Related papers: Green function of the P\"{o}schl-Teller potential
Gravitational waves generated by moving sources in Schwarzschild spacetime can be decomposed into three principal components: quasinormal modes, tail, and prompt response. While the first two have been extensively studied, a systematic and…
We study two singular spectral components of the Green's function of a Schwarzschild black hole and their interpretation in the frequency domain: (i) the low-frequency branch cut, which yields corrections to Price's law tails in the form of…
We study static massless minimally coupled scalar field created by a source in a static D-dimensional spacetime. We demonstrate that the corresponding equation for this field is invariant under a special transformation of the background…
The computation of the gravitational radiation emitted by a particle falling into a Schwarzschild black hole is a classic problem studied already in the 1970s. Here we present a detailed numerical analysis of the case of radial infall…
We present a novel theoretical framework for analysing the stability of rotating black hole spacetimes through the conformal properties of the Weyl tensor. By introducing a new conformal invariant constructed from the electric and magnetic…
We consider perturbations of a Schwarzschild black hole that can be of both even and odd parity, keeping terms up to second order in perturbation theory, for the $\ell=2$ axisymmetric case. We develop explicit formulae for the evolution…
In this paper, we present a detailed analysis of first-order perturbations of the Kerr metric in the slow-rotation limit. We perform the calculation by perturbing the Schwarzschild metric plus up to second-order corrections in the spin in…
Reconsideration of the Regge-Wheeler equation is processed by using the Painlev\'{e} coordinate and "good" timelier to define the initial time. We find that: the Regge-Wheeler equation could has positive imaginary frequency. Because the…
On the basis of a recently proposed strategy of finite element integration in time domain for partial differential equations with a singular source term, we present a fourth order algorithm for non-rotating black hole perturbations in the…
We investigate the pole structure of Kerr black-hole perturbations in the frequency domain, focusing on the building blocks of the Green's function for the radial Teukolsky equation: the homogeneous radial solutions, the connection…
We prove sharp pointwise $t^{-3}$ decay for scalar linear perturbations of a Schwarzschild black hole without symmetry assumptions on the data. We also consider electromagnetic and gravitational perturbations for which we obtain decay rates…
The foundations are laid for the numerical computation of the actual worldline for a particle orbiting a black hole and emitting gravitational waves. The essential practicalities of this computation are here illustrated for a scalar…
We study the early-time component of the Green's function of a Schwarzschild black hole, traveling on the curved light cone and usually denoted as the prompt response. Working in a post-Minkowskian approximation, we show for the first time…
We improve upon the simple model studied by Casadio and Orlandi [JHEP 1308 (2013) 025] for a black hole as a condensate of gravitons. Instead of the harmonic oscillator potential, the P\"oschl-Teller potential is used, which allows for a…
Quasinormal modes describe the return to equilibrium of a perturbed system, in particular the ringdown phase of a black hole merger. But as globally-defined quantities, the quasinormal spectrum can be highly sensitive to global structure,…
We calculate the gravitational energy spectrum of the perturbations of a Schwarzschild black hole described by quasinormal modes, in the framework of the teleparallel equivalent of general relativity (TEGR). We obtain a general formula for…
We construct a series of charged dilatonic black holes which share zero entropy in the zero temperature limit using Einstein-Maxwell-Dilaton theories. In these black holes, the wave functions and the Green's functions of massless fermions…
The Wheeler-DeWitt equation arising from a Kantowski-Sachs model is considered for a Schwarzschild black hole under the assumption that the scale factors and the associated momenta satisfy a noncanonical noncommutative extension of the…
In black hole perturbation formalism, the gravitational waveform is obtained by the convolution of the Green's function and the source term causing radiation emission. Hence, the ringdown properties, namely its start time, depend on both…
The pointwise space-time behavior of the Green's function of the three-dimensional relativistic Boltzmann equation is studied in this paper. It is shown that the Green's function has a decomposition of the macroscopic diffusive waves and…