Related papers: Free evolution of the hyperboloidal initial value …
We present improvements to construction of binary black hole initial data used in SpEC (the Spectral Einstein Code). We introduce new boundary conditions for the extended conformal thin sandwich elliptic equations that enforce the excision…
Initial data for the spherically symmetric Einstein-Vlasov system is constructed whose past evolution is regular and whose future evolution contains a black hole. This is the first example of initial data with these properties for the…
We construct a formalism for evolving spherically symmetric black hole initial data sets within a canonical approach to quantum gravity. This problem can be formulated precisely in quantum reduced loop gravity, a framework which has been…
A first order symmetric hyperbolic tetrad formulation of the Einstein equations developed by Estabrook and Wahlquist and put into a form suitable for numerical relativity by Buchman and Bardeen (the WEBB formulation) is adapted to explicit…
We investigate the asymptotic stability of solutions to the characteristic initial value problem for the Einstein (massless) scalar field system with a positive cosmological constant. We prescribe spherically symmetric initial data on a…
The Good-Bad-Ugly-F model is a system of semi-linear wave equations that mimics the asymptotic form of the Einstein field equations in generalized harmonic gauge with specific constraint damping and suitable gauge source functions. These…
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…
We propose a physically sensible formulation of initial value problem for black hole perturbations in higher-order scalar-tensor theories. As a first application, we study monopole perturbations around stealth Schwarzschild solutions in a…
We present an analytic, perturbative solution to the Einstein equations with a scalar field that describes dynamical black holes in a slow-roll inflationary cosmology. We show that the metric evolves quasi-statically through a sequence of…
This is the first in a series of articles on the numerical solution of Friedrich's conformal field equations for Einstein's theory of gravity. We will discuss in this paper why one should be interested in applying the conformal method to…
In a recent work, Ringstr\"om proposed a geometric notion of initial data on big bang singularities. Moreover, he conjectured that initial data on the singularity could be used to parameterize quiescent solutions to Einstein's equations;…
Under weak regularity assumptions, only, we develop a fully geometric theory of vacuum Einstein spacetimes with T2 symmetry, establish the global well-posedness of the initial value problem for Einstein's field equations, and investigate…
Quasinormal modes and power-law late-time decay tails of a charged scalar field on a charged black hole have been considered in the literature, and here we use the hyperboloidal formalism to present an independent comparison to prior…
We are interested in the global dynamics of a massive scalar field evolving under its own gravitational field and, in this paper, we study spherically symmetric solutions to Einstein's field equations coupled with a Klein-Gordon equation…
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…
We prove the well-posedness of the initial boundary value problem for the Einstein equations with sole boundary condition the requirement that the timelike boundary is totally geodesic. This provides the first well-posedness result for this…
We study the backwards-in-time stability of the Schwarzschild singularity from a dynamical PDE point of view. More precisely, considering a spacelike hypersurface $\Sigma_0$ in the interior of the black hole region, tangent to the singular…
A new numerical scheme to solve the Einstein field equations based upon the generalized harmonic decomposition of the Ricci tensor is introduced. The source functions driving the wave equations that define generalized harmonic coordinates…
The null-timelike initial-boundary value problem for a hyperbolic system of equations consists of the evolution of data given on an initial characteristic surface and on a timelike worldtube to produce a solution in the exterior of the…
In recent work of Allen at. al., heuristic and numerical arguments were put forth to suggest that boundary value problems for black hole evolution, where an appropriate Sommerfeld radiation condition is imposed, would fail to produce Price…