arXiv · 0709.4682
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Alessandra Buonanno. 2007-09-28. Gravitational waves. https://arxiv.org/abs/0709.4682
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Horizon fluxes of energy and angular momentum are a key strong-field effect in the dynamics of black holes, encoding direct information about their nature. In this work, we present a numerical study of these fluxes for a test particle orbiting a Kerr black hole on equatorial geodesics, covering circular, eccentric, and hyperbolic trajectories across a wide range of orbital parameters and black hole spins. We reproduce known results for circular orbits and uncover a richer phenomenology for eccentric and hyperbolic ones: the instantaneous fluxes can exhibit multiple peaks and sign changes, indicating a complex interplay between orbital dynamics and horizon perturbation. We then compare these results against existing analytical post-Newtonian expressions, exploring resummation strategies to improve their performance against numerical data. In particular, we propose a factorized and resummed representation of the horizon fluxes that predicts the onset frequency of the superradiant regime to within $10\%$ for $\gtrsim 83\%$ for both the energy and angular momentum fluxes of bound configurations; high-energy open orbits however remain a challenge. This representation exactly reduces to the circular limit by construction, independently of the perturbative order of the remaining analytical terms. For peak and orbit-averaged fluxes, the analytical models achieve acceptable accuracy -- with relative errors at the $10\%$ level or below -- at large separations and low eccentricities. However, they can exhibit deviations of $\sim \mathcal{O}(100\%)$ in the strong-field regime, motivating the need for improved flux prescriptions and further investigations.
Motivated by the recent rebuttal of black hole--dark matter solutions based on velocity-matching, we reconstruct the spacetime by treating the dark matter halo density directly as an energy-density source in the Einstein field equations. We obtain an exact static, spherically symmetric black hole solution and investigate the effects of the halo on its geometry, optical properties, quasinormal modes, and thermodynamics. Using null geodesics, we show that the halo modifies photon trajectories, shifts the circular photon orbit, and enlarges the photon sphere and apparent shadow. The Lyapunov exponent of the unstable null orbit further determines the eikonal quasinormal modes, yielding explicit halo-induced corrections to their oscillation and damping rates. We also compute the mass, Hawking temperature, entropy, heat capacity, and Gibbs free energy to characterize the thermodynamic stability and phase structure. We find that the dark matter halo enlarges the domain of thermodynamic stability and introduces nontrivial phase behavior absent in the Schwarzschild case, demonstrating that astrophysical dark matter environments can leave potentially observable imprints on black hole observables.
We formulate an inverse reconstruction procedure for spherically symmetric Datta--Bondi--Gair spacetimes with vanishing radial pressure and non-zero tangential pressure supported by angular momentum. Extending the logic of Krasiński--Hellaby reconstruction for Lemaître--Tolman--Bondi dust, we determine the full, exact space-time information from prescribed density, velocity or equilibrium state. Two specific constructions are developed. The first represents an initially expanding fluid with a finite turnaround, followed by an asymptotic collapse to an unstable Einstein cluster configuration. In the second, a static equilibrium density and a finite time density-velocity pair determine finite amplitude oscillations around a stable Einstein cluster. Numerical examples use a Jaffe-type final profile and an Einasto equilibrium with an approximate Navarro--Frenk--White finite time profile. The latter admits many oscillations before the first shell crossing is detected. The constructions provide diagnostics of the admissibility of prescribed configurations.