Related papers: Testing outer boundary treatments for the Einstein…
An inverse boundary value problem for the Helmholtz equation in a bounded domain is considered. The problem is to extract information about an unknown obstacle embedded in the domain with unknown impedance boundary condition (the Robin…
The on-shell gravitational action and the boundary stress tensor are essential ingredients in the study of black hole thermodynamics. We employ the Hamilton-Jacobi method to calculate the boundary counterterms necessary to remove the…
The main objective of this work is the construction of regular black hole solutions in the context of the Einstein-Maxwell theory. The strategy is to match an interior regular solution to an exterior electrovacuum solution. With this…
Einstein field equations are notoriously challenging to solve due to their complex mathematical form, with few analytical solutions available in the absence of highly symmetric systems or ideal matter distribution. However, accurate…
This article develops a solution for an inverse problem through the generalized method of lines. We consider a Laplace equation on a domain with internal and external boundaries with standard Dirichlet boundary conditions. Also, we specify…
The Weiss variation of the Einstein-Hilbert action with an appropriate boundary term has been studied for general boundary surfaces; the boundary surfaces can be spacelike, timelike, or null. To achieve this we introduce an auxiliary…
We extend the theoretical framework of non-local optimized Schwarz methods as introduced in [Claeys,2021], considering an Helmholtz equation posed in a bounded cavity supplemented with a variety of conditions modeling material boundaries.…
One method of studying the asymptotic structure of spacetime is to apply Penrose's conformal rescaling technique. In this setting, the Einstein equations for the metric and the conformal factor in the unphysical spacetime degenerate where…
Inspiralling and coalescing binary black holes are promising sources of gravitational radiation. The orbital motion and gravitational-wave emission of such system can be modelled using a variety of approximation schemes and numerical…
We study the bound state solutions for the polar perturbations in the interior of the Schwarzschild black hole. It is shown that for a given value of the spherical harmonic index $\ell$, there are a total of $\ell-1$ bound states for polar…
We consider accelerated black hole horizons with and without defects. These horizons appear in the $C$-metric solution to Einstein equations and in its generalization to the case where external fields are present. These solutions realize a…
We solve for the spectrum of the Laplacian as a Hamiltonian on $\mathbb{R}^{2}-\mathbb{D}$ and in $\mathbb{R}^{3}-\mathbb{B}$. A self-adjointness analysis with $\partial\mathbb{D}$ and $\partial\mathbb{B}$ as the boundary for the two cases…
The harmonic formulation of Einstein's field equations is considered, where the gauge conditions are introduced as dynamical constraints. The difference between the fully constrained approach (used in analytical approximations) and the free…
An exact and analytical solution, in four-dimensional general relativity coupled with Maxwell electromagnetism, is built by means of a Lie point symmetry of the Ernst equations, the Harrison transformation. The new spacetime describes a…
The first proof of well-posedness of an initial boundary value problem for the Einstein equations was given in 1999 by Friedrich and Nagy. They used a frame formalism with a particular gauge for formulating the equations. This…
In recent work, we used pseudo-differential theory to establish conditions that the initial-boundary value problem for second order systems of wave equations be strongly well-posed in a generalized sense. The applications included the…
Black holes have long served as a testing ground for probing theories of gravity and quantum mechanics. Notably, fundamental fields in the neighborhood of black holes exhibit rich phenomena that could yield astrophysical observable…
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…
We consider the initial boundary value problem for the Einstein vacuum equations in the maximal gauge, or more generally, in a gauge where the mean curvature of a timelike foliation is fixed near the boundary. We prove the existence of…
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…