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Through detection by low gravitational wave space interferometers, the capture of stars by supermassive black holes will constitute a giant step forward in the understanding of gravitation in strong field. The impact of the perturbations on the motion of the star is computed via the tail, the back-scattered part of the perturbations, or via a radiative Green function. In the former approach, the self-force acts upon the background geodesic, while in the latter, the geodesic is conceived in the total (background plus perturbations) field. Regularisations (mode-sum and Riemann-Hurwitz $zeta$ function) intervene to cancel divergencies coming from the infinitesimal size of the particle. The non-adiabatic trajectories require the most sophisticated techniques for studying the evolution of the motion, like the self-consistent approach.
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[abridged] The inspiral of a stellar compact object into a massive black hole is one of the main sources of gravitational waves for the future space-based Laser Interferometer Space Antenna. We expect to be able to detect and analyze many cycles of these slowly inspiraling systems. To that end, the use of very precise theoretical waveform templates in the data analysis is required. To build them we need to have a deep understanding of the gravitational backreaction mechanism responsible for the inspiral. The self-force approach describes the inspiral as the action of a local force that can be obtained from the regularization of the perturbations created by the stellar compact object on the massive black hole geometry. In this paper we extend a new time-domain technique for the computation of the self-force from the circular case to the case of eccentric orbits around a non-rotating black hole. The main idea behind our scheme is to use a multidomain framework in which the small compact object, described as a particle, is located at the interface between two subdomains. Then, the equations at each subdomain are homogeneous wave-type equations, without distributional sources. In this particle-without-particle formulation, the solution of the equations is smooth enough to provide good convergence properties for the numerical computations. This formulation is implemented by using a pseudospectral collocation method for the spatial discretization, combined with a Runge Kutta algorithm for the time evolution. We present results from several simulations of eccentric orbits in the case of a scalar charged particle around a Schwarzschild black hole. In particular, we show the convergence of the method and its ability to resolve the field and its derivatives across the particle location. Finally, we provide numerical values of the self-force for different orbital parameters.
Rotating black holes without equatorial reflection symmetry can naturally arise in effective low-energy theories of fundamental quantum gravity, in particular, when parity-violating interactions are introduced. Adopting a theory-agnostic approach and considering a recently proposed Kerr-like black hole model, we investigate the structure and properties of accretion disk around a rotating black hole without reflection symmetry. In the absence of reflection symmetry, the accretion disk is in general a curved surface in shape, rather than a flat disk lying on the equatorial plane. Furthermore, the parameter $epsilon$ that controls the reflection asymmetry would shrink the size of the innermost stable circular orbits, and enhance the efficiency of the black hole in converting rest-mass energy to radiation during accretion. In addition, we find that spin measurements based on the gravitational redshift observations of the disk, assuming a Kerr geometry, may overestimate the true spin values if the central object is actually a Kerr-like black hole with conspicuous equatorial reflection asymmetry.
We study force-free magnetospheres in the Blandford-Znajek process from rapidly rotating black holes by adopting the near-horizon geometry of near-extreme Kerr black holes (near-NHEK). It is shown that the Znajek regularity condition on the horizon can be directly derived from the resulting stream equation. In terms of the condition, we split the full stream equation into two separate equations. Approximate solutions around the rotation axis are derived. They are found to be consistent with previous solutions obtained in the asymptotic region. The solutions indicate energy and angular-momentum extraction from the hole.
In a recent paper (Phys. Dark Univ. {bf 31}, 100744 (2021)) it has been obtained new static black hole solutions with primary hairs by the Gravitational Decoupling. In this work we either study the geodesic motion of massive and massless particles around those solutions and restrict the values of the primary hairs by observational data. In particular, we obtain the effective potential, the innermost stable circular orbits, the marginally bounded orbit, and the periastron advance for time--like geodesics. In order to restrict the values taken by the primary hairs we explore their relationship with the rotation parameter of the Kerr black hole giving the same innermost stable circular orbit radius and give the numerical values for the supermassive black holes at Ark 564 and NGC 1365. The photon sphere and the impact parameter associated to null geodesics are also discussed.
Much of the success of gravitational-wave astronomy rests on perturbation theory. Historically, perturbative analysis of gravitational-wave sources has largely focused on post-Newtonian theory. However, strong-field perturbation theory is essential in many cases such as the quasinormal ringdown following the merger of a binary system, tidally perturbed compact objects, and extreme-mass-ratio inspirals. In this review, motivated primarily by small-mass-ratio binaries but not limited to them, we provide an overview of essential methods in (i) black hole perturbation theory, (ii) orbital mechanics in Kerr spacetime, and (iii) gravitational self-force theory. Our treatment of black hole perturbation theory covers most common methods, including the Teukolsky and Regge-Wheeler-Zerilli equations, methods of metric reconstruction, and Lorenz-gauge formulations, presenting them in a new consistent and self-contained form. Our treatment of orbital mechanics covers quasi-Keplerian and action-angle descriptions of bound geodesics and accelerated orbits, osculating geodesics, near-identity averaging transformations, multiscale expansions, and orbital resonances. Our summary of self-force theorys foundations is brief, covering the main ideas and results of matched asymptotic expansions, local expansion methods, puncture schemes, and point particle descriptions. We conclude by combining the above methods in a multiscale expansion of the perturbative Einstein equations, leading to adiabatic and post-adiabatic evolution schemes. Our presentation is intended primarily as a reference for practitioners but includes a variety of new results. In particular, we present the first complete post-adiabatic waveform-generation framework for generic (nonresonant) orbits in Kerr.
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