Related papers: On the link between the Maxwell and linearised Ein…
We obtain the static spherically symmetric solutions of a class of gravitational models whose additions to the General Relativity (GR) action forbid Ricci-flat, in particular, Schwarzschild geometries. These theories are selected to…
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…
We construct a scattering theory for the linearised Einstein equations on a Schwarzschild background in a double null gauge. We build on the results of Part I \cite{Mas20}, where we used the energy conservation enjoyed by the Regge--Wheeler…
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…
The Kerr solution is generated from the Schwarzschild solution by a simple combination of real global coordinate transformations and of invariance transformations acting on the space of stationary solutions of the Einstein-Maxwell…
We consider the vector and the Lichnerowicz wave equations on the Schwarzschild spacetime, which correspond to the Maxwell and linearized Einstein equations in harmonic gauges (or, respectively, in Lorenz and de Donder gauges). After a…
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…
A discussion is given of the conformal Einstein field equations coupled with matter whose energy-momentum tensor is trace-free. These resulting equations are expressed in terms of a generic Weyl connection. The article shows how in the…
In previous papers of this series we analysed the reduced phase space approach to perturbations of Einstein-Maxwell theory to second order around spherically symmetric backgrounds in the Gullstrand Painlev\'e Gauge and confirmed consistency…
Time-dependent spherically-symmetric perturbations of Schwarzschild black holes are studied within torsion bigravity, i.e., within generalized Einstein-Cartan theories where the dynamical torsion carries massive spin-2 excitation. We reduce…
The linearisation of a second-order formulation of the conformal Einstein field equations (CEFEs) in Generalised Harmonic Gauge (GHG), with trace-free matter is derived. The linearised equations are obtained for a general background and…
In the purely affine formulation of gravity, the gravitational field is represented by the symmetric part of the Ricci tensor of the affine connection. The classical electromagnetic field can be represented in this formulation by the second…
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…
A proof is given that the space $\L$ of solutions of the linearized vacuum Einstein's equation around a Schwarzschild black hole is parameterized by two scalar fields which are gauge invariant combinations of perturbed algebraic and…
This is the Part III paper of our series of papers on a gauge-invariant perturbation theory on the Schwarzschild background spacetime. After reviewing our general framework of the gauge-invariant perturbation theory and the proposal on the…
This is the Part II paper of our series of papers on a gauge-invariant perturbation theory on the Schwarzschild background spacetime. After reviewing our general framework of the gauge-invariant perturbation theory and the proposal on the…
We observe that the radial gauge can be consistently imposed \emph{together} with the Lorenz gauge in Maxwell theory, and with the harmonic traceless gauge in linearized general relativity. This simple observation has relevance for some…
A Lorentz and conformally invariant `Schr\"{o}dinger-like' equation for a massless complex scalar function $\psi$ is derived from an invariant action, and it is shown how the same $\psi$ can be used to calculate both the gravitational field…
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 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…