV) equations. Starting from these results, we systematically investigate the presence of integrable structures in BH perturbation theory. We first study them in Cauchy slices and then extend the analysis to hyperboloidal foliations. This second step introduces a splitting of the master equation into bulk and boundary contributions, unveiling an underlying structural relation with the slow and fast DoFs. This insight represents a first step to establish the integrable structures associated to the slow DoFs as bulk symmetries of the dynamics of perturbed BHs., Comment: 23 pages, comments are welcome

LISA (Laser Interferometer Space Antenna) is a space mission that has recently entered the implementation phase. The main goal of LISA is to survey, for the first time, the observable universe by detecting low-frequency gravitational waves (GWs). One of the main GW sources that LISA will detect is the coalescence and merger of Massive Black Hole Binaries (MBHBs). In this work, we explore the application of Sequential Neural Likelihood, a simulation-based inference algorithm, to the detection and parameter estimation of MBHBs signals in the LISA data. Instead of sampling from the conventional likelihood function, which typically relies on the assumptions of Gaussianity and stationarity of the noise and requires a forward simulation for each evaluation, this method constructs a surrogate likelihood that is ultimately described by a neural network trained from a dataset of simulations (noise + MBHB). Since the likelihood is independent of the priors, we can iteratively train models that target specific observations in a fraction of the time and computational cost that other traditional and machine learning-based strategies would require. One key aspect of the method is the compression of the data. Because of the iterative nature of the method, we are able to train models to obtain qualitatively similar posteriors with less than 2% of the simulator calls that Markov Chain Monte Carlo methods would require. We compare these posteriors with those obtained from standard techniques and discuss the differences that appear, some of which can be identified as caused by the loss of information from the data compression we use. We also discuss future improvements to this method., Comment: RevTeX 4.2, 28 pages, 17 figures, 20 plots. Comments welcome

Perturbation theory of vacuum spherically-symmetric spacetimes (including the cosmological constant) has greatly contributed to the understanding of black holes, relativistic compact stars and even inhomogeneous cosmological models. The perturbative equations can be decoupled in terms of (gauge-invariant) master functions satisfying $1+1$ wave equations. In this work, building on previous work on the structure of the space of master functions and equations, we study the reconstruction of the metric perturbations in terms of the master functions. To that end, we consider the general situation in which the perturbations are driven by an arbitrary energy-momentum tensor. Then, we perform the metric reconstruction in a completely general perturbative gauge. In doing so, we investigate the role of Darboux transformations and Darboux covariance, responsible for the isospectrality between odd and even parity in the absence of matter sources and also of the physical equivalence between the descriptions based on all the possible master equations. We also show that the metric reconstruction can be carried out in terms of any of the possible master functions and that the expressions admit an explicitly covariant form., Comment: 27 pages, comments are welcome

The Laser Interferometer Space Antenna (LISA) is the first scientific endeavour to detect and study gravitational waves from space. LISA will survey the sky for Gravitational Waves in the 0.1 mHz to 1 Hz frequency band which will enable the study of a vast number of objects ranging from Galactic binaries and stellar mass black holes in the Milky Way, to distant massive black-hole mergers and the expansion of the Universe. This definition study report, or Red Book, presents a summary of the very large body of work that has been undertaken on the LISA mission over the LISA definition phase., Comment: 155 pages, with executive summary and table of contents

Extreme-mass-ratio inspirals consist of binary systems of compact objects, with orders of magnitude differences in their masses, in the regime where the dynamics are driven by gravitational wave emission. The unique nature of extreme-mass-ratio inspirals facilitates the exploration of diverse and stimulating tests related to various aspects of black holes and General Relativity. These tests encompass investigations into the spacetime geometry, the dissipation of the binary system energy and angular momentum, and the impact of the intrinsic non-linear effects of the gravitational interaction. This review accounts for the manifold opportunities for testing General Relativity, ranging from examinations of black hole properties to cosmological and multimessenger tests., Comment: V2. Updated to match published version. V1: 67+19 pages, 2 figures. Review Chapter for the book "Recent Progress on Gravity Tests" (Eds. C. Bambi and A. C\'ardenas-Avenda\~no, Springer Singapore)

LISA, the Laser Interferometer Space Antenna, will usher in a new era in gravitational-wave astronomy. As the first anticipated space-based gravitational-wave detector, it will expand our view to the millihertz gravitational-wave sky, where a spectacular variety of interesting new sources abound: from millions of ultra-compact binaries in our Galaxy, to mergers of massive black holes at cosmological distances; from the beginnings of inspirals that will venture into the ground-based detectors' view to the death spiral of compact objects into massive black holes, and many sources in between. Central to realising LISA's discovery potential are waveform models, the theoretical and phenomenological predictions of the pattern of gravitational waves that these sources emit. This white paper is presented on behalf of the Waveform Working Group for the LISA Consortium. It provides a review of the current state of waveform models for LISA sources, and describes the significant challenges that must yet be overcome., Comment: 239 pages, 11 figures, white paper from the LISA Consortium Waveform Working Group, invited for submission to Living Reviews in Relativity, updated with comments from community

This document presents a summary of the 2023 Terrestrial Very-Long-Baseline Atom Interferometry Workshop hosted by CERN. The workshop brought together experts from around the world to discuss the exciting developments in large-scale atom interferometer (AI) prototypes and their potential for detecting ultralight dark matter and gravitational waves. The primary objective of the workshop was to lay the groundwork for an international TVLBAI proto-collaboration. This collaboration aims to unite researchers from different institutions to strategize and secure funding for terrestrial large-scale AI projects. The ultimate goal is to create a roadmap detailing the design and technology choices for one or more km-scale detectors, which will be operational in the mid-2030s. The key sections of this report present the physics case and technical challenges, together with a comprehensive overview of the discussions at the workshop together with the main conclusions., Comment: Summary of the Terrestrial Very-Long-Baseline Atom Interferometry Workshop held at CERN: https://indico.cern.ch/event/1208783/

The waveform of a binary black hole coalescence appears to be both simple and universal. In this essay we argue that the dynamics should admit a separation into 'fast and slow' degrees of freedom, such that the latter are described by an integrable system of equations, accounting for the simplicity and universality of the waveform. Given that Painlev\'e transcendents are a smoking gun of integrable structures, we propose the Painlev\'e-II transcendent as the key structural element threading a hierarchy of asymptotic models aiming at capturing different (effective) layers in the dynamics. Ward's conjecture relating integrable and (anti)self-dual solutions can provide the avenue to encode background binary black hole data in (non-local) twistor structures., Comment: 17 pages, no figures. Essay awarded a honorable mention in the 2023 Gravity Research Foundation essay competition

It has recently been shown that the dynamics of perturbed non-rotating black holes (BHs) admits an infinite number of symmetries that are generated by the flow of the Korteweg-de Vries (KdV) equation. These symmetries lead to an infinite number of conserved quantities that can be obtained as integrals of differential polynomials in the potential appearing in the gauge-invariant master equations describing the BH perturbations, the KdV integrals. These conserved quantities are the same for all the possible potentials, which means that they are invariant under Darboux transformations, and they fully determine the BHs transmission amplitudes, or greybody factors, via a moment problem. In this paper we introduce a new semi-analytical method to obtain the greybody factors associated with BH scattering processes by solving the moment problem using only the KdV integrals. The method is based on the use of Pad\'e approximants and we check it first by comparing with results from the case of a P\"oschl-Teller potential, for which we have analytical expressions for the greybody factors. Then, we apply it to the case of a Schwarzschild BH and compare with results from computations based on the Wentzel-Kramers-Brillouin (WKB) approximation. It turns out that the new method provides accurate results for the BH greybody factors for all frequencies. The method is also computationally very efficient., Comment: 21 pages, 13 figures, 26 plots, picture in Fig.(12) (bottom panel) replaced as it was duplicated

The dynamics of perturbed non-rotating black holes (BHs) can be described in terms of master equations of the wave type with a potential. In the frequency domain, the master equations become time-independent Schr\"odinger equations with no discrete spectrum. It has been recently shown that these wave equations possess an infinite number of symmetries that correspond to the flow of the infinite hierarchy of Korteweg-de Vries (KdV) equations. As a consequence, the infinite set of associated conserved quantities, the KdV integrals, are the same for all the different master equations that we can consider. In this paper we show that the BH scattering reflection and transmission coefficients characterizing the continuous spectrum can be fully determined via a moment problem, in such a way that the KdV integrals provide the momenta of a distribution function depending only on the reflection coefficient. We also discuss the existence and uniqueness of solutions, strategies to solve the moment problem, and finally show the case of the P\"oschl-Teller potential where all the steps can be carried out analytically., Comment: 22 pages, 5 figures

An M-class mission proposal in response to the 2021 call in ESA's science programme with a broad range of objectives in fundamental physics, which include testing the Equivalence Principle and Lorentz Invariance, searching for Ultralight Dark Matter and probing Quantum Mechanics., Comment: As submitted to the M7 call in July 2022, except updated for the recent (Sept. 2022) MICROSCOPE results, and new section 2.5 summarizing the information provided to ESA during the September 2022 audition

The Laser Interferometer Space Antenna (LISA) has the potential to reveal wonders about the fundamental theory of nature at play in the extreme gravity regime, where the gravitational interaction is both strong and dynamical. In this white paper, the Fundamental Physics Working Group of the LISA Consortium summarizes the current topics in fundamental physics where LISA observations of GWs can be expected to provide key input. We provide the briefest of reviews to then delineate avenues for future research directions and to discuss connections between this working group, other working groups and the consortium work package teams. These connections must be developed for LISA to live up to its science potential in these areas., Comment: Accepted in: Living Reviews in Relativity

The Laser Interferometer Space Antenna (LISA) will be a transformative experiment for gravitational wave astronomy, and, as such, it will offer unique opportunities to address many key astrophysical questions in a completely novel way. The synergy with ground-based and space-born instruments in the electromagnetic domain, by enabling multi-messenger observations, will add further to the discovery potential of LISA. The next decade is crucial to prepare the astrophysical community for LISA's first observations. This review outlines the extensive landscape of astrophysical theory, numerical simulations, and astronomical observations that are instrumental for modeling and interpreting the upcoming LISA datastream. To this aim, the current knowledge in three main source classes for LISA is reviewed; ultracompact stellar-mass binaries, massive black hole binaries, and extreme or intermediate mass ratio inspirals. The relevant astrophysical processes and the established modeling techniques are summarized. Likewise, open issues and gaps in our understanding of these sources are highlighted, along with an indication of how LISA could help making progress in the different areas. New research avenues that LISA itself, or its joint exploitation with upcoming studies in the electromagnetic domain, will enable, are also illustrated. Improvements in modeling and analysis approaches, such as the combination of numerical simulations and modern data science techniques, are discussed. This review is intended to be a starting point for using LISA as a new discovery tool for understanding our Universe.

We summarize the discussions at a virtual Community Workshop on Cold Atoms in Space concerning the status of cold atom technologies, the prospective scientific and societal opportunities offered by their deployment in space, and the developments needed before cold atoms could be operated in space. The cold atom technologies discussed include atomic clocks, quantum gravimeters and accelerometers, and atom interferometers. Prospective applications include metrology, geodesy and measurement of terrestrial mass change due to, e.g., climate change, and fundamental science experiments such as tests of the equivalence principle, searches for dark matter, measurements of gravitational waves and tests of quantum mechanics. We review the current status of cold atom technologies and outline the requirements for their space qualification, including the development paths and the corresponding technical milestones, and identifying possible pathfinder missions to pave the way for missions to exploit the full potential of cold atoms in space. Finally, we present a first draft of a possible road-map for achieving these goals, that we propose for discussion by the interested cold atom, Earth Observation, fundamental physics and other prospective scientific user communities, together with ESA and national space and research funding agencies., Comment: Summary of the Community Workshop on Cold Atoms in Space and corresponding Road-map: https://indico.cern.ch/event/1064855/

Starting from the infinite set of possible master equations for the perturbations of Schwarzschild black holes, with master functions linear in the metric perturbations and their first-order derivatives, we show that of all them are connected via Darboux transformations. These transformations preserve physical quantities like the quasinormal mode frequencies and the infinite hierarchy of Korteweg-de Vries conserved quantities, revealing a new hidden symmetry in the description of the perturbations of Schwarzschild black holes: Darboux covariance., Comment: 6 pages, revtex 4-2

Perturbation theory of vacuum spherically-symmetric spacetimes is a crucial tool to understand the dynamics of black hole perturbations. Spherical symmetry allows for an expansion of the perturbations in scalar, vector, and tensor harmonics. The resulting perturbative equations are decoupled for modes with different parity and different harmonic numbers. Moreover, for each harmonic and parity, the equations for the perturbations can be decoupled in terms of (gauge-invariant) master functions that satisfy 1+1 wave equations. By working in a completely general perturbative gauge, in this paper we study what is the most general master function that is linear in the metric perturbations and their first-order derivatives and satisfies a wave equation with a potential. The outcome of the study is that for each parity we have two branches of solutions with similar features. One of the branches includes the known results: In the odd-parity case, the most general master function is an arbitrary linear combination of the Regge-Wheeler and the Cunningham-Price-Moncrief master functions whereas in the even-parity case it is an arbitrary linear combination of the Zerilli master function and another master function that is new to our knowledge. The other branch is very different since it includes an infinite collection of potentials which in turn lead to an independent collection master of functions which depend on the potential. The allowed potentials satisfy a non-linear ordinary differential equation. Finally, all the allowed master functions are gauge invariant and can be written in a fully covariant form., Comment: 22 pages, revtex 4-2. (v2: title update) (v3: new conventions for a master function; update of a reference)

An idealized "test" object in general relativity moves along a geodesic. However, if the object has a finite mass, this will create additional curvature in the spacetime, causing it to deviate from geodesic motion. If the mass is nonetheless sufficiently small, such an effect is usually treated perturbatively and is known as the gravitational self-force due to the object. This issue is still an open problem in gravitational physics today, motivated not only by basic foundational interest, but also by the need for its direct application in gravitational-wave astronomy. In particular, the observation of extreme-mass-ratio inspirals by the future space-based detector LISA will rely crucially on an accurate modeling of the self-force driving the orbital evolution and gravitational wave emission of such systems. In this paper, we present a novel derivation, based on conservation laws, of the basic equations of motion for this problem. They are formulated with the use of a quasilocal (rather than matter) stress-energy-momentum tensor---in particular, the Brown-York tensor---so as to capture gravitational effects in the momentum flux of the object, including the self-force. Our formulation and resulting equations of motion are independent of the choice of the perturbative gauge. We show that, in addition to the usual gravitational self-force term, they also lead to an additional "self-pressure" force not found in previous analyses, and also that our results correctly recover known formulas under appropriate conditions. Our approach thus offers a fresh geometrical picture from which to understand the self-force fundamentally, and potentially useful new avenues for computing it practically., Comment: v1: 41 pages, 12 figures. To be submitted for publication, comments welcome; v2: 42 pages. Comments and references added; v3: Matches published version

The inspiral of a stellar-mass compact object into a massive ($\sim 10^{4}$-$10^{7} M_{\odot}$) black hole produces an intricate gravitational-wave signal. Due to the extreme-mass ratios involved, these systems complete $\sim 10^{4}$-$10^{5}$ orbits, most of them in the strong-field region of the massive black hole, emitting in the frequency range $\sim10^{-4}-1~$Hz. This makes them prime sources for the space-based observatory LISA (Laser Interferometer Space Antenna). LISA observations will enable high-precision measurements of the physical characteristics of these extreme-mass-ratio inspirals (EMRIs): redshifted masses, massive black hole spin and orbital eccentricity can be determined with fractional errors $\sim 10^{-4}$-$10^{-6}$, the luminosity distance with better than $\sim 10\%$ precision, and the sky localization to within a few square degrees. EMRIs will provide valuable information about stellar dynamics in galactic nuclei, as well as precise data about massive black hole populations, including the distribution of masses and spins. They will enable percent-level measurements of the multipolar structure of massive black holes, precisely testing the strong-gravity properties of their spacetimes. EMRIs may also provide cosmographical data regarding the expansion of the Universe if inferred source locations can be correlated with galaxy catalogs., Comment: 13 pages, 1 figure; white paper submitted to Astro2020 (2020 Decadal Survey on Astronomy and Astrophysics); Section III is arXiv-only

The grand challenges of contemporary fundamental physics---dark matter, dark energy, vacuum energy, inflation and early universe cosmology, singularities and the hierarchy problem---all involve gravity as a key component. And of all gravitational phenomena, black holes stand out in their elegant simplicity, while harbouring some of the most remarkable predictions of General Relativity: event horizons, singularities and ergoregions. The hitherto invisible landscape of the gravitational Universe is being unveiled before our eyes: the historical direct detection of gravitational waves by the LIGO-Virgo collaboration marks the dawn of a new era of scientific exploration. Gravitational-wave astronomy will allow us to test models of black hole formation, growth and evolution, as well as models of gravitational-wave generation and propagation. It will provide evidence for event horizons and ergoregions, test the theory of General Relativity itself, and may reveal the existence of new fundamental fields. The synthesis of these results has the potential to radically reshape our understanding of the cosmos and of the laws of Nature. The purpose of this work is to present a concise, yet comprehensive overview of the state of the art in the relevant fields of research, summarize important open problems, and lay out a roadmap for future progress., Comment: White Paper for the COST action "Gravitational Waves, Black Holes, and Fundamental Physics", 272 pages, 12 figures; v4: updated references and author list. Overall improvements and corrections. To appear in Classical and Quantum Gravity

Numerical Relativity is a mature field with many applications in Astrophysics, Cosmology and even in Fundamental Physics. As such, we are entering a stage in which new sophisticated methods adapted to open problems are being developed. In this paper, we advocate the use of Pseudo-Spectral Collocation (PSC) methods in combination with high-order precision arithmetic for Numerical Relativity problems with high accuracy and performance requirements. The PSC method provides exponential convergence (for smooth problems, as is the case in many problems in Numerical Relativity) and we can use different bit precision without the need of changing the structure of the numerical algorithms. Moreover, the PSC method provides high-compression storage of the information. We introduce a series of techniques for combining these tools and show their potential in two problems in relativistic gravitational collapse: (i) The classical Choptuik collapse, estimating with arbitrary precision the location of the apparent horizon. (ii) Collapse in asympotically anti-de Sitter spacetimes, showing that the total energy is preserved by the numerical evolution to a very high degree of precision., Comment: Revised version. 30 pages, 12 figures

Partial differential equations with distributional sources---in particular, involving (derivatives of) delta distributions---have become increasingly ubiquitous in numerous areas of physics and applied mathematics. It is often of considerable interest to obtain numerical solutions for such equations, but any singular ("particle"-like) source modeling invariably introduces nontrivial computational obstacles. A common method to circumvent these is through some form of delta function approximation procedure on the computational grid; however, this often carries significant limitations on the efficiency of the numerical convergence rates, or sometimes even the resolvability of the problem at all. In this paper, we present an alternative technique for tackling such equations which avoids the singular behavior entirely: the "Particle-without-Particle" method. Previously introduced in the context of the self-force problem in gravitational physics, the idea is to discretize the computational domain into two (or more) disjoint pseudospectral (Chebyshev-Lobatto) grids such that the "particle" is always at the interface between them; thus, one only needs to solve homogeneous equations in each domain, with the source effectively replaced by jump (boundary) conditions thereon. We prove here that this method yields solutions to any linear PDE the source of which is any linear combination of delta distributions and derivatives thereof supported on a one-dimensional subspace of the problem domain. We then implement it to numerically solve a variety of relevant PDEs: hyperbolic (with applications to neuroscience and acoustics), parabolic (with applications to finance), and elliptic. We generically obtain improved convergence rates relative to typical past implementations relying on delta function approximations., Comment: 41 pages, 11 figures; v2: references and clarifications added (mostly in the introduction), matches the published version in Journal of Scientific Computing

One of the key astrophysical sources for the Laser Interferometer Space Antenna (LISA) are the inspirals of stellar-origin compact objects into massive black holes in the centres of galaxies. These extreme-mass-ratio inspirals (EMRIs) have great potential for astrophysics, cosmology and fundamental physics. In this paper we describe the likely numbers and properties of EMRI events that LISA will observe. We present the first results computed for the 2.5 Gm interferometer that was the new baseline mission submitted in January 2017 in response to the ESA L3 mission call. In addition, we attempt to quantify the astrophysical uncertainties in EMRI event rate estimates by considering a range of different models for the astrophysical population. We present both likely event rates and estimates for the precision with which the parameters of the observed sources could be measured. We finish by discussing the implications of these results for science using EMRIs., Comment: 12 pages, 3 figures, 5 tables. These proceedings are a summary of the results presented in arXiv:1703.09722

The space-based Laser Interferometer Space Antenna (LISA) will be able to observe the gravitational-wave signals from systems comprised of a massive black hole and a stellar-mass compact object. These systems are known as extreme-mass-ratio inspirals (EMRIs) and are expected to complete $\sim 10^4$-$10^5$ cycles in band, thus allowing exquisite measurements of their parameters. In this work, we attempt to quantify the astrophysical uncertainties affecting the predictions for the number of EMRIs detectable by LISA, and find that competing astrophysical assumptions produce a variance of about three orders of magnitude in the expected intrinsic EMRI rate. However, we find that irrespective of the astrophysical model, at least a few EMRIs per year should be detectable by the LISA mission, with up to a few thousands per year under the most optimistic astrophysical assumptions. We also investigate the precision with which LISA will be able to extract the parameters of these sources. We find that typical fractional statistical errors with which the intrinsic parameters (redshifted masses, massive black hole spin and orbital eccentricity) can be recovered are $\sim 10^{-6}$-$10^{-4}$. Luminosity distance (which is required to infer true masses) is inferred to about $10\%$ precision and sky position is localized to a few square degrees, while tests of the multipolar structure of the Kerr metric can be performed to percent-level precision or better., Comment: 13 figures, 22 pages; updated to match published version

We extend our previous analysis of holographic heavy ion collisions in non-conformal theories. We provide a detailed description of our numerical code. We study collisions at different energies in gauge theories with different degrees of non-conformality. We compare four relaxation times: the hydrodynamization time (when hydrodynamics becomes applicable), the EoSization time (when the average pressure approaches its equilibrium value), the isotropization time (when the longitudinal and transverse pressures approach each other) and the condensate relaxation time (when the expectation value of a scalar operator approaches its equilibrium value). We find that these processes can occur in several different orderings. In particular, the condensate can remain far from equilibrium even long after the plasma has hydrodynamized and EoSized. We also explore the rapidity distribution of the energy density at hydrodynamization. This is far from boost-invariant and its width decreases as the non-conformality increases. Nevertheless, the velocity field at hydrodynamization is almost exactly boost-invariant regardless of the non-conformality. This result may be used to constrain the initialization of hydrodynamic fields in heavy ion collisions., Comment: 45 pages, 17 figures. Expanded some sections. Matches published version in JHEP

The gravitational waves emitted by binary systems with extreme mass ratios carry unique astrophysical information expected to be probed by the next generation of gravitational wave detectors such as LISA. The detection of these binaries rely on an accurate modeling of the gravitational self-force that drives their orbital evolution. Although the theoretical formalism to compute the self-force has been largely established, the mathematical tools needed to implement it are still under development, and the self-force computation remains an open problem. We present here a frequency-domain implementation of the particle-without-particle (PwP) technique previously developed for the computation of the scalar self-force -- a helpful testbed for the gravitational self-force., Comment: 2 pages, to appear in the proceedings of the 11th International LISA Symposium (Zurich, 5-9 September 2016), in Journal of Physics: Conference Series

In classical Hamiltonian theories, entropy may be understood either as a statistical property of canonical systems, or as a mechanical property, that is, as a monotonic function of the phase space along trajectories. In classical mechanics, there are theorems which have been proposed for proving the non-existence of entropy in the latter sense. We explicate, clarify and extend the proofs of these theorems to some standard matter (scalar and electromagnetic) field theories in curved spacetime, and then we show why these proofs fail in general relativity; due to properties of the gravitational Hamiltonian and phase space measures, the second law of thermodynamics holds. As a concrete application, we focus on the consequences of these results for the gravitational two-body problem, and in particular, we prove the non-compactness of the phase space of perturbed Schwarzschild-Droste spacetimes. We thus identify the lack of recurring orbits in phase space as a distinct sign of dissipation and hence entropy production., Comment: 39 pages, 3 figures; v2: version to appear in Phys. Rev. D, references added

We present a new hybrid Cauchy-characteristic evolution method that is particularly suited for the study of gravitational collapse in spherically-symmetric asymptotically (global) Anti-de Sitter (AdS) spacetimes. The Cauchy evolution allows us to track the scalar field through the different bounces off the AdS boundary while the characteristic method can bring us very close to the point of formation of an apparent horizon. Here, we describe all the details of the method, including the transition between the two evolution schemes and the details of the numerical implementation for the case of massless scalar fields. We use this scheme to provide more numerical evidence for a recent conjecture on the power-law scaling of the apparent horizon mass resulting from the collapse of subcritical configurations. We also compute the critical exponents and echoing periods for a number of critical points and confirm the expectation that their values should be the same as in the asymptotically-flat case., Comment: 25 pages, 14 figures

Gravitational collapse of a massless scalar field in spherically symmetric anti-de Sitter (AdS) spacetimes presents a new phenomenology with a series of critical points whose dynamics is discretely self-similar as in the asymptotically flat case. Each critical point is the limit of a branch of scalar field configurations that have bounced off the AdS boundary a fixed number of times before forming an apparent horizon. We present results from a numerical study that focus on the interfaces between branches. We find that there is a mass gap between branches and that subcritical configurations near the critical point form black holes with an apparent horizon mass that follows a power law of the form $M_{AH}-M_{g} \propto (p_{c}-p)^{\xi}$, where $M_g$ is the mass gap and the exponent $\xi\simeq 0.7$ appears to be universal., Comment: 5 pages, 5 figures. Corrects typos and adds clarifications to match the published version

Atom interferometers have a multitude of proposed applications in space including precise measurements of the Earth's gravitational field, in navigation & ranging, and in fundamental physics such as tests of the weak equivalence principle (WEP) and gravitational wave detection. While atom interferometers are realized routinely in ground-based laboratories, current efforts aim at the development of a space compatible design optimized with respect to dimensions, weight, power consumption, mechanical robustness and radiation hardness. In this paper, we present a design of a high-sensitivity differential dual species $^{85}$Rb/$^{87}$Rb atom interferometer for space, including physics package, laser system, electronics and software. The physics package comprises the atom source consisting of dispensers and a 2D magneto-optical trap (MOT), the science chamber with a 3D-MOT, a magnetic trap based on an atom chip and an optical dipole trap (ODT) used for Bose-Einstein condensate (BEC) creation and interferometry, the detection unit, the vacuum system for $10^{-11}$ mbar ultra-high vacuum generation, and the high-suppression factor magnetic shielding as well as the thermal control system. The laser system is based on a hybrid approach using fiber-based telecom components and high-power laser diode technology and includes all laser sources for 2D-MOT, 3D-MOT, ODT, interferometry and detection. Manipulation and switching of the laser beams is carried out on an optical bench using Zerodur bonding technology. The instrument consists of 9 units with an overall mass of 221 kg, an average power consumption of 608 W (819 W peak), and a volume of 470 liters which would well fit on a satellite to be launched with a Soyuz rocket, as system studies have shown., Comment: 30 pages, 23 figures, accepted for publication in Experimental Astronomy

The inspirals of stellar-mass mass compact objects into massive black holes in the centres of galaxies are one of the most important sources of gravitational radiation for space-based detectors like LISA or eLISA. These extreme-mass-ratio inspirals (EMRIs) will enable an ambitious research program with implications for astrophysics, cosmology, and fundamental physics. This article is a summary of the talks delivered at the plenary session on EMRIs at the 10th International LISA Symposium. It contains research updates on the following topics: astrophysics of EMRIs; EMRI science potential; and EMRI modeling., Comment: 17 pages, no figures. Proceedings of the LISA Symposium X, to be published at the Journal of Physics

The gravitational waves emitted by binary systems with extreme-mass ratios carry unique astrophysical information that can only be detected by space-based detectors like eLISA. To that end, a very accurate modelling of the system is required. The gravitational self-force program, which has been fully developed in the Lorenz gauge, is the best approach we have so far. However, the computations required would be done more efficiently if we could work in other gauges, like the Regge-Wheeler (RW) one in the case of Schwarzschild black holes. In this letter we present a new scheme, based on the Particle-without-Particle formulation of the field equations, where the gravitational self-force can be obtained from just solving individual wave-type equations like the master equations of the RW gauge. This approach can help to tackle the yet unsolved Kerr case., Comment: 5 pages, 1 figure

Neutron stars and black holes are the most compact astrophysical objects we can think of and as a consequence they are the main sources of gravitational waves. There are many astrophysically relevant scenarios in which these objects are immersed in or endowed with strong magnetic fields, in such a way that gravitational perturbations can couple to electromagnetic ones and can potentially trigger synergistic electromagnetic signatures. In a recent paper we derived the main equations for gravito-electromagnetic perturbations and studied in detail the case of polar electromagnetic perturbations driven by axial gravitational perturbations. In this paper we deal with the case of axial electromagnetic perturbations driven by polar black-hole or neutron stars oscillations, in which the energy emitted in case is considerably larger than in the previous case. In the case of neutron stars the phenomenon lasts considerably longer since the fluid acts as an energy reservoir that shakes the magnetic field for a timescale of the order of secs., Comment: accepted for publication in GRG

The main goal of the LISA Pathfinder (LPF) mission is to fully characterize the acceleration noise models and to test key technologies for future space-based gravitational-wave observatories similar to the eLISA concept. The data analysis team has developed complex three-dimensional models of the LISA Technology Package (LTP) experiment on-board LPF. These models are used for simulations, but more importantly, they will be used for parameter estimation purposes during flight operations. One of the tasks of the data analysis team is to identify the physical effects that contribute significantly to the properties of the instrument noise. A way of approaching this problem is to recover the essential parameters of a LTP model fitting the data. Thus, we want to define the simplest model that efficiently explains the observations. To do so, adopting a Bayesian framework, one has to estimate the so-called Bayes Factor between two competing models. In our analysis, we use three main different methods to estimate it: The Reversible Jump Markov Chain Monte Carlo method, the Schwarz criterion, and the Laplace approximation. They are applied to simulated LPF experiments where the most probable LTP model that explains the observations is recovered. The same type of analysis presented in this paper is expected to be followed during flight operations. Moreover, the correlation of the output of the aforementioned methods with the design of the experiment is explored.

Gravitational perturbations of neutron stars and black holes are well known sources of gravitational radiation. If the compact object is immersed in or endowed with a magnetic field, the gravitational perturbations would couple to electromagnetic perturbations and potentially trigger synergistic electromagnetic signatures. We present a detailed analytic calculation of the dynamics of coupled gravitational and electromagnetic perturbations for both neutron stars and black holes. We discuss the prospects for detecting the electromagnetic waves in these scenarios and the potential that these waves have for providing information about their source., Comment: accepted for publication in PRD

The capture of a compact object in a galactic nucleus by a massive black hole (MBH), an extreme-mass ratio inspiral (EMRI), is the best way to map space and time around it. Recent work on stellar dynamics has demonstrated that there seems to be a complot in phase space acting on low-eccentricity captures, since their rates decrease significantly by the presence of a blockade in the rate at which orbital angular momenta change takes place. This so-called "Schwarzschild barrier" is a result of the impact of relativistic precession on to the stellar potential torques, and thus it affects the enhancement on lower-eccentricity EMRIs that one would expect from resonant relaxation. We confirm and quantify the existence of this barrier using a statistical sample of 2,500 direct-summation N-body simulations using both a post-Newtonian and also for the first time in a direct-summation code a geodesic approximation for the relativistic orbits. The existence of the barrier prevents low-eccentricity EMRIs from approaching the central MBH, but high-eccentricity EMRIs, which have been wrongly classified as "direct plunges" until recently, ignore the presence of the barrier, because they are driven by two-body relaxation. Hence, since the rates are significantly affected in the case of low-eccentricity EMRIs, we predict that a LISA-like observatory such as eLISA will predominantly detect high-eccentricity EMRIs., Comment: 10 pages, submitted

The capture of a compact object in a galactic nucleus by a massive black hole (MBH) is the best way to map space and time around it. Compact objects such as stellar black holes on a capture orbit with a very high eccentricity have been wrongly assumed to be lost for the system after an intense burst of radiation, which has been described as a "direct plunge". We prove that these very eccentric capture orbits spend actually a similar number of cycles in a LISA-like detector as those with lower eccentricities if the central MBH is spinning. Although the rates are higher for high-eccentricity EMRIs, the spin also enhances the rates of lower-eccentricity EMRIs. This last kind have received more attention because of the fact that high-eccentricity EMRIs were thought to be direct plunges and thus negligible. On the other hand, recent work on stellar dynamics has demonstrated that there seems to be a complot in phase space acting on these lower-eccentricity captures, since their rates decrease significantly by the presence of a blockade in the rate at which orbital angular momenta change takes place. This so-called "Schwarzschild barrier" is a result of the impact of relativistic precession on to the stellar potential torques, and thus it affects the enhancement on lower-eccentricity EMRIs that one would expect from resonant relaxation. We confirm and quantify the existence of this barrier using a statitical sample of 2,500 direct-summation N-body simulations using both a post-Newtonian but also, and for the first time, a geodesic approximation for the relativistic orbits. The existence of the barrier prevents "traditional EMRIs" from approaching the central MBH, but if the central MBH is spinning the rate will be anyway dominated by highly-eccentric extreme-mass ratio inspirals, which insolently ignore the presence of the barrier, because they are driven by two-body relaxation., Comment: Some rephrasing of two sentences in this version. arXiv admin note: substantial text overlap with arXiv:1205.4713

The capture of a stellar-mass compact object by a supermassive black hole and the subsequent inspiral (driven by gravitational radiation emission) constitute one of the most important sources of gravitational waves for space-based observatories like eLISA/NGO. In this article we describe their potential as high-precision tools that can be used to perform tests of the geometry of black holes and also of the strong field regime of gravity., Comment: 10 pages, 2 figures. LaTeX, ASP style. Plenary talk presented at the 9th International LISA Symposium, 21-25 May 2012, BnF-Paris, France

General Relativity (GR) describes gravitation well at the energy scales which we have so far been able to achieve or detect. However, we do not know whether GR is behind the physics governing stronger gravitational field regimes, such as near neutron stars or massive black-holes (MBHs). Gravitational-wave (GW) astronomy is a promising tool to test and validate GR and/or potential alternative theories of gravity. The information that a GW waveform carries not only will allow us to map the strong gravitational field of its source, but also determine the theory of gravity ruling its dynamics. In this work, we explore the extent to which we could distinguish between GR and other theories of gravity through the detection of low-frequency GWs from extreme-mass-ratio inspirals (EMRIs) and, in particular, we focus on dynamical Chern-Simons modified gravity (DCSMG). To that end, we develop a framework that enables us, for the first time, to perform a parameter estimation analysis for EMRIs in DCSMG. Our model is described by a 15-dimensional parameter space, that includes the Chern-Simons (CS) parameter which characterises the deviation between the two theories, and our analysis is based on Fisher information matrix techniques together with a (maximum-mismatch) criterion to assess the validity of our results. In our analysis, we study a 5-dimensional parameter space, finding that a GW detector like the Laser Interferometer Space Antenna (LISA) or eLISA (evolved LISA) should be able to discriminate between GR and DCSMG with fractional errors below 5%, and hence place bounds four orders of magnitude better than current Solar System bounds., Comment: 5 pages, 1 figure, 2 tables. Proceeding of the 9th LISA Symposium

Extreme-Mass-Ratio Inspirals (EMRIs) are one of the most promising sources of gravitational waves (GWs) for space-based detectors like the Laser Interferometer Space Antenna (LISA). EMRIs consist of a compact stellar object orbiting around a massive black hole (MBH). Since EMRI signals are expected to be long lasting (containing of the order of hundred thousand cycles), they will encode the structure of the MBH gravitational potential in a precise way such that features depending on the theory of gravity governing the system may be distinguished. That is, EMRI signals may be used to test gravity and the geometry of black holes. However, the development of a practical methodology for computing the generation and propagation of GWs from EMRIs in theories of gravity different than General Relativity (GR) has only recently begun. In this paper, we present a parameter estimation study of EMRIs in a particular modification of GR, which is described by a four-dimensional Chern-Simons (CS) gravitational term. We focus on determining to what extent a space-based GW observatory like LISA could distinguish between GR and CS gravity through the detection of GWs from EMRIs., Comment: 10 pages, JPCS of the Amaldi 9 and NRDA 2011

A common result to all EMRI investigations on rates is that the possibility that a compact object merges with the MBH after only one intense burst of GWs is much more likely than a slow adiabatic inspiral, an EMRI. The later is referred to as a "plunge" because the compact object dives into the MBH. The event rates for plunges are orders of magnitude larger than slow inspirals. On the other hand, nature MBH's are most likely Kerr and the magnitude of the spin has been sized up to be high. We calculate the number of periapsis passages that a compact object set on to an extremely radial orbit goes through before being actually swallowed by the Kerr MBH and we then translate it into an event rate for a LISA-like observatory, such as the proposed ESA mission eLISA/NGO. We prove that a "plunging" compact object is conceptually indistinguishable from an adiabatic, slow inspiral; plunges spend on average up to hundred of thousands of cycles in the bandwidth of the detector for a two years mission. This has an important impact on the event rate, enhancing in some cases significantly, depending on the spin of the MBH and the inclination. Moreover, it has been recently proved that the production of low-eccentricity EMRIs is severely blocked by the presence of a blockade in the rate at which orbital angular momenta change takes place. This is the result of relativistic precession on to the stellar potential torques and hence affects EMRIs originating via resonant relaxation at distances of about $\sim 10^{-2}$ pc from the MBH. Since high-eccentricity EMRIs are a result of two-body relaxation, they are not affected by this phenomenon. Therefore we predict that eLISA EMRI event rates will be dominated by high-eccentricity binaries, as we present here., Comment: Accepted for publication MNRAS. Abstract abridged

[abridged] The detection of gravitational waves from extreme-mass-ratio (EMRI) binaries, comprising a stellar-mass compact object orbiting around a massive black hole, is one of the main targets for low-frequency gravitational-wave detectors in space, like the Laser Interferometer Space Antenna (LISA or eLISA/NGO). The long-duration gravitational-waveforms emitted by such systems encode the structure of the strong field region of the massive black hole, in which the inspiral occurs. The detection and analysis of EMRIs will therefore allow us to study the geometry of massive black holes and determine whether their nature is as predicted by General Relativity and even to test whether General Relativity is the correct theory to describe the dynamics of these systems. To achieve this, EMRI modeling in alternative theories of gravity is required to describe the generation of gravitational waves. In this paper, we explore to what extent EMRI observations with LISA or eLISA/NGO might be able to distinguish between General Relativity and a particular modification of it, known as Dynamical Chern-Simons Modified Gravity. Our analysis is based on a parameter estimation study that uses approximate gravitational waveforms obtained via a radiative-adiabatic method and is restricted to a five-dimensional subspace of the EMRI configuration space. This includes a Chern-Simons parameter that controls the strength of gravitational deviations from General Relativity. We find that, if Dynamical Chern-Simons Modified Gravity is the correct theory, an observatory like LISA or even eLISA/NGO should be able to measure the Chern-Simons parameter with fractional errors below 5%. If General Relativity is the true theory, these observatories should put bounds on this parameter at the level xi^(1/4) < 10^4 km, which is four orders of magnitude better than current Solar System bounds., Comment: RevTeX 4.1. 21 pages, 2 Figures, 7 Tables. Revision to match the published version

We describe a new kludge scheme to model the dynamics of generic extreme-mass-ratio inspirals (EMRIs; stellar compact objects spiraling into a spinning supermassive black hole) and their gravitational-wave emission. The Chimera scheme is a hybrid method that combines tools from different approximation techniques in General Relativity: (i) A multipolar, post-Minkowskian expansion for the far-zone metric perturbation (the gravitational waveforms) and for the local prescription of the self-force; (ii) a post-Newtonian expansion for the computation of the multipole moments in terms of the trajectories; and (iii) a BH perturbation theory expansion when treating the trajectories as a sequence of self-adjusting Kerr geodesics. The EMRI trajectory is made out of Kerr geodesic fragments joined via the method of osculating elements as dictated by the multipolar post-Minkowskian radiation-reaction prescription. We implemented the proper coordinate mapping between Boyer-Lindquist coordinates, associated with the Kerr geodesics, and harmonic coordinates, associated with the multipolar post-Minkowskian decomposition. The Chimera scheme is thus a combination of approximations that can be used to model generic inspirals of systems with extreme to intermediate mass ratios, and hence, it can provide valuable information for future space-based gravitational-wave observatories, like LISA, and even for advanced ground detectors. The local character in time of our multipolar post-Minkowskian self-force makes this scheme amenable to study the possible appearance of transient resonances in generic inspirals., Comment: 10 pages, 3 figures. LaTeX, JPCS style. Submitted to the proceedings of the 9th Edoardo Amaldi Conference on Gravitational Waves, and the 2011 Numerical Relativity - Data Analysis (NRDA) meeting, held 10-15 July 2011 in Cardiff, Wales, UK, July 10-15 2011

The Numerical INJection Analysis (NINJA) project is a collaborative effort between members of the numerical relativity and gravitational wave data analysis communities. The purpose of NINJA is to study the sensitivity of existing gravitational-wave search and parameter-estimation algorithms using numerically generated waveforms, and to foster closer collaboration between the numerical relativity and data analysis communities. The first NINJA project used only a small number of injections of short numerical-relativity waveforms, which limited its ability to draw quantitative conclusions. The goal of the NINJA-2 project is to overcome these limitations with long post-Newtonian - numerical relativity hybrid waveforms, large numbers of injections, and the use of real detector data. We report on the submission requirements for the NINJA-2 project and the construction of the waveform catalog. Eight numerical relativity groups have contributed 63 hybrid waveforms consisting of a numerical portion modelling the late inspiral, merger, and ringdown stitched to a post-Newtonian portion modelling the early inspiral. We summarize the techniques used by each group in constructing their submissions. We also report on the procedures used to validate these submissions, including examination in the time and frequency domains and comparisons of waveforms from different groups against each other. These procedures have so far considered only the $(\ell,m)=(2,2)$ mode. Based on these studies we judge that the hybrid waveforms are suitable for NINJA-2 studies. We note some of the plans for these investigations., Comment: Presented at Amaldi 9

Physics in curved spacetime describes a multitude of phenomena, ranging from astrophysics to high energy physics. The last few years have witnessed further progress on several fronts, including the accurate numerical evolution of the gravitational field equations, which now allows highly nonlinear phenomena to be tamed. Numerical relativity simulations, originally developed to understand strong field astrophysical processes, could prove extremely useful to understand high-energy physics processes like trans-Planckian scattering and gauge-gravity dualities. We present a concise and comprehensive overview of the state-of-the-art and important open problems in the field(s), along with guidelines for the next years. This writeup is a summary of the "NR/HEP Workshop" held in Madeira, Portugal from August 31st to September 3rd 2011., Comment: 68 pages, 4 Figures

We introduce a new kludge scheme to model the dynamics of generic extreme mass-ratio inspirals (stellar compact objects spiraling into a spinning supermassive black hole) and to produce the gravitational waveforms that describe the gravitational-wave emission of these systems. This scheme combines tools from different techniques in General Relativity: It uses a multipolar, post-Minkowskian (MPM) expansion for the far-zone metric perturbation (which provides the gravitational waveforms, here taken up to mass hexadecapole and current octopole order) and for the local prescription of the self-force (since we are lacking a general prescription for it); a post-Newtonian expansion for the computation of the multipole moments in terms of the trajectories; and a BH perturbation theory expansion when treating the trajectories as a sequence of self-adjusting Kerr geodesics. The orbital evolution is thus equivalent to solving the geodesic equations with time-dependent orbital elements, as dictated by the MPM radiation-reaction prescription. To complete the scheme, both the orbital evolution and wave generation require to map the Boyer-Lindquist coordinates of the orbits to the harmonic coordinates in which the different MPM quantities have been derived, a mapping that we provide explicitly in this paper. This new kludge scheme is thus a combination of approximations that can be used to model generic inspirals of systems with extreme mass ratios to systems with more moderate mass ratios, and hence can provide valuable information for future space-based gravitational-wave observatories like LISA and even for advanced ground detectors. Finally, due to the local character in time of our MPM self-force, this scheme can be used to perform studies of the possible appearance of transient resonances in generic inspirals., Comment: RevTeX 4.1. 35 pages, 10 Figures, 3 Tables. Version to match the published article in Physical Review D

When a stellar-mass compact object is captured by a supermassive black hole located in a galactic centre, the system losses energy and angular momentum by the emission of gravitational waves. Subsequently, the stellar compact object evolves inspiraling until plunging onto the massive black hole. These EMRI systems are expected to be one of the main sources of gravitational waves for the future space-based Laser Interferometer Space Antenna (LISA). However, the detection of EMRI signals will require of very accurate theoretical templates taking into account the gravitational self-force, which is the responsible of the stellar-compact object inspiral. Due to its potential applicability on EMRIs, the obtention of an efficient method to compute the scalar self-force acting on a point-like particle orbiting around a massive black hole is being object of increasing interest. We present here a review of our time-domain numerical technique to compute the self-force acting on a point-like particle and we show its suitability to deal with both circular and eccentric orbits., Comment: 4 pages, 2 figures, JPCS latex style. Submitted to JPCS (special issue for the proceedings of the Spanish Relativity Meeting (ERE2010))

The computation of the self-force constitutes one of the main challenges for the construction of precise theoretical waveform templates in order to detect and analyze extreme-mass-ratio inspirals with the future space-based gravitational-wave observatory LISA. Since the number of templates required is quite high, it is important to develop fast algorithms both for the computation of the self-force and the production of waveforms. In this article we show how to tune a recent time-domain technique for the computation of the self-force, what we call the Particle without Particle scheme, in order to make it very precise and at the same time very efficient. We also extend this technique in order to allow for highly eccentric orbits., Comment: IOP LaTeX style. 11 pages, 4 pages. Contribution to the NRDA/CAPRA 2010 Conference

The calculation of the self force in the modeling of the gravitational-wave emission from extreme-mass-ratio binaries is a challenging task. Here we address the question of the possible emergence of a persistent spurious solution in time-domain schemes, referred to as a {\em Jost junk solution} in the literature, that may contaminate self force calculations. Previous studies suggested that Jost solutions are due to the use of zero initial data, which is inconsistent with the singular sources associated with the small object, described as a point mass. However, in this work we show that the specific origin is an inconsistency in the translation of the singular sources into jump conditions. More importantly, we identify the correct implementation of the sources at late times as the sufficient condition guaranteeing the absence of Jost junk solutions., Comment: RevTeX. 5 pages, 2 figures. Version updated to match the contents of the published article

We analyse an eleven-orbit inspiral of a non-spinning black-hole binary with mass ratio q=M1/M2=4. The numerically obtained gravitational waveforms are compared with post-Newtonian (PN) predictions including several sub-dominant multipoles up to multipolar indices (l=5,m=5). We find that (i) numerical and post-Newtonian predictions of the phase of the (2,2) mode accumulate a phase difference of about 0.35 rad at the PN cut off frequency 0.1 for the Taylor T1 approximant when numerical and PN waveforms are matched over a window in the early inspiral phase; (ii) in contrast to previous studies of equal-mass and specific spinning binaries, we find the Taylor T4 approximant to agree less well with numerical results, provided the latter are extrapolated to infinite extraction radius; (iii) extrapolation of gravitational waveforms to infinite extraction radius is particularly important for subdominant multipoles with l unequal m; (iv) 3PN terms in post-Newtonian multipole expansions significantly improve the agreement with numerical predictions for sub-dominant multipoles., Comment: Matches version to be published in CQG, 16 pages, 8 figures

The emergent area of gravitational wave astronomy promises to provide revolutionary discoveries in the areas of astrophysics, cosmology, and fundamental physics. One of the most exciting possibilities is to use gravitational-wave observations to test alternative theories of gravity. In this contribution we describe how to use observations of extreme-mass-ratio inspirals by the future Laser Interferometer Space Antenna to test a particular class of theories: Chern-Simons modified gravity., Comment: 10 pages, 2 figures, Springer Verlag LaTeX style. To appear in the proceedings of Cosmology, the Quantum Vacuum, and Zeta Functions: A workshop with a celebration of Emilio Elizalde's sixtieth birthday, Bellaterra, Barcelona, Spain, 8-10 Mar 2010. Eds. S. D. Odintsov, D. Saez-Gomez, and S. Xambo