Related papers: Quasilinear wave equations on Schwarzschild-de Sit…
This is the main paper of a series establishing the linear stability of Schwarzschild-Anti-de Sitter (AdS) black holes to gravitational perturbations. Specifically, we prove that solutions to the linearisation of the Einstein equations…
We introduce a new, physical-space-based method for deriving the precise leading-order late-time behaviour of solutions to geometric wave equations on asymptotically flat spacetime backgrounds and apply it to the setting of wave equations…
The first-order semiclassical Einstein field equations are solved in the interior of the Schwarzschild-Tangherlini black holes. The source term is taken to be the stress-energy tensor of the quantized massive scalar field with arbitrary…
We consider semilinear wave equations with small initial data in two space dimensions. For a class of wave equations with cubic nonlinearity, we show the global existence of small amplitude solutions, and give an asymptotic description of…
The decay of massive scalar field in the Schwarzschild black hole background is investigated here by consideration its quasinormal spectrum. It has been proved that the so-called $quasi-resonant$ modes, which are arbitrary long living…
In ``Global existence and scattering for the nonlinear Schrodinger equation on Schwarzschild manifolds'' (math-ph/0002030), ``Semilinear wave equations on the Schwarzschild manifold I: Local Decay Estimates'' (gr-qc/0310091), and ``The wave…
We study the quasi-periodic oscillations from the accretion disk around the distorted Schwarzschild black hole in the framework of the resonant models. We confine ourselves to the case of a quadrupole distortion which can be caused for…
Black holes typically inhabit highly dynamical galactic environments and are frequently permeated by accretion media. The inevitable scattering of scalar, electromagnetic and gravitational waves off rotating and charged black holes provides…
In this paper, we derive the early-time asymptotics for fixed-frequency solutions $\phi_\ell$ to the wave equation $\Box_g \phi_\ell=0$ on a fixed Schwarzschild background ($M>0$) arising from the no incoming radiation condition on…
We consider the global existence and blow up of solutions of the Cauchy problem of the quasilinear wave equation: $\partial_{t}^2 u = \partial_x(c(u)^2 \partial_x u)$, which has richly physical backgrounds. Under the assumption that…
We present a concise review of known analytic results for quasinormal modes of black holes and related spacetimes. Our emphasis is on those regimes where the perturbation equations admit exact or perturbative solutions, providing insights…
We obtained new hairy black hole solutions in Einstein-scalar theory, including asymptotic flat, de Sitter and anti-de Sitter black holes. The theory is inspired by Ref. [1], where traversable wormhole solutions from an Einstein-phantom…
In a previous work, it was shown that all Ricci-flat spacetimes are exact solutions for a large class of non-local gravitational theories. Here we prove that, for a subclass of non-local theories, the Schwarzschild singularity is stable…
The explicit form of perturbation equation for the $\Psi_4$ Weyl scalar, containing the matter source terms, is derived for general type D spacetimes. It is described in detail the particular case of the Schwarzschild spacetime using…
Pseudospectral analyses have broadened our understanding of ringdown waveforms from binary remnants, by providing insight into both the stability of their characteristic frequencies under environmental perturbations, as well as the…
We study the scattering behavior of global solutions to stochastic nonlinear Schr\"odinger equations with linear multiplicative noise. In the case where the quadratic variation of the noise is globally finite and the nonlinearity is…
We show that, given any static spacetime whose spatial slices are asymptotically Euclidean (or, more generally, asymptotically conic) manifolds modeled on the large end of the Schwarzschild exterior, there exist stationary solutions to the…
The quasilocal energy associated with a constant stationary time slice of the Kerr spacetime is presented. The calculations are based on a recent proposal \cite{by} in which quasilocal energy is derived from the Hamiltonian of spatially…
We consider a class of scalar quasilinear wave equations in three spatial dimensions satisfying the weak null condition. For solutions arising from small, localized, smooth data, we give an asymptotic formula describing the global…
We investigated the evolution of a scalar field propagating in small Schwarzschild Anti-de Sitter black holes. The imaginary part of the quasinormal frequency decreases with the horizon size and the real part of the quasinormal frequency…