2024-0103

• [2401.00932] Black holes surrounded by generic matter distributions: polar perturbations and energy flux
Abstract: We develop a numerical approach to compute polar parity perturbations within fully relativistic models of black hole systems embedded in generic, spherically symmetric, anisotropic fluids. We apply this framework to study gravitational wave generation and propagation from extreme mass-ratio inspirals in the presence of several astrophysically relevant dark matter models, namely the Hernquist, Navarro-Frenk-White, and Einasto profiles. We also study dark matter spike profiles obtained from a fully relativistic calculation of the adiabatic growth of a BH within the Hernquist profile, and provide a closed-form analytic fit of these profiles. Our analysis completes prior numerical work in the axial sector, yielding a fully numerical pipeline to study black hole environmental effects. We study the dependence of the fluxes on the DM halo mass and compactness. We find that, unlike the axial case, polar fluxes are not adequately described by simple gravitational-redshift effects, thus offering an exciting avenue for the study of black hole environments with gravitational waves.

Tags: EMRI; GW; dark matter

2024-0104

• [2401.01541] Temperature of a steady system around a black hole
Abstract: We study the issue of temperature in a steady system around a black hole event horizon, contrasting it with the appearance of divergence in a thermal equilibrium system. We focus on a spherically symmetric system governed by general relativity, particularly examining the steady state with radial heat conduction. Employing an appropriate approximation, we derive exact solutions that illuminate the behaviors of number density, local temperature, and heat in the proximity of a black hole. We demonstrate that a carefully regulated heat inflow can maintain finite local temperatures at the black hole event horizon, even without considering the back-reaction of matter. This discovery challenges conventional expectations that the local temperature near the event horizon diverges in scenarios of thermal equilibrium. This implications shows that there's an intricate connection between heat and gravity in the realm of black hole thermodynamics.

Tags: black hole; black hole thermodynamics

2024-0105

• [2401.02003] Naked Singularity Censoring with Anisotropic Apparent Horizon
Abstract: Employing the Einstein-scalar field system, we demonstrate an approach for proving high co-dimensional nonlinear instability of naked-singularity solutions as constructed by Christodoulou in [18]. We further investigate the censorship of Christodoulou's naked singularity and show that a tiny anisotropic perturbation arising from the outgoing characteristic initial data would lead to the emergence of an anisotropic apparent horizon, which covers and censors the naked singularity. Our approach advances the hyperbolic short-pulse method by not requiring the aid of additional large parameters, by permitting the use of initial perturbations for the shear tensor and the derivative of scalar field to be with finite  and  norms, and by allowing the initial perturbation to be arbitrarily small in scale-critical norms. New elliptic arguments based on non-perturbative methods are also developed.

Tags: nake singularity; scc;

2024-0110

• [arXiv:2401.04467] Detecting dark matter with extreme mass-ratio inspirals
Arstract: Extreme mass ratio inspirals (EMRIs), where a small compact object inspiralls onto a supermassive black hole, are excellent sources for the space-based laser interferometer gravitational wave (GW) detectors. The presence of dark matter surrounding the supermassive black hole will influence the binary orbital evolution and emitted gravitational waveform. By direct observation of GW signals, we assess the detector"s capability to detect whether an EMRI is immersed in a dark matter halo and to measure its characteristic spatial scale a_0 and mass M_{ m halo}. Apart from the GW emission, the dynamical friction and accretion caused by the dark matter halo can also affect the dynamics of an EMRI, leaving detectable signatures in the emitted gravitational signal. We perform a Fisher-matrix error analysis to estimate the errors of parameters a_0 and M_{ m halo}, as well as their correlation. The results show that the highly correlated parameters a_0 and M_{ m halo} deteriorate the detector"s ability to measure dark matter even though the dephasing and mismatch between signals with and without dark matter indicate much difference. The effects of the dynamical friction and accretion can break possible degeneracies between parameters a_0 and M_{ m halo}, thus greatly decreasing the uncertainty by about one order of magnitude.

Tags: EMRI; Dark matter;

2024-0112

• [arXiv:2401.05454] Gravitational lensing by a stable rotating regular black hole
Arstract: Recent observational data from the Event Horizon Telescope (EHT) collaboration provide convincing realistic evidence for the existence of black hole rotation. From a phenomenological perspective, a recently proposed stable rotating regular (SRR) black hole circumvents the theoretical flaws of the Kerr solution. For the purpose of obtaining observational signatures of this black hole, we study its gravitational lensing effect. In the strong field limit, we calculate the deflection angle of light, the radius of the photon sphere, and other observables. The observables include the relativistic image position, separation, magnification, and time delays between different images. Then, by modeling and as the SRR black hole, we compute their observables and evaluate the deviation of the observables from the Kerr case. In the weak field limit, we calculate the light deflection angle of and via the Gauss-Bonnet theorem (GBT). With the growth of deviation parameter , the gravitational lensing effect in the weak field limit intensifies monotonically, and the gravitational lensing effect in the strong field limit changes dramatically only at high spins. Our research may contribute to distinguish between SRR black holes from Kerr black holes under higher-precision astronomical observations.

Tags: regular black hole