Search

We study spherical evolution in scalar-Gauss-Bonnet gravity with additional Ricci coupling and use the gauge-invariant approach of Ref.~\cite{Reall:2021voz} to track well-posedness. Our results show that loss of hyperbolicity when it occurs, is due to the behaviour of physical degrees of freedom. They provide further support to the idea that this behaviour can be tamed by additional interactions of scalar. We also point out a limitation of this gauge-invariant approach: the fact that field redefinitions can change the character of the evolution equations.

Massive scalar fields are promising candidates to address many unresolved problems in fundamental physics. We report the first model-agnostic Bayesian search of massive scalar fields in LIGO/Virgo/KAGRA gravitational-wave data. We find no evidence for such fields and place the most stringent upper limits on their coupling for scalar masses $\lesssim 2\times10^{-12}\,{\rm eV}$. We exemplify the strength of these bounds by applying them to massive scalar-Gauss-Bonnet gravity, finding the tightest constraints on the coupling constant to date, $\sqrt{\alpha_{\rm GB}}\lesssim 1\,{\rm km}$ for scalar masses $\lesssim 10^{-13}\,{\rm eV}$ to 90% confidence., Comment: 18 pages, 7 figures

We study the dynamics of spherically symmetric black holes in scalar Gauss-Bonnet gravity with an additional coupling between the scalar field and the Ricci scalar using non-linear simulations that employ excision. In this class of theories, black holes possess hair if they lie in a specific mass range, in which case they exhibit a finite-area singularity, unlike general relativity. Our results show that the Ricci coupling can mitigate the loss of hyperbolicity in spherical evolution with black hole initial data. Using excision can enlarge the parameter space for which the system remains well-posed, as one can excise the elliptic region that forms inside the horizon. Furthermore, we explore a possible relation between the loss of hyperbolicity and the formation of the finite-area singularity inside the horizon. We find that the location of the singularity extracted from the static analysis matches the location of the sonic line well. Finally, when possible, we extract the monopolar quasi-normal modes and the time scale of the linear tachyonic instability associated with scalarization. We also check our results by utilizing a continued fraction analysis and supposing linear perturbations of the static solutions.

Extreme Mass Ratio Inspirals (EMRIs) are key sources for the future space-based gravitational wave detector LISA, and are considered promising probes of fundamental physics. Here, we present the first complete Bayesian analysis of EMRI signals in theories with an additional massless scalar, which could arise in an extension of General Relativity or of the Standard Model of Particle Physics. We develop a waveform model accurate at adiabatic order for equatorial eccentric orbits around spinning black holes. Using full Bayesian inference, we forecast LISA's ability to probe the presence of new fundamental fields with EMRI observations.

In this note, we discuss the effect of light, non-gauge, bosonic degrees of freedom on the exterior spacetime of an exotic compact object. We show that such fields generically introduce large deviations from black hole spacetimes of General Relativity near and outside the surfaces of ultra-compact exotic objects unless one assumes they totally decouple from the standard model or new heavy fields. Hence, using black hole spacetimes of General Relativity to model ultra-compact exotic objects and their perturbations relies implicitly on this assumption or on the absence of such fields., Comment: v3: minor changes, published version

Phase transitions can play an important role in the cosmological constant problem, allowing the underlying vacuum energy, and therefore the value of the cosmological constant, to change. Deep within the core of neutron stars, the local pressure may be sufficiently high to trigger the QCD phase transition, thus generating a shift in the value of the cosmological constant. The gravitational effects of such a transition should then be imprinted on the properties of the star. Working in the framework of General Relativity, we provide a new model of the stellar interior, allowing for a QCD and a vacuum energy phase transition. We determine the impact of a vacuum energy jump on mass-radius relations, tidal deformability-radius relations, I-Love-Q relations and on the combined tidal deformability measured in neutron star binaries., Comment: 21 pages, 15 figures

Wearable, implantable, and ingestible antennas are continuously evolving in biomedical applications, as they are crucial components in devices used for monitoring and controlling physiological parameters. This work presents an experimentally validated wearable pad which can improve transmission of electromagnetic waves into the human body. This metamaterial-inspired matching pad, which is based on small metallic loops encased in a thin dielectric layer, is mechanically stable, flexible, and passive. As such, the pad can serve as a coupling medium for microwave medical systems and implantable device communication. Operating in the 2.4-2.5 GHz range, the pad demonstrates significant improvement in signal penetration levels (and, hence, depth) into a biological tissue. The study presents design methodology, simulation studies, in-lab development, and experimental characterization of this pad, which can offer a practical solution for enhanced communication and functionality in various medical diagnostic systems., Comment: 6 pages, 8 figures

Gravitational wave observations can test the validity of General Relativity (GR) in the strong field regime. Certain classes of scalar-tensor theories indeed predict that compact objects can exhibit significant deviations from their GR counterparts. Here we explore the quasinormal modes of axial perturbations in spherically symmetric black holes in three such classes: (i) dilatonic black holes with an additional scalar-Ricci coupling (EdRGB), (ii) spontaneously scalarized black holes (EsRGB) with a quadratic coupling to the Gauss-Bonnet invariant and the Ricci scalar, (iii) spontaneously scalarized black holes with a quadratic and a quartic coupling to the Gauss-Bonnet invariant., Comment: 12 pages, 7 figures

In this work, we explore the properties and shadows of spin-induced scalarized black holes, as well as investigate how a Ricci coupling influences them. Our findings reveal significant deviations from the Kerr metric in terms of the location and geodesic frequencies of the innermost stable circular orbit and light ring, with the former exhibiting more pronounced disparities. The shadows of scalarized black holes exhibit relatively minor deviations when compared to those of Kerr black holes with the same mass and spin. Overall, the presence of a Ricci coupling is observed to mitigate deviations from the Kerr metric., Comment: 8 pages, 6 figures

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

Deviations from General Relativity can alter the quasi-normal mode (QNM) ringdown of perturbed black holes. It is known that a shift-symmetric (hence massless) scalar can only introduce black hole hair if it couples to the Gauss-Bonnet invariant, in which case the scalar charge is fixed with respect to the black hole mass and controlled by the strength of that coupling. The charge per unit mass decreases with the mass and can, therefore, be used as a perturbative parameter for black holes that are sufficiently large with respect to the scale suppressing the deviation from General Relativity or the Standard model. We construct an effective field theory scheme for QNMs using this perturbative parameter to capture deviations from Kerr for both the background and the perturbations. We demonstrate that up to second order in the charge per unit mass, QNMs can be calculated by solving standard linearised perturbation equations for the Kerr metric with sources depending on solutions of the same equations up to first order. It follows that corrections to the QNM frequencies are heavily suppressed for sufficiently massive black holes, meaning that LISA is very unlikely to detect any evidence of scalar hair in ringdown signals., Comment: 6 pages

Using the self-force approach, we present the premier first-post-adiabatic accuracy formalism for modelling compact binaries in theories with a massless scalar field non-minimally coupled to gravity. We limit the binary secondary to being a non-spinning compact body with no scalar dipole (we will address the spinning and scalar dipole cases in an upcoming paper). By producing an ansatz for the scalar charged point particle action, we derive first- and second-order perturbative field equations and equations of motion for the secondary compact object. Under our assumptions, implementing this formalism will produce sufficiently accurate waveform templates for precision measurements of the scalar charge of the secondary with LISA data on extreme-mass-ratio inspirals. Our formalism is consistent with almost general scalar-tensor theories of gravity. Implementing our formalism builds on self-force models in General Relativity; we show the incorporation into the two-timescale formalism is straightforward. Excitingly, implementation poses no significantly more challenging barriers than computing first-post adiabatic waveforms in General Relativity., Comment: 15 pages, 0 figures

Theories of gravity with auxiliary fields are of particular interest since they are able to circumvent Lovelock's theorem while avoiding to introduce new degrees of freedom. This type of theories introduces derivatives of the stress-energy tensor in the modified Einstein equation. This peculiar structure of the field equations was shown to lead to spacetime singularities on the surface of stars. Here we focus on yet another problem afflicting gravity theories with auxiliary field. We show that such theories introduce deviations to the Standard Model unless one severely constrains the parameters of the theory, preventing them to produce significant phenomenology at large scales. We first consider the specific case of Palatini $f({\cal R})$ gravity, to clarify the results previously obtained in arXiv:astro-ph/0308111. We show that the matter fields satisfy the Standard Model field equations which reduce to those predicted by General Relativity in the local frame only at tree level, whereas at higher orders in perturbation theory they are affected by corrections that percolate from the gravity sector regardless of the specific $f({\cal R})$ model considered. Finally, we show that this is a more general issue affecting theories with auxiliary fields connected to the same terms responsible for the appearance of surface singularities., Comment: 12 pages, added references, corrected typos, revised argument in section IV, results unchanged

We study spherical collapse of a scalar cloud in scalar-Gauss-Bonnet gravity - a theory in which black holes can develop scalar hair if they are in a certain mass range. We show that an additional quadratic coupling of the scalar field to the Ricci scalar can mitigate loss of hyperbolicity problems that have plagued previous numerical collapse studies and instead lead to well-posed evolution. This suggests that including specific additional interactions can be a successful strategy for tackling well-posedness problems in effective field theories of gravity with nonminimally coupled scalars. Our simulations also show that spherical collapse leads to black holes with scalar hair when their mass is below a mass threshold and above a minimum mass bound and that above the mass threshold the collapse leads to black holes without hair, in line with results in the static case and perturbative analyses. For masses below the minimum mass bound we find that the scalar cloud smoothly dissipates, leaving behind flat space., Comment: 6 pages, 4 figures

We study the imprint of light scalar fields on gravitational waves from extreme mass ratio inspirals -- binary systems with a very large mass asymmetry. We first show that, to leading order in the mass ratio, any effects of the scalar on the waveform are captured fully by two parameters: the mass of the scalar and the scalar charge of the secondary compact object. We then use this theory-agnostic framework to show that the future observations by LISA will be able to simultaneously measure both of these parameters with enough accuracy to detect ultra-light scalars., Comment: 11 pages, 7 figures

It is known that, for shift-symmetric scalars, only a linear coupling with the Gauss-Bonnet invariant can introduce black hole hair. Such hairy black holes have a minimum mass, determined by the coupling of this interaction, and a scalar charge that is uniquely determined by their mass and spin for a fixed value of that coupling. Here we explore how additional shift-symmetric interactions affect the structure of the black hole, the value of the minimum mass, and the scalar charge., Comment: 23 pages, 9 figures

Scalarization is a mechanism that endows strongly self-gravitating bodies, such as neutron stars and black holes, with a scalar-field configuration. It resembles a phase transition in that the scalar configuration appears only when a certain quantity that characterizes the compact object, for example, its compactness or spin, is beyond a threshold. A critical and comprehensive review of scalarization, including the mechanism itself, theories that exhibit it, its manifestation in neutron stars, black holes and their binaries, potential extension to other fields, and a thorough discussion of future perspectives, is provided., Comment: 51 pages, 24 figures. Review commissioned by Reviews of Modern Physics, submitted version, comments welcome. v2: more references, improved text, and typos corrected. Updated to match the published version

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

It has been shown that the synergy of a scalar field coupling with both the Ricci scalar and the Gauss-Bonnet invariant significantly affects the properties of scalarized black holes and neutron stars, including their domain of existence and the amount of scalar hair they carry. Here we study the radial stability of scalarized black-hole solutions. We demonstrate that they are stable against radial perturbations for Ricci couplings consistent with both a late-time cosmological attractor and the evasion of binary pulsar constraints. In addition, we investigate the effect of the Ricci coupling on the hyperbolicity of the equation governing linear, radial perturbations and show that it significantly reduces the region over which hyperbolicity is lost., Comment: 11 pages, 8 figures

We study binary systems in which a stellar mass compact object spirals into a massive black hole, known as extreme mass ratio inspirals, in scenarios with a new fundamental scalar field. Earlier work has shown that, in most interesting such scenarios and to leading order in the mass ratio, the massive black holes can be adequately approximated by the Kerr metric and the imprint of the scalar field on the waveform is fully controlled by the scalar charge of the stellar mass object. Here we use this drastic simplification in the inspiral modelling and consider eccentric equatorial orbits. We study how the scalar charge affects the orbital evolution for different eccentricities and different values of the black hole spin. We then determine how changes in the orbital evolution get imprinted on the waveform and assess LISA's capability to detect or constrain the scalar charge., Comment: Minor changes to match the version published on Phys. Rev. D

The next generation of ground-based gravitational-wave detectors will observe coalescences of black holes and neutron stars throughout the cosmos, thousands of them with exceptional fidelity. The Science Book is the result of a 3-year effort to study the science capabilities of networks of next generation detectors. Such networks would make it possible to address unsolved problems in numerous areas of physics and astronomy, from Cosmology to Beyond the Standard Model of particle physics, and how they could provide insights into workings of strongly gravitating systems, astrophysics of compact objects and the nature of dense matter. It is inevitable that observatories of such depth and finesse will make new discoveries inaccessible to other windows of observation. In addition to laying out the rich science potential of the next generation of detectors, this report provides specific science targets in five different areas in physics and astronomy and the sensitivity requirements to accomplish those science goals. This report is the second in a six part series of reports by the GWIC 3G Subcommittee: i) Expanding the Reach of Gravitational Wave Observatories to the Edge of the Universe, ii) The Next Generation Global Gravitational Wave Observatory: The Science Book (this report), iii) 3G R&D: R&D for the Next Generation of Ground-based Gravitational Wave Detectors, iv) Gravitational Wave Data Analysis: Computing Challenges in the 3G Era, v) Future Ground-based Gravitational-wave Observatories: Synergies with Other Scientific Communities, and vi) An Exploration of Possible Governance Models for the Future Global Gravitational-Wave Observatory Network., Comment: 69 pages, 18 figures

The exploration of the universe has recently entered a new era thanks to the multi-messenger paradigm, characterized by a continuous increase in the quantity and quality of experimental data that is obtained by the detection of the various cosmic messengers (photons, neutrinos, cosmic rays and gravitational waves) from numerous origins. They give us information about their sources in the universe and the properties of the intergalactic medium. Moreover, multi-messenger astronomy opens up the possibility to search for phenomenological signatures of quantum gravity. On the one hand, the most energetic events allow us to test our physical theories at energy regimes which are not directly accessible in accelerators; on the other hand, tiny effects in the propagation of very high energy particles could be amplified by cosmological distances. After decades of merely theoretical investigations, the possibility of obtaining phenomenological indications of Planck-scale effects is a revolutionary step in the quest for a quantum theory of gravity, but it requires cooperation between different communities of physicists (both theoretical and experimental). This review is aimed at promoting this cooperation by giving a state-of-the art account of the interdisciplinary expertise that is needed in the effective search of quantum gravity footprints in the production, propagation and detection of cosmic messengers., Comment: This review was written by participants of the COST Action CA18108. Further information on the review can be found at https://qg-mm.unizar.es/review/, updated to published version

Spontaneous scalarization of neutron stars has been extensively studied in the Damour and Esposito-Far\`ese model, in which a scalar field couples to the Ricci scalar or, equivalently, to the trace of the energy-momentum tensor. However, scalarization of both black holes and neutron stars may also be triggered by a coupling of the scalar field to the Gauss-Bonnet invariant. The case of the Gauss-Bonnet coupling has also received a lot of attention lately, but the synergy of the Ricci and Gauss-Bonnet couplings has been overlooked for neutron stars. Here, we show that combining both couplings has interesting effects on the properties of scalarized neutron stars, such as affecting their domain of existence or the amount of scalar charge they carry., Comment: 14 pages, 9 figures

Spontaneous scalarization is a mechanism that allows a scalar field to go undetected in weak gravity environments and yet develop a nontrivial configuration in strongly gravitating systems. At the perturbative level it manifests as a tachyonic instability around spacetimes that solve Einstein's equations. The endpoint of this instability is a nontrivial scalar field configuration that can significantly modify a compact object's structure and can produce observational signatures of the scalar field's presence. Does such a mechanism exists for vector fields? Here we revisit the model that constitutes the most straightforward generalization of the original scalarization model to a vector field and perform a perturbative analysis. We show that a ghost appears as soon as the square of the naive effective mass squared becomes negative anywhere. This result poses a serious obstacle in generalizing spontaneous scalarization to vector fields., Comment: 12 pages. v2: corrections to Eqs. (23)-(24), new references. v3: matches published version

The Laser Interferometer Space Antenna, LISA, will detect gravitational wave signals from Extreme Mass Ratio Inspirals, where a stellar mass compact object orbits a supermassive black hole and eventually plunges into it. Here we report on LISA's capability to detect whether the smaller compact object in an Extreme Mass Ratio Inspiral is endowed with a scalar field, and to measure its scalar charge -- a dimensionless quantity that acts as a measure of how much scalar field the object carries. By direct comparison of signals, we show that LISA will be able to detect and measure the scalar charge with an accuracy of the order of percent, which is an unprecedented level of precision. This result is independent of the origin of the scalar field and of the structure and other properties of the small compact object, so it can be seen as a generic assessment of LISA's capabilities to detect new fundamental fields., Comment: Typo corrected to match the version in press

Spontaneous scalarization is a gravitational phenomenon in which deviations from general relativity arise once a certain threshold in curvature is exceeded, while being entirely absent below that threshold. For black holes, scalarization is known to be triggered by a coupling between a scalar and the Gauss-Bonnet invariant. A coupling with the Ricci scalar, which can trigger scalarization in neutron stars, is instead known to not contribute to the onset of black hole scalarization, and has so far been largely ignored in the literature when studying scalarized black holes. In this paper, we study the combined effect of both these couplings on black hole scalarization. We show that the Ricci coupling plays a significant role in the properties of scalarized solutions and their domain of existence. This work is an important step in the construction of scalarization models that evade binary pulsar constraints and have general relativity as a cosmological late-time attractor, while still predicting deviations from general relativity in black hole observations., Comment: 8 pages, 8 figures

We extend a recently developed numerical code to obtain stationary, axisymmetric solutions that describe rotating black hole spacetimes in a wide class of modified theories of gravity. The code utilizes a relaxed Newton-Raphson method to solve the full nonlinear modified Einstein's Equations on a two-dimensional grid with a Newton polynomial finite difference scheme. We validate this code by considering static and axisymmetric black holes in General Relativity. We obtain rotating black hole solutions in scalar-Gauss-Bonnet gravity with a linear (linear scalar-Gauss-Bonnet) and an exponential (Einstein-dilaton-Gauss-Bonnet) coupling and compare them to analytical and numerical perturbative solutions. From these numerical solutions, we construct a fitted analytical model and study observable properties calculated from the numerical results.

It was recently shown that a scalar field suitably coupled to the Gauss-Bonnet invariant $\mathcal{G}$ can undergo a spin-induced linear tachyonic instability near a Kerr black hole. This instability appears only once the dimensionless spin $j$ is sufficiently large, that is, $j \gtrsim 0.5$. A tachyonic instability is the hallmark of spontaneous scalarization. Focusing, for illustrative purposes, on a class of theories that do exhibit this instability, we show that stationary, rotating black hole solutions do indeed have scalar hair once the spin-induced instability threshold is exceeded, while black holes that lie below the threshold are described by the Kerr solution. Our results provide strong support for spin-induced black hole scalarization., Comment: 8 pages, 3 figures. v2 matches version published in PRL

We study scalar fields in a black hole background and show that, when the scalar is suitably coupled to curvature, rapid rotation can induce a tachyonic instability. This instability, which is the hallmark of spontaneous scalarization in the linearized regime, is expected to be quenched by nonlinearities and endow the black hole with scalar hair. Hence, our results demonstrate the existence of a broad class of theories that share the same stationary black hole solutions with general relativity at low spins, but which exhibit black hole hair at sufficiently high spins ($a/M\gtrsim 0.5$). This result has clear implications for tests of general relativity and the nature of black holes with gravitational and electromagnetic observations., Comment: Typos corrected in proof to match version published in PRL

In gravity theories that exhibit spontaneous scalarization, astrophysical objects are identical to their general relativistic counterpart until they reach a certain threshold in compactness or curvature. Beyond this threshold, they acquire a non-trivial scalar configuration, which also affects their structure. The onset of scalarization is controlled only by terms that contribute to linear perturbation around solutions of general relativity. The complete set of these terms has been identified for generalized scalar-tensor theories. Stepping on this result, we study the onset on scalarization in generalized scalar-tensor theories and determine the relevant thresholds in terms of the contributing coupling constants and the properties of the compact object., Comment: 10 pages, 10 figures. References added

We demonstrate that there are theories that exhibit spontaneous scalarization in the strong gravity regime while having General Relativity with a constant scalar as a cosmological attractor. We identify the minimal model that has this property and discuss its extensions., Comment: 5 pages, 3 figures; v2: corrected typo in legend of Fig. 1

We study Extreme Mass Ratio Inspirals (EMRIs), during which a small body spirals into a supermassive black hole, in gravity theories with additional scalar fields. We first argue that no-hair theorems and the properties of known theories that manage to circumvent them introduce a drastic simplification to the problem: the effects of the scalar on supermassive black holes, if any, are mostly negligible for EMRIs in vast classes of theories. We then exploit this simplification to model the inspiral perturbatively and we demonstrate that the scalar charge of the small body leaves a significant imprint on gravitational wave emission. Although much higher precision is needed for waveform modelling, our results strongly suggest that this imprint is observable with LISA, rendering EMRIs promising probes of scalar fields., Comment: Minor changes to match the version in press on Phys. Rev. Lett

In this paper, which is of programmatic rather than quantitative nature, we aim to further delineate and sharpen the future potential of the LISA mission in the area of fundamental physics. Given the very broad range of topics that might be relevant to LISA, we present here a sample of what we view as particularly promising directions, based in part on the current research interests of the LISA scientific community in the area of fundamental physics. We organize these directions through a "science-first" approach that allows us to classify how LISA data can inform theoretical physics in a variety of areas. For each of these theoretical physics classes, we identify the sources that are currently expected to provide the principal contribution to our knowledge, and the areas that need further development. The classification presented here should not be thought of as cast in stone, but rather as a fluid framework that is amenable to change with the flow of new insights in theoretical physics., Comment: 22 pages, 1 figure, to appear in General Relativity and Gravitation

Black holes are unique among astrophysical sources: they are the simplest macroscopic objects in the Universe, and they are extraordinary in terms of their ability to convert energy into electromagnetic and gravitational radiation. Our capacity to probe their nature is limited by the sensitivity of our detectors. The LIGO/Virgo interferometers are the gravitational-wave equivalent of Galileo's telescope. The first few detections represent the beginning of a long journey of exploration. At the current pace of technological progress, it is reasonable to expect that the gravitational-wave detectors available in the 2035-2050s will be formidable tools to explore these fascinating objects in the cosmos, and space-based detectors with peak sensitivities in the mHz band represent one class of such tools. These detectors have a staggering discovery potential, and they will address fundamental open questions in physics and astronomy. Are astrophysical black holes adequately described by general relativity? Do we have empirical evidence for event horizons? Can black holes provide a glimpse into quantum gravity, or reveal a classical breakdown of Einstein's gravity? How and when did black holes form, and how do they grow? Are there new long-range interactions or fields in our universe, potentially related to dark matter and dark energy or a more fundamental description of gravitation? Precision tests of black hole spacetimes with mHz-band gravitational-wave detectors will probe general relativity and fundamental physics in previously inaccessible regimes, and allow us to address some of these fundamental issues in our current understanding of nature., Comment: 24 pages, 4 figures. White paper submitted to ESA's Voyage 2050 on behalf of the LISA Consortium 2050 Task Force

Spontaneous scalarization is a mechanism that endows relativistic stars and black holes with a nontrivial configuration only when their spacetime curvature exceeds some threshold. The standard way to trigger spontaneous scalarization is via a tachyonic instability at the linear level, which is eventually quenched due to the effect of non-linear terms. In this paper, we identify all of the terms in the Horndeski action that contribute to the (effective) mass term in the linearized equations and, hence, can cause or contribute to the tachyonic instability that triggers scalarization., Comment: Added a term than had accidentally been omitted in equations (24), (25), (40), (42). Typos corrected. Results unchanged

Future gravitational-wave observations will enable unprecedented and unique science in extreme gravity and fundamental physics answering questions about the nature of dynamical spacetimes, the nature of dark matter and the nature of compact objects., Comment: 14 pages, 2 figures, White Paper submitted to the Astro-2020 (2020 Astronomy and Astrophysics Decadal Survey) by GWIC-3G Science Case Team (GWIC: Gravitational-Wave International Committee); replaced Figure 1 with a revised version that incorporates Gravity IR Flare data point

It has recently been shown that nontrivial couplings between a scalar and the Gauss-Bonnet invariant can give rise to black hole spontaneous scalarization. Theories that exhibit this phenomenon are among the leading candidates for testing gravity with upcoming black hole observations. All models considered so far have focused on specific forms for the coupling, neglecting scalar self-interactions. In this work, we take the first steps towards placing this phenomenon on a more robust theoretical footing by considering the leading-order scalar self-interactions as well as the scalar-Gauss-Bonnet coupling. Our approach is consistent with the principles of effective field theory and yields the simplest and most natural model. We find that a mass term for the scalar alters the threshold for the onset of scalarization, and we study the mass range over which scalarized black hole solutions exist. We also demonstrate that the quartic self-coupling is sufficient to produce scalarized solutions that are stable against radial perturbations, without the need to resort to higher-order terms in the Gauss-Bonnet coupling function. Our model therefore represents a canonical model that can be studied further, with the ultimate aim of developing falsifiable tests of black hole scalarization., Comment: 10 Pages, six figures

We study the cosmological evolution of a scalar field in Horndeski gravity, assuming that the scalar field is subdominant with respect to the cosmic fluid. We first analyse the most general shift-symmetric action that respects local Lorentz symmetry. We show that the bound on the speed of gravitational waves set by GW170817+GRB170817A imposes a constraint only on the linear coupling between the scalar and the Gauss-Bonnet invariant and this constraint is rather mild. Then, we consider some interesting examples of theories that break shift-symmetry, such as the Damour-Esposito-Far\`ese model of spontaneous scalarization and a theory with a quadratic coupling to the Gauss-Bonnet invariant that can lead to black hole scalarization. In both cases, tuning of cosmological initial conditions is necessary to keep the scalar field dormant during cosmic evolution., Comment: v2: published version

Detailed observations of phenomena involving black holes, be it via gravitational waves or more traditional electromagnetic means, can probe the strong field regime of the gravitational interaction. The prediction of features in such observations requires detailed knowledge of the black hole spacetime, both within and outside of General Relativity. We present here a new numerical code that can be used to obtain stationary solutions that describe black hole spacetimes in a wide class of modified theories of gravity. The code makes use of a relaxed Newton-Raphson method to solve the discretized field equations with a Newton's polynomial finite difference scheme. We test and validate this code by considering static and spherically symmetric black holes both in General Relativity, as well as in scalar-Gauss-Bonnet gravity with a linear (linear scalar-Gauss-Bonnet) and an exponential (Einstein-dilaton-Gauss-Bonnet) coupling. As a by-product of the latter, we find that analytic solutions obtained in the small coupling approximation are in excellent agreement with our fully non-linear solutions when using a linear coupling. As expected, differences arise when using an exponential coupling. We then use these numerical solutions to construct a fitted analytical model, which we then use to calculate physical observables such as the innermost stable circular orbit and photon sphere and compare them to the numerical results. This code lays the foundation for more detailed calculations of black hole observables that can be compared with data in the future., Comment: 27 pages, 11 figures

No-hair theorems for scalar-tensor theories imply that the trivial scalar field configuration is the unique configuration around stationary black hole spacetimes. The most basic assumption in these theorems is that a constant scalar configuration is actually admissible. In this paper, we classify shift-symmetric Horndeski theories according to whether or not they admit the trivial scalar configuration as a solution and under which conditions. Local Lorentz symmetry and the presence of a linear coupling between the scalar field and Gauss-Bonnet invariant plays feature prominently in this classification. We then use the classification to show that any theory without linear Gauss-Bonnet coupling that respects Local Lorentz symmetry admits all GR solutions. We also study the scalar hair configuration around black hole spacetimes in theories where the linear Gauss-Bonnet coupling is present. We show that the scalar hair of the configuration is secondary, fixed by the regularity of the horizon, and is determined by the black hole horizon properties.

Scalar-tensor theories of gravity where a new scalar degree of freedom couples to the Gauss-Bonnet invariant can exhibit the phenomenon of spontaneous black hole scalarization. These theories admit both the classic black holes predicted by general relativity as well as novel hairy black hole solutions. The stability of the hairy black holes is strongly dependent on the precise form of the scalar-gravity coupling. A radial stability investigation revealed that all scalarized black hole solutions are unstable when the coupling between the scalar field and the Gauss-Bonnet invariant is quadratic in the scalar, whereas stable solutions exist for exponential couplings. Here we elucidate this behavior. We demonstrate that, while the quadratic term controls the onset of the tachyonic instability that gives rise to the black hole hair, the higher-order coupling terms control the nonlinearities that quench that instability, and hence also control the stability of the hairy black hole solutions., Comment: 8 pages, 3 figures. Added citations, updated Fig.2, minor changes to the text. v3: Updated to match published version

In recent years there has been a surge of interest in what has come to be known as the `universal relations' between various global properties of neutron stars. These universal relations are equation of state independent relations between quantities such as the moment of inertia $I$, the tidal deformability or Love number $\lambda$, and the quadrupole $Q$ (I-Love-Q relations), or the relativistic multipole moments (3-hair relations). While I-Love-Q relations have been studied extensively in both general relativity and various alternatives, 3-hair relations have been studied only in general relativity. Recent progress on the definition of the multipole moments of a compact object in the case of scalar-tensor theories allows for the study of 3-hair relations in modified theories of gravity. Specifically, the aim of this work is to study them for scalarized stars in scalar-tensor theories with a massless scalar field that admit spontaneous scalarization. We find that the 3-hair relations between the mass and angular momentum moments that hold in general relativity hold for scalarized stars as well. The scalar moments also exhibit a universal behaviour, which is equation of state independent within one specific theory, but differs between different theories. Combining astrophysical observations one can in principle measure the different properties of scalarized neutron star and tell different theories apart., Comment: 15 pages 5 figures

We study the nonlinear dynamics of black holes that carry scalar hair and binaries composed of such black holes. The scalar hair is due to a linear or exponential coupling between the scalar and the Gauss--Bonnet invariant. We work perturbatively in the coupling constant of that interaction but nonperturbatively in the fields. We first consider the dynamical formation of hair for isolated black holes of arbitrary spin and determine the final state. This also allows us to compute for the first time the scalar quasinormal modes of rotating black holes in the presence of this coupling. We then study the evolution of nonspinning black-hole binaries with various mass ratios and produce the first scalar waveform for a coalescence. An estimate of the energy loss in scalar radiation and the effect this has on orbital dynamics and the phase of the GWs (entering at quadratic order in the coupling) show that GW detections can set the most stringent constraint to date on theories that exhibit a coupling between a scalar field and the Gauss--Bonnet invariant., Comment: 24 pages; 12 figures; Numerical code based on the Einstein Toolkit with new thorns available at https://bitbucket.org/canuda/. v2: updated references and discussion

In theories with derivative (self-)interactions, the propagation of perturbations on nontrivial field configurations is determined by effective metrics. Generalized scalar-tensor theories belong in this class and this implies that the matter fields and gravitational perturbations do not necessarily experience the same causal structure. Motivated by this, we explore the causal structure of black holes as perceived by scalar fields in the Horndeski class. We consider linearized perturbations on a fixed background metric that describes a generic black hole. The effective metric that determines the propagation of these perturbations does not generally coincide with the background metric (to which matter fields couple minimally). Assuming that the metric and the scalar respect stationarity and that the surface gravity of the horizon is constant, we prove that Killing horizons of the background metric are always Killing horizons of the effective metric as well. Hence, scalar perturbations cannot escape the region that matter fields perceive as the interior of the black hole. This result does not depend on asymptotics but only on local considerations and does not make any reference to no-hair theorems. We then demonstrate that, when one relaxes the stationarity assumption for the scalar, solutions where the horizons of the effective and the background metrics do not match can be found in the decoupling limit., Comment: v3: 10 pages, published version

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

Black holes in Lorentz-violating theories have been claimed to violate the second law of thermodynamics by perpetual motion energy extraction. We revisit this question for a Penrose splitting process in a spherically symmetric setting with two species of particles that move on radial geodesics that extend to infinity. We show that energy extraction by this process cannot happen in any theory in which gravity is attractive, in the sense of a geometric inequality that we describe. This inequality is satisfied by all known Einstein-\ae{}ther and Ho\v{r}ava black hole solutions., Comment: 10 pages. v2: minor additions to discussion, version accepted in PRD

The recent detection of gravitational wave GW170817 has placed a severe bound on the deviation of the speed of gravitational waves from the speed of light. We explore the consequences of this detection for Horava gravity.

We identify a class of scalar-tensor theories with coupling between the scalar and the Gauss-Bonnet invariant that exhibit spontaneous scalarization for both black holes and compact stars. In particular, these theories formally admit all of the stationary solutions of general relativity, but these are not dynamically preferred if certain conditions are satisfied. Remarkably, black holes exhibit scalarization if their mass lies within one of many narrow bands. We find evidence that scalarization can occur in neutron stars as well., Comment: v2: Five pages, three figures. Minor corrections, references added. v3: Matches version published in Phys. Rev. Lett

Gravitational wave observations have been used to test Lorentz symmetry by looking for dispersive effects that are caused by higher order corrections to the dispersion relation. In this Letter I argue on general grounds that, when such corrections are present, there will also be a scalar excitation. Hence, a smoking-gun observation of Lorentz symmetry breaking would be the direct detection of scalar waves that travel at a speed other than the speed of the standard gravitational wave polarisations or the speed of light. Interestingly, in known Lorentz-breaking gravity theories the difference between the speeds of scalar and tensor waves is virtually unconstrained, whereas the difference between the latter and the speed of light is already severely constrained by the coincident detection of gravitational waves and gamma rays from a binary neutron star merger., Comment: v1: 4 pages; v2: Version accepted for publication in PRL. Note that v1 and PRL submission preceded GW170817 announcement but v2 includes discussion about GW170817, as requested by PRL editor

In scalar-tensor theories, spontaneous scalarization is a phase transition that can occur in ultra-dense environments such as neutron stars. The scalar field develops a non-trivial configuration once the stars exceeds a compactness threshold. We recently pointed out that, if the scalar exhibits some additional coupling to matter, it could give rise to significantly different microphysics in these environments. In this work we study, at the non-perturbative level, a toy model in which the photon is given a large mass when spontaneous scalarization occurs. Our results demonstrate clearly the effectiveness of spontaneous scalarization as a Higgs-like mechanism in neutron stars., Comment: 8 pages, 5 figures