Search

The motion of compact binaries is influenced by the spin of their components starting at the 1.5 post-Newtonian (PN) order. On the other hand, in the large mass ratio limit, the spin of the lighter object appears in the equations of motion at first order in the mass ratio, coinciding with the leading gravitational self-force. Frame and gauge choices make it challenging to compare between the two limits, especially for generic spin configurations. We derive novel closed formulas for the gauge-invariant actions and frequencies for the motion of spinning test particles near Kerr black holes. We use this to express the Hamiltonian perturbatively in terms of action variables up to 3PN and compare it with the 1.5 PN action-angle Hamiltonian at finite mass ratios. This allows us to match the actions across both systems, providing a new gauge-invariant dictionary for interpolation between the two limits., Comment: Supplemental notebook with 3PN expressions in "Ancillary files"

Quasi-periodic eruptions (QPEs) are recurring bursts of soft X-rays from the nuclei of galaxies. Their physical origin is currently a subject of debate, with models typically invoking an orbiter around a massive black hole or disk instabilities. Here we present and analyze the temporal and spectral evolution of the QPE source eRO-QPE2 over 3.5 years. We find that eRO-QPE2 1) is remarkably stable over the entire 3.5-year temporal baseline in its eruption peak luminosity, eruption temperature, quiescent temperature, and quiescent luminosity, 2) has a stable mean eruption recurrence time of 2.35 hours, with marginal ($\sim$2$\sigma$) evidence for a $0.1$ hour reduction over the 3.5 yr period, and 3) has a long-short variation in its recurrence time in August 2020, but this pattern is absent from all subsequent observations. The stability of its peak eruption luminosity and that of the quiescent state are notably dissimilar from three previously tracked QPEs (GSN069, eRO-QPE1, eRO-QPE3), which show declines in eruption and quiescent flux over comparable temporal baselines. This stability is even more pronounced in eRO-QPE2 due to its 2.4 hour average recurrence time compared to GSN-069's 9 hour, eRO-QPE1's 16 hour, and eRO-QPE3's 20 hour recurrence times, i.e., this system has undergone 4-8 times more cycles than these other systems over the 3.5 years of observations. We discuss the implications of these observations within the context of some proposed extreme mass ratio inspiral (EMRI) models., Comment: Under review (ApJ)

Extreme mass ratio inspirals (EMRIs) are among the key sources of gravitational waves for the LISA space-based gravitational wave detector. Achieving sufficient accuracy in the gravitational wave template for these binaries requires modeling the effects of the spin of the comparably light secondary compact object. In this work, we employ the solution of the Hamilton-Jacobi equation for the motion of spinning bodies in Kerr space-time to obtain their generic orbits. Then, using the Teukolsky formalism we compute gravitational wave energy and angular momentum fluxes sourced by these orbits valid to linear order in secondary spin, and provide waveform snapshots corresponding to the motion. The solver we have developed substantially improves on previous studies in terms of speed and accuracy, and includes the case of a fully precessing secondary spin. As such, it provides a significant building block for the modelling of waveforms of precessing compact binaries at large mass ratios., Comment: 23 pages + appendices and references; 10 tables ; 10 figures. Supplemental Mathematica notebooks available at https://github.com/gabriel-andres-piovano/Spinning-Body-Hamilton-Jacobi

Space-based gravitational-wave detectors such as LISA are expected to detect inspirals of stellar-mass compact objects into massive black holes. Modeling such inspirals requires fully relativistic computations to achieve sufficient accuracy at leading order. However, subleading corrections such as the effects of the spin of the inspiraling compact object may potentially be treated in weak-field expansions such as the post-Newtonian (PN) approach. In this work, we calculate the PN expansion of eccentric orbits of spinning bodies around Schwarzschild black holes. Then we use the Teukolsky equation to compute the energy and angular momentum fluxes from these orbits up to the 5PN order. Some of these PN orders are exact in eccentricity, while others are expanded up to the tenth power in eccentricity. Then we use the fluxes to construct a hybrid inspiral model, where the leading part of the fluxes is calculated numerically in the fully relativistic regime, while the part linear in the small spin is analytically approximated using the PN series. We calculate LISA-relevant inspirals and respective waveforms with this model and a fully relativistic model. Through the calculation of mismatch between the waveforms from both models we conclude that the PN approximation of the linear-in-spin part of the fluxes is sufficient for lower eccentricities., Comment: 22 pages, 8 figures

Extreme mass ratio inspirals (EMRIs), where a compact object orbits a massive black hole, are a key source of gravitational waves for the future Laser Interferometer Space Antenna (LISA). Due to their small mass ratio, ($\epsilon \sim 10^{-4}$--$10^{-7}$), the binary evolves slowly and EMRI signals will be in-band for years. Additionally, astrophysical EMRIs are expected to have complex dynamics featuring both spin-precession and eccentricity. A standard approach to modelling these inspirals is via the method of osculating geodesics (OG) which we employ along with a toy model for the gravitational self-force. Using this method requires resolving tens of thousands radial and polar orbital librations over the long duration of the signal which makes the inspiral trajectory expensive to compute. In this work we accelerate these calculations by employing Near-Identity (averaging) Transformations. However, this averaging technique breaks down at orbital resonances where the radial and polar frequencies are an integer ratio of each other. Thus, we switch to a partial averaging transformation in the vicinity of the resonance where the dynamics are characterised by the slow evolution of the so-called "resonant phase". Additionally, we develop an optimal switching criterion to minimise the computation time while maximising accuracy. We find the error in the waveform phase is improved from $\mathcal{O}(\epsilon^{-1/2})$ in the fully averaged scheme to $\mathcal{O}(\epsilon^{4/7})$ in the switching scheme. At the same time, this scheme improves the scaling of the computation time from being inversely proportional to $\epsilon$ using OG, to a very weak scaling with $\epsilon$. This results in a speed-up of at least two orders of magnitude for LISA EMRIs with room for further optimisation., Comment: 50 pages, 11 figures

Extreme-mass-ratio inspirals (EMRIs) are one of the primary targets for the recently adopted millihertz gravitational-wave (GW) observatory LISA. Some previous studies have argued that a fraction of all EMRIs form in matter-rich environments, and can potentially explain the dozens of soft X-ray band ($\sim 10^{-1} \rm keV$), low-frequency ($\sim 0.1$ mHz) periodic phenomena known as quasi-periodic eruptions (QPEs) and quasi-periodic oscillations (QPOs). Here, using a representative EMRI population retrofitted with cutoffs on LISA-band SNRs and luminosity distances to account for the sensitivity of current instruments, we estimate the mean frequency band in which QPEs and QPOs originating from detectable LISA EMRIs may be emitting an X-ray signal ``today'' (i.e., in 2024) to be $0.46 \pm 0.22$ mHz. We also model the well-known QPO source, RE J1034+396, which falls in this frequency band, as an EMRI assuming its primary black hole mass to be $10^6-10^7 M_\odot$. Through a prior-predictive analysis, we estimate the orbiting compact object's mass to be $46^{+ 10}_{-40} M_\odot$ and the source's LISA-band SNR as $\approx 14$, highlighting it as a candidate multi-messenger EMRI target. We also highlight the role of current and near-future X-ray and UV observatories in enabling multi-messenger observations of EMRIs in conjunction with LISA, and conclude with a discussion of caveats of the current analysis, such as the exclusion of eccentricity and inclination from the model, and the measurability of sub-solar mass compact object EMRIs., Comment: (Before-proofs-accepted) 15 + 1 pages, 10 + 1 figures

Binaries containing a compact object orbiting a supermassive black hole are thought to be precursors of gravitational wave events, but their identification has been extremely challenging. Here, we report quasi-periodic variability in X-ray absorption which we interpret as quasi-periodic outflows (QPOuts) from a previously low-luminosity active galactic nucleus after an outburst, likely caused by a stellar tidal disruption. We rule out several models based on observed properties and instead show using general relativistic magnetohydrodynamic simulations that QPOuts, separated by roughly 8.3 days, can be explained with an intermediate-mass black hole secondary on a mildly eccentric orbit at a mean distance of about 100 gravitational radii from the primary. Our work suggests that QPOuts could be a new way to identify intermediate/extreme-mass ratio binary candidates., Comment: Accepted for publication in Science Advances. We report a new supermassive black hole phenomenon that we call quasi-periodic outflows (QPOuts)

Quasi-periodic Eruptions (QPEs) represent a novel class of extragalactic X-ray transients that are known to repeat at roughly regular intervals of a few hours to days. Their underlying physical mechanism is a topic of heated debate, with most models proposing that they originate either from instabilities within the inner accretion flow or from orbiting objects. At present, our knowledge of how QPEs evolve over an extended timescale of multiple years is limited, except for the unique QPE source GSN 069. In this study, we present results from strategically designed Swift observing programs spanning the past three years, aimed at tracking eruptions from eRO-QPE1. Our main results are: 1) the recurrence time of eruptions can vary between 0.6 and 1.2 days, 2) there is no detectable secular trend in evolution of the recurrence times, 3) consistent with prior studies, their eruption profiles can have complex shapes, and 4) the peak flux of the eruptions has been declining over the past 3 years with the eruptions barely detected in the most recent Swift dataset taken in June of 2023. This trend of weakening eruptions has been reported recently in GSN 069. However, because the background luminosity of eRO-QPE1 is below our detection limit, we cannot verify if the weakening is correlated with the background luminosity (as is claimed to be the case for GSN 069). We discuss these findings within the context of various proposed QPE models., Comment: Resubmitted to ApJ Letters after implementing referee comments

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

Galactic nuclei showing recurrent phases of activity and quiescence have recently been discovered, with recurrence times as short as a few hours to a day -- known as quasi-periodic X-ray eruption (QPE) sources -- to as long as hundreds to a thousand days for repeating nuclear transients (RNTs). Here we present a multi-wavelength overview of Swift J023017.0+283603 (hereafter Swift J0230+28), a source that exhibits repeating and quasi-periodic X-ray flares from the nucleus of a previously unremarkable galaxy at $\sim$ 165 Mpc, with a recurrence time of approximately 22 days, an intermediary timescale between known RNTs and QPE sources. The source also shows transient radio emission, likely associated with the X-ray emission. Such recurrent soft X-ray eruptions, with no accompanying UV/optical emission, are strikingly similar to QPE sources. However, in addition to having a recurrence time that is $\sim 25$ times longer than the longest-known QPE source, Swift J0230+28's eruptions exhibit somewhat distinct shapes and temperature evolution than the known QPE sources. Scenarios involving extreme mass ratio inspirals are favored over disk instability models. The source reveals an unexplored timescale for repeating extragalactic transients and highlights the need for a wide-field, time-domain X-ray mission to explore the parameter space of recurring X-ray transients., Comment: Final version, appeared on Nature Astronomy on 12 January 2024

Rapidly rotating bodies moving in curved space-time experience the so-called spin-curvature force, which becomes important for the motion of compact objects in gravitational-wave inspirals. As a first approximation, this effect is captured in the motion of a spinning test particle. We solve the equations motion of a spinning particle to leading order in spin in arbitrary static and spherically symmetric space-times in terms of one-dimensional closed-form integrals. This solves the problem and proves its integrability in a wide range of modified gravities and near exotic compact objects. Then, by specializing to the case of bound orbits in Schwarzschild space-time, we demonstrate how to express the solution in the form of Jacobi elliptic functions., Comment: The notebooks and machine-readable formulas can be found in the repo https://github.com/VojtechW/Analytical-Solution-Spinning-particle-Spherical

Inspirals of stellar-mass compact objects into massive black holes, known as extreme mass ratio inspirals (EMRIs), are one of the key targets for upcoming space-based gravitational-wave detectors. In this paper we take the first steps needed to systematically incorporate the effect of external gravitating matter on EMRIs. We model the inspiral as taking place in the field of a Schwarzschild black hole perturbed by the gravitational field of a far axisymmetric distribution of mass enclosing the system. We take into account the redshift, frame-dragging, and quadrupolar tide caused by the enclosing matter, thus incorporating all effects to inverse third order of the characteristic distance of the enclosing mass. Then, we use canonical perturbation theory to obtain the action-angle coordinates and Hamiltonian for mildly eccentric precessing test-particle orbits in this background. Finally, we use this to efficiently compute mildly eccentric inspirals in this field and document their properties. This work shows the advantages of canonical perturbation theory for the modeling EMRIs, especially in the cases when the background deviates from the standard black hole fields.

Action-angle coordinates are a tool commonly used in celestial mechanics to systematically parametrize and store general solutions of the equations of motion of astrophysical bodies. I perturbatively construct action-angle coordinates for bound test particle motion in static, spherically symmetric space-times using a post-circular expansion. Then I specialise the expressions to the motion in the gravitational fields of Schwarzschild black holes and give explicit formulas for the Hamiltonian to the 10th power in the radial action (20th power in eccentricity), and the transformation to angle coordinates up to the 8th harmonic with respect to a relativistic orbital anomaly. The results provide a closed-form perturbative solution for the orbital motion parametrized by coordinate time that will find applications in the modelling of compact binary inspirals and other fields of astrophysics., Comment: Supplemental materials at https://github.com/VojtechW/Action-Angle-Schwarzschild

Results ranging from Ashtekar variables to the perturbative Bern-Carrasco-Johansson (BCJ) double copy suggest a deep relation between Yang-Mills theory and Einstein gravity. I examine this relation by writing down the tetradic Palatini action for Einstein gravity and covariantly decomposing its variables into two $SL(2,\mathbb{C})$ connections and two soldering forms. This leads to a conjecture that the BCJ double copy can be understood through a "holomorphic trail", a series of injection maps between two copies of $SU(2)$ theories and Einstein gravity., Comment: Comments welcome, submitted to PRL

The largest part of any gravitational-wave inspiral of a compact binary can be understood as a slow, adiabatic drift between the trajectories of a certain referential conservative system. In many contexts, the phase space of this conservative system is smooth and there are no "topological transitions" in the phase space, meaning that there are no sudden qualitative changes in the character of the orbital motion during the inspiral. However, in this chapter we discuss the cases where this assumption fails and non-linear and/or non-smooth transitions come into play. In integrable conservative systems under perturbation, topological transitions suddenly appear at resonances, and we sketch how to implement the passage through such regions in an inspiral model. Even though many of the developments of this chapter apply to general inspirals, we focus on a particular scenario known as the Extreme mass ratio inspiral (EMRI). An EMRI consists of a compact stellar-mass object inspiralling into a supermassive black hole. At leading order, the referential conservative system is simply geodesic motion in the field of the supermassive black hole and the rate of the drift is given by radiation reaction. In Einstein gravity the supermassive black hole field is the Kerr space-time in which the geodesic motion is integrable. However, the equations of motion can be perturbed in various ways so that prolonged resonances and chaos appear in phase space as well as the inspiral, which we demonstrate in simple physically motivated examples., Comment: 44 pages, 9 figures, 1 table. Invited chapter for "Handbook of Gravitational Wave Astronomy" (Eds. C. Bambi, S. Katsanevas, and K. Kokkotas; Springer, Singapore, 2021)

The close neighbourhood of a supermassive black hole contains not only the accreting gas and dust but also stellar-sized objects, such as late-type and early-type stars and compact remnants that belong to the nuclear star cluster. When passing through the accretion flow, these objects perturb it by the direct action of stellar winds, as well as their magnetic and gravitational effects. By performing General-Relativistic Magnetohydrodynamic (GRMHD) simulations, we investigate how the passages of a star can influence the supermassive black hole gaseous environment. We focus on the changes in the accretion rate and the emergence of blobs of plasma in the funnel of an accretion torus. We compare results from 2D and 3D numerical computations that have been started with comparable initial conditions. We find that a quasi-stationary inflow can be temporarily inhibited by a transiting star, and the plasmoids can be ejected along the magnetic field lines near the rotation axis. We observe the characteristic signatures of the perturbing motion in the power spectrum of the accretion variability, which provides an avenue for a multi-messenger detection of these transient events. Finally, we discuss the connection of our results to multi-wavelength observations of galactic nuclei, with the emphasis on ten promising sources (Sgr~A*, OJ 287, J0849$+$5108, RE J1034$+$396, 1ES 1927+65, ESO 253--G003, GSN 069, RX J1301.9$+$2747, eRO-QPE1, eRO-QPE2)., Comment: 43 pages, 22 figures, 4 tables, accepted to ApJ, comments welcome! Links to animations of Run A - https://youtu.be/eERYioirgQc and Run B - https://youtu.be/7Fz4g0lfpP4

The close neighbourhood of a supermassive black hole contains not only accreting gas and dust, but also stellar-sized objects like stars, stellar-mass black holes, neutron stars, and dust-enshrouded objects that altogether form a dense nuclear star-cluster. These objects interact with the accreting medium and they perturb the otherwise quasi-stationary configuration of the accretion flow. We investigate how the passages of a star can influence the black hole gaseous environment with GRMHD 2D and 3D simulations. We focus on the changes in the accretion rate and the associated emergence of outflowing blobs of plasma., Comment: 18 pages, 8 figures, 2 tables, to appear in the Proceedings of RAGtime 20-22

In the Galactic center nuclear star cluster, bright late-type stars exhibit a flat or even a decreasing surface-density profile, while fainter late-type stars maintain a cusp-like profile. Historically, the lack of red giants in the Galactic center was discovered via the drop in the strength of the CO absorption bandhead by Kris Sellgren et al. (1990), later followed by the stellar number counts based on the high angular resolution near-infrared observations. Several mechanisms were put forward that could have led to the preferential depletion of bright red giants: star-star collisions, tidal stripping, star-accretion disc collisions, or an infall of a massive cluster or a secondary black hole. Here we propose a novel scenario for the bright red-giant depletion based on the collisions between red giants and the nuclear jet, which was likely active in the Galactic center a few million years ago and could have led to the formation of the large-scale $\gamma$-ray Fermi bubbles. The process of the jet-induced ablation of red giants appears to be most efficient within $\sim 0.04\,{\rm pc}$ (S-cluster), while at larger distances it was complemented by star-accretion disc collisions and at smaller scales, tidal stripping operated. These three mechanisms likely operated simultaneously and created an apparent core of late-type stars within $\sim 0.5\,{\rm pc}$., Comment: 18 pages, 6 figures, 1 table; to appear in the proceedings of the online RAGtime 22 conference (organized in honour of Prof. Zdenek Stuchlik); minor additions

Inspirals of stellar mass compact objects into supermassive black holes are known as extreme mass ratio inspirals. In the simplest approximation, the motion of the compact object is modeled as a geodesic in the space-time of the massive black hole with the orbit decaying due to radiated energy and angular momentum, thus yielding a highly regular inspiral. However, once the spin of the secondary compact body is taken into account, integrability is broken and prolonged resonances along with chaotic motion appear. We numerically integrate the motion of a spinning test body in the field of a non-spinning black hole and analyse it using various methods. We show for the first time that resonances and chaos can be found even for astrophysical values of spin. On the other hand, we devise a method to analyse the growth of the resonances, and we conclude that the resonances we observe are only caused by terms quadratic in spin and will generally stay very small in the small-mass-ratio limit. Last but not least, we compute gravitational waveforms by solving numerically the Teukolsky equations in the time-domain and establish that they carry information on the motion's dynamics. In particular, we show that the time series of the gravitational wave strain can be used to discern regular from chaotic motion of the source., Comment: 18 pages, 14 figures

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

Inspirals of rotating stellar-mass compact objects into massive black holes are influenced by the spin-curvature coupling, which drives the compact body away from geodesic motion due to its rotation. I formulate the Hamilton-Jacobi equation for a spinning test body orbiting a Kerr black hole, solve it to linear order in spin, and use the perturbative solution to compute the fundamental frequencies of motion along the orbit. This result provides one of the necessary ingredients for waveform models for the upcoming space-based gravitational-wave detector LISA., Comment: In review at PRL, comments welcome

A compact stellar-mass object inspiralling onto a massive black hole deviates from geodesic motion due to radiation-reaction forces as well as finite-size effects. Such post-geodesic deviations need to be included with sufficient precision into wave-form models for the upcoming space-based gravitational-wave detector LISA. I present the formulation and solution of the Hamilton-Jacobi equation of geodesics near Kerr black holes perturbed by the so-called spin-curvature coupling, the leading order finite-size effect. In return, this solution allows to compute a number of observables such as the turning points of the orbits as well as the fundamental frequencies of motion. This result provides one of the necessary ingredients for waveform models for LISA and an important contribution useful for the relativistic two-body problem in general., Comment: Published in Phys. Rev. D

In this work the dynamics of a spinning particle moving in the Schwarzschild background is studied. In particular, the methods of Poincar\'{e} section and recurrence analysis are employed to discern chaos from order. It is shown that the chaotic or regular nature of the orbital motion is reflected on the gravitational waves., Comment: 8 pages, 2 figures, to appear in the RAGtime20 conference proceedings (Opava, October 15-19 2018)

The spin-curvature coupling as captured by the so-called Mathisson-Papapetrou-Dixon (MPD) equations is the leading order effect of the finite size of a rapidly rotating compact astrophysical object moving in a curved background. It is also a next-to-leading order effect in the phase of gravitational waves emitted by extreme-mass-ratio inspirals (EMRIs), which are expected to become observable by the LISA space mission. Additionally, exploring the Hamiltonian formalism for spinning bodies is important for the construction of the so-called Effective-One-Body waveform models that should eventually cover all mass ratios. The MPD equations require supplementary conditions determining the frame in which the moments of the body are computed. We review various choices of these supplementary spin conditions and their properties. Then, we give Hamiltonians either in proper-time or coordinate-time parametrization for the Tulczyjew-Dixon, Mathisson-Pirani, and Kyrian-Semer\'ak conditions. Finally, we also give canonical phase-space coordinates parametrizing the spin tensor. We demonstrate the usefulness of the canonical coordinates for symplectic integration by constructing Poincar\'e surfaces of section for spinning bodies moving in the equatorial plane in Schwarzschild space-time. We observe the motion to be essentially regular for EMRI-ranges of the spin, but for larger values the Poincar\'e surfaces of section exhibit the typical structure of a weakly chaotic system. A possible future application of the numerical integration method is the inclusion of spin effects in EMRIs at the precision requirements of LISA., Comment: 37 pages, 2 figures. Accepted at CQG

When a black hole is accreting well below the Eddington rate, a geometrically thick, radiatively inefficient state of the accretion disk is established. There is a limited number of closed-form physical solutions for geometrically thick (non-selfgravitating) toroidal equilibria of perfect fluids orbiting a spinning black hole, and these are predominantly used as initial conditions for simulations of accretion in the aforementioned mode. However, different initial configurations might lead to different results and thus observational predictions drawn from such simulations. We expand the known equilibria by a number of closed multiparametric solutions with various possibilities of rotation curves and geometric shapes. Then, we ask whether choosing these as initial conditions influences the onset of accretion and the asymptotic state of the disk. We investigate a set of examples from the derived solutions in detail; we analytically estimate the growth of the magneto-rotational instability (MRI) from their rotation curves and evolve the analytically obtained tori using the 2D magneto-hydrodynamical code HARM. Properties of the evolutions are then studied through the mass, energy, and angular-momentum accretion rates. The rotation curve has a decisive role in the numerical onset of accretion in accordance with our analytical MRI estimates: In the first few orbital periods, the average accretion rate is linearly proportional to the initial MRI rate in the toroids. The final state obtained from any initial condition within the studied class after an evolution of $\gtrsim 10$ orbital periods is mostly qualitatively identical and the quantitative properties vary within a single order of magnitude. The average values of the energy of the accreted fluid have an irregular dependency on initial data, and in some cases fluid with energies many times its rest mass is systematically accreted., Comment: Accepted at A&A

The Kerr black hole is stationary and axisymmetric, which leads to conservation of energy and azimuthal angular momentum along the orbits of free test particles in its vicinity, but also to conservation laws for the evolution of continuum matter fields. However, the Kerr space-time possesses an additional "hidden symmetry" which exhibits itself in an unexpected conserved quantity along geodesics known as the Carter constant. We investigate the possibility of using this hidden symmetry to obtain conservation laws and other identities which could be used to test astrophysical simulations of the evolution of matter fields near spinning black holes. After deriving such identities, we set up a simple numerical toy model on which we demonstrate how they can detect the violations of evolution equations in a numerical simulation. Even though one of the expressions we derive is in the form of a conservation law, we end up recommending an equivalent but simpler expression that is not in the form of a conservation law for practical implementation., Comment: Submitted to MNRAS

Carter and Lichnerowicz have established that barotropic fluid flows are conformally geodesic and obey Hamilton's principle. This variational approach can accommodate neutral, or charged and poorly conducting, fluids. We show that, unlike what has been previously thought, this approach can also accommodate perfectly conducting magnetofluids, via the Bekenstein-Oron description of ideal magnetohydrodynamics. When Noether symmetries associated with Killing vectors or tensors are present in geodesic flows, they lead to constants of motion polynomial in the momenta. We generalize these concepts to hydrodynamic flows. Moreover, the Hamiltonian descriptions of ideal magnetohydrodynamics allow one to cast the evolution equations into a hyperbolic form useful for evolving rotating or binary compact objects with magnetic fields in numerical general relativity. Conserved circulation laws, such as those of Kelvin, Alfv\'en and Bekenstein-Oron, emerge simply as special cases of the Poincar\'e-Cartan integral invariant of Hamiltonian systems. We use this approach to obtain an extension of Kelvin's theorem to baroclinic (non-isentropic) fluids, based on a temperature-dependent time parameter. We further extend this result to perfectly or poorly conducting baroclinic magnetoflows. Finally, in the barotropic case, such magnetoflows are shown to also be geodesic, albeit in a Finsler (rather than Riemann) space., Comment: 23 pages

Pseudo-Newtonian potentials are a tool often used in theoretical astrophysics to capture some key features of a black-hole space-time in a Newtonian framework. As a result, one can use Newtonian numerical codes, and Newtonian formalism in general, in an effective description of important astrophysical processes such as accretion onto black holes. In this paper we develop a general pseudo-Newtonian formalism which pertains to the motion of particles, light, and fluids in stationary space-times. In return, we are able to assess the applicability of the pseudo-Newtonian scheme. The simplest and most elegant formulas are obtained in space-times without gravitomagnetic effects, such as the Schwarzschild rather than the Kerr space-time; the quantitative errors are smallest for motion with low binding energy. Included is a ready-to-use set of fluid equations in Schwarzschild space-time in Cartesian and radial coordinates., Comment: Published in ApJ