相关论文: Explicit Triangular Decoupling of the Separated Li…

We consider the vector wave equation on the Schwarzschild spacetime, which can be considered as coming from the harmonic (or Lorenz) gauge fixed Maxwell equations. After a separation of variables, the radial mode equations form a…

Black hole perturbation theory on spherically symmetric backgrounds has been instrumental in establishing various aspects about the gravitational dynamics close to black holes, and continues to be an interesting avenue to confront current…

High-accuracy gravitational-wave modeling demands going beyond linear, first-order perturbation theory. Particularly motivated by the need for second-order perturbative models of extreme-mass-ratio inspirals and black hole ringdowns, we…

We concisely summarize a method of finding all rational solutions to an inhomogeneous rational ODE system of arbitrary order (but solvable for its highest order terms) by converting it into a finite dimensional linear algebra problem. This…

We present a new covariant and gauge-invariant perturbation formalism for dealing with spacetimes having spherical symmetry (or some preferred spatial direction) in the background, and apply it to the case of gravitational wave propagation…

We extend the formulation for perturbations of maximally symmetric black holes in higher dimensions developed by the present authors in a previous paper (hep-th/0305147) to a charged black hole background whose horizon is described by an…

In this last part of the series we prove that the slow (inverse logarithmic) decay in time of solutions to the linearised Einstein equations on Schwarzschild-Anti-de Sitter backgrounds obtained in~\cite{Gra.Hol24,Gra.Hol24a} is in fact…

We derive a geometrical version of the Regge-Wheeler and Zerilli equations, which allows us to study gravitational perturbations on an arbitrary spherically symmetric slicing of a Schwarzschild black hole. We explain how to obtain the…

We reformulate the theory of Schwarzschild black hole perturbations in terms of the metric perturbation in the Lorenz gauge. In this formulation, each tensor-harmonic mode of the perturbation is constructed algebraically from 10 scalar…

We show that the gravitational waves generated by the perturbations of general relativistic black holes can be considered as a direct probe of the existence of dark sector interactions. Working within the framework of Horndeski theory and…

One of the longstanding problems of modern gravitational physics is the detection of gravitational waves, for which the standard theoretical analysis relies upon the split of the space-time metric into a background metric plus perturbation.…

In this paper, we study solutions to the linearized vacuum Einstein equations centered at higher-dimensional Schwarzschild met- rics. We employ Hodge decomposition to split solutions into scalar, co-vector, and two-tensor pieces; the first…

We calculate the gravitational perturbations produced by a small mass in eccentric orbit about a much more massive Schwarzschild black hole and use the numerically computed perturbations to solve for the metric. The calculations are…

It is shown that the axial and polar perturbations of the spherically symmetric black hole can be described in a gauge-invariant way. The reduced phase space describing gravitational waves outside of the horizon is described by the…

The Maxwell equations for the electromagnetic potential, supplemented by the Lorenz gauge condition, are decoupled and solved exactly in de Sitter space-time studied in static spherical coordinates. There is no source besides the…

We develop a nonlinear perturbation theory of Reissner-Nordstr\"om black holes. We show that, at each perturbation level, Einstein-Maxwell equations can be reduced to four inhomogeneous wave equations, two for polar and two for axial…

Odd-type spin 2 perturbations of Einstein's equation can be reduced to the scalar Regge-Wheeler equation. We show that the weighted norms of solutions are in L^2 of time and space. This result uses commutator methods and applies uniformly…

We present a new covariant, gauge-invariant formalism describing linear metric perturbation fields on any spherically symmetric background in general relativity. The advantage of this formalism relies in the fact that it does not require a…

The propagation of (massless) scalar, electromagnetic and gravitational waves on fixed Schwarzschild background spacetime is described by the general time-dependent Regge-Wheeler equation. We transform this wave equation to usual…

The Einstein-Bianchi system uses symmetric and traceless tensors to reformulate Einstein's original field equations. However, preserving these algebraic constraints simultaneously remains a challenge for numerical methods. This paper…