Related papers: Explicit Triangular Decoupling of the Separated Li…
We provide simple and accurate analytical expressions for the Regge poles of the Schwarzschild black hole. This is achieved by using third-order WKB approximations to solve the radial wave equations for spins 0, 1 and 2. These results…
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…
We present a fully covariant and gauge-invariant formulation of electromagnetic wave propagation in static, spherically symmetric black hole spacetimes, developed entirely within Schwarzschild-like coordinates. Start ing from the…
The satellite observatory LISA will be capable of detecting gravitational waves from extreme mass ratio inspirals (EMRIs), such as a small black hole orbiting a supermassive black hole. The gravitational effects of the much smaller mass can…
We present a method of post-Newtonian expansion to solve the homogeneous Regge-Wheeler equation which describes gravitational waves on the Schwarzschild spacetime. The advantage of our method is that it allows a systematic iterative…
In this paper, we study the odd solution of the linearlized Einstein equation on the Schwarzschild background and in the harmonic gauge. With the aid of Regge-Wheeler quantities, we are able to estimate the odd part of Lichnerowicz…
We show that in four or more spacetime dimensions, the Einstein equations for gravitational perturbations of maximally symmetric vacuum black holes can be reduced to a single 2nd-order wave equation in a two-dimensional static spacetime for…
We identify a set of Hertz potentials for solutions to the vector wave equation on black hole spacetimes. The Hertz potentials yield Lorenz gauge electromagnetic vector potentials that represent physical solutions to the Maxwell equations,…
We prove in this paper the linear stability of the celebrated Schwarzschild family of black holes in general relativity: Solutions to the linearisation of the Einstein vacuum equations around a Schwarzschild metric arising from regular…
An efficient approach to tensor perturbation calculations by proper use of computer algebra methods is described, reaching the sufficient generality required for a comprehensive analysis of the Schwarzschild and Reissner-Nordstroem metric…
The Regge-Wheeler equation describes the axial perturbations of Schwarzschild metric in linear approximation. We present its exact solutions in terms of the confluent Heun's functions, the basic properties of the general solution, novel…
We investigate how GWs pass through the spacetime of a Schwarzschild black hole using time-domain numerical simulations. Our work is based on the perturbed 3+1 Einstein's equations up to the linear order. We show explicitly that our…
The aim of the article to clarify the status of Shapiro plane wave solutions of the Schr\"odinger's equation in the frames of the well-known general method of separation of variables. To solve this task, we use the well-known cylindrical…
The method of geodesic deviations has been applied to derive accurate analytic approximations to geodesics in Schwarzschild space-time. The results are used to construct analytic expressions for the source terms in the Regge-Wheeler and…
In this paper, we study the theory of linearized gravity and prove the linear stability of Schwarzschild black holes as solutions of the vacuum Einstein equations. In particular, we prove that solutions to the linearized vacuum Einstein…
Gravitational waves from the inspiral of a stellar-size black hole to a supermassive black hole can be accurately approximated by a point particle moving in a Kerr background. This paper presents progress on finding the electromagnetic and…
The well-known Regge-Wheeler equation describes the axial perturbations of Schwarzschild metric in the linear approximation. From a mathematical point of view it presents a particular case of the confluent Heun equation and can be solved…
The Regge-Wheeler equation for black-hole gravitational waves is analyzed for large negative imaginary frequencies, leading to a calculation of the cut strength for waves outgoing to infinity. In the--limited--region of overlap, the results…
A Regge--Wheeler analysis is performed for a novel black hole mimicker `the regular black hole with asymptotically Minkowski core', followed by an approximation of the permitted quasi-normal modes for propagating waveforms. A first-order…
In this short note we shall demonstrate that given a smooth solution $\gamma$ to the linearised Einstein equations on Schwarzschild which is supported on the $l\geq 2$ spherical harmonics and expressed relative to a transverse and traceless…