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Complex formalism of Riemann - Silberstein - Majorana - Oppenheimer in Maxwell electrodynamics is extended to the case of arbitrary pseudo-Riemannian space - time in accordance with the tetrad recipe of Tetrode - Weyl - Fock - Ivanenko. In…

Mathematical Physics · Physics 2009-05-12 N. G. Tokarevskaya , E. M. Ovsiyuk , V. M. Red'kov

The wave equation for vectors and symmetric tensors in spherical coordinates is studied under the divergence-free constraint. We describe a numerical method, based on the spectral decomposition of vector/tensor components onto spherical…

General Relativity and Quantum Cosmology · Physics 2009-11-23 Jerome Novak , Jean-Louis Cornou , Nicolas Vasset

We prove in this paper that the Schwarzschild famiily of black holes are linearly stable as a family of solutions to the system of equations that result from expressing the Einstein vacuum equations in a generalised wave gauge. In…

General Relativity and Quantum Cosmology · Physics 2020-04-20 Thomas William Johnson

The Duffin-Kemmer form of massless vector field (Maxwell field) is extended to the case of arbitrary pseudo-Riemannian space-time in accordance with the tetrad recipe of Tetrode-Weyl-Fock-Ivanenko. In this approach, the Maxwell equations…

Mathematical Physics · Physics 2009-05-12 A. A. Bogush , E. M. Ovsiyuk , V. M. Red'kov

A decoupled system of hyperbolic partial differential equations for linear perturbations around any spatially flat FRW universe is obtained for a wide class of perturbations. The considered perturbing energy momentum-tensors can be…

General Relativity and Quantum Cosmology · Physics 2009-11-07 J. Ramirez , S. Kopeikin

We study the properties of the outgoing gravitational wave produced when a non-spinning black hole is excited by an ingoing gravitational wave. Simulations using a numerical code for solving Einstein's equations allow the study to be…

General Relativity and Quantum Cosmology · Physics 2009-11-10 Yosef Zlochower , Roberto Gomez , Sascha Husa , Luis Lehner , Jeffrey Winicour

We develop a novel technique through spectral decompositions to study the gravitational perturbations of a black hole, without needing to decouple the linearized field equations into master equations and separate their radial and angular…

General Relativity and Quantum Cosmology · Physics 2023-06-19 Adrian Ka-Wai Chung , Pratik Wagle , Nicolas Yunes

We revisit the problem of scalar and electromagnetic waves impinging upon a Schwarzschild black hole from complex angular momentum techniques. We focus more particularly on the associated differential scattering cross sections. We derive an…

General Relativity and Quantum Cosmology · Physics 2019-06-04 Antoine Folacci , Mohamed Ould El Hadj

We revisit the problem of plane monochromatic gravitational waves impinging upon a Schwarzschild black hole using complex angular momentum techniques. By extending our previous study concerning scalar and electromagnetic waves [A. Folacci…

General Relativity and Quantum Cosmology · Physics 2019-09-06 Antoine Folacci , Mohamed Ould El Hadj

In a recent seminal paper \cite{D-H-R} of Dafermos, Holzegel and Rodnianski the linear stability of the Schwarzschild family of black hole solutions to the Einstein vacuum equations was established by imposing a double null gauge. In this…

General Relativity and Quantum Cosmology · Physics 2018-10-03 Thomas Johnson

A relativistic model for the emission of gravitational waves from an initially unperturbed Schwarzschild black hole, or spherical collapsing configuration, is completely integrated. The model consists basically of gravitational…

General Relativity and Quantum Cosmology · Physics 2007-05-23 M. C. Lima , I. Damião Soares

We show a stability result for the Schwarzschild singularity (inside the black hole region) for the Einstein vacuum equations. The result is proven in the class of polarized axial symmetry, under perturbations of the Schwarzschild data…

Analysis of PDEs · Mathematics 2020-05-07 Spyros Alexakis , Grigorios Fournodavlos

We study the metric perturbations induced by a classical spinning particle moving along a circular orbit on a Schwarzschild background, limiting the analysis to effects which are first order in spin. The particle is assumed to move on the…

General Relativity and Quantum Cosmology · Physics 2018-05-23 Donato Bini , Thibault Damour , Andrea Geralico , Chris Kavanagh

We carefully study the stable problem of the Rindler space time by the scalar wave perturbation. Using the two different coordinate systems, the scalar wave equation is investigated. The results are different in these two cases. They are…

General Relativity and Quantum Cosmology · Physics 2007-05-23 Tian Gui-hua , Shi-kun Wang , Shuquan Zhong

We present a formalism to study the metric perturbations of the Schwarzschild spacetime. The formalism is gauge invariant, and it is also covariant under two-dimensional coordinate transformations that leave the angular coordinates…

General Relativity and Quantum Cosmology · Physics 2009-11-11 Karl Martel , Eric Poisson

In the class of vacuum Petrov type D spacetimes with cosmological constant, which includes the Kerr-(A)dS black hole as a particular case, we find a set of four-dimensional operators that, when composed {\em off shell} with the Dirac,…

General Relativity and Quantum Cosmology · Physics 2017-03-28 Bernardo Araneda

In this paper we study the even part of the linear stability of the Schwarzschild spacetime as a continuation of [22]. By taking the harmonic gauge, we prove that the energy decays at a rate $\tau^{-2+}$ for the solution of the linearized…

General Relativity and Quantum Cosmology · Physics 2019-09-17 Pei-Ken Hung

Perturbations of Kerr spacetime are typically studied with the Teukolsky formalism, in which a pair of invariant components of the perturbed Weyl tensor are expressed in terms of separable modes that satisfy ordinary differential equations.…

General Relativity and Quantum Cosmology · Physics 2022-04-13 Sam R. Dolan , Chris Kavanagh , Barry Wardell

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…

General Relativity and Quantum Cosmology · Physics 2023-06-14 Nicola Franchini

We derive the linearly perturbed matching conditions between a Schwarzschild spacetime region with stationary and axially symmetric perturbations and a FLRW spacetime with arbitrary perturbations. The matching hypersurface is also perturbed…

General Relativity and Quantum Cosmology · Physics 2008-11-26 Marc Mars , Filipe C. Mena , Raül Vera