Related papers: Treating instabilities in a hyperbolic formulation…
We study the perturbations of two classes of static black ellipsoid solutions of four dimensional vacuum Einstein equations. Such solutions are described by generic off--diagonal metrics which are generated by anholonomic transforms of…
In this paper we consider the single patch pseudo-spectral scheme for tensorial and spinorial evolution problems on the 2-sphere presented in [3,4] which is based on the spin-weighted spherical harmonics transform. We apply and extend this…
In general relativity, the Einstein equations provide spherically symmetric static spacetimes with dynamics defined as an evolution along the radial coordinate $r$. The geometrical sector becomes a one-dimensional mechanical system, with…
Combining deeper insight of Einstein's equations with sophisticated numerical techniques promises the ability to construct accurate numerical implementations of these equations. We illustrate this in two examples, the numerical evolution of…
In this paper we prove that the four-dimensional hyperbolic supersymmetric black holes can be unstable in the canonical ensemble. To this end, we work with an infinite class of $\,\mathcal{N}=2$ supergravity theories interpolating between…
A class of nonstationary spacetimes is obtained by means of a conformal transformation of the Schwarzschild metric, where the conformal factor $a(t)$ is an arbitrary function of the time coordinate only. We investigate several situations…
In this paper, we study the global behavior of solutions to the spherically symmetric coupled Einstein-Klein-Gordon (EKG) system in the presence of a negative cosmological constant. We prove that the Schwarzschild-AdS spacetimes (the…
We discuss the stability of (charged) static black holes in higher-dimensional spacetimes with and without cosmological constant by using gauge-invariant master equations of the Schroedinger equation type for black hole perturbations…
We analyze the tensor mode perturbations of static, spherically symmetric solutions of the Einstein equations with a quadratic Gauss-Bonnet term in dimension $D > 4$. We show that the evolution equations for this type of perturbations can…
We describe numerical techniques used in the construction of our 4th order evolution for the full Einstein equations, and assess the accuracy of representative solutions. The code is based on a null gauge with a quasi-spherical radial…
In [7] Klainerman introduced the hyperboloidal method to prove the global existence results for nonlinear Klein-Gordon equations by using commuting vector fields. In this paper, we extend the hyperboloidal method from Minkowski space to…
We construct dynamical many-black-hole spacetimes with well-controlled asymptotic behavior as solutions of the Einstein vacuum equation with positive cosmological constant. We accomplish this by gluing Schwarzschild-de Sitter or Kerr-de…
The causal structure of Einstein's evolution equations is considered. We show that in general they can be written as a first order system of balance laws for any choice of slicing or shift. We also show how certain terms in the evolution…
There are a number of publications on relativistic objects dealing either with black holes or naked singularities in the center. Here we show that there exist static spherically symmetric solutions of Einstein equations with a strongly…
This is the third paper in a series describing a numerical implementation of the conformal Einstein equation. This paper describes a scheme to calculate (three) dimensional data for the conformal field equations from a set of free…
We study scalarization of slowly rotating black holes in the Einstein-scalar-Gauss-Bonnet (GB)-Chern-Simons (CS) theory. In the slow rotation approximation of $a\ll1$ with rotation parameter $a$, the GB term is given by a term for…
New, simple models of ``black hole interiors'', namely spherically symmetric solutions of the Einstein field equations in matter matching the Schwarzschild vacuum at spacelike hypersurfaces ``R<2M'' are constructed. The models satisfy the…
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…
We study the full time-domain evolution of gravitational perturbations in black hole spacetimes arising in Einstein-Weyl gravity, a renormalizable extension of general relativity containing quadratic curvature corrections. We analyze both…
Detailed observations of phenomena involving black holes, be it via gravitational waves or more traditional electromagnetic means, can probe the strong field regime of the gravitational interaction. The prediction of features in such…