Related papers: An intrinsic hyperboloid approach for Einstein Kle…
In Poincar\'e gauge theory of gravity and in $\overline{\mbox{Poincar\'e}}$ gauge theory of gravity, we give the necessary and sufficient condition in order that the Schwarzschild space-time expressed in terms of the Schwarzschild…
We study the nonlinear stability of the $(3+1)$-dimensional Minkowski spacetime as a solution of the Einstein vacuum equation. Similarly to our previous work on the stability of cosmological black holes, we construct the solution of the…
We introduce a new family of horizon-penetrating coordinate systems for the Schwarzschild black hole geometry featuring time coordinates that are Cauchy temporal functions for which the level sets are smooth, asymptotically flat, spacelike…
The 3+1 Hamiltonian formulation in the gauge $D_tN=-K$ on the lapse function fixes the direction of time associated with the trace $K$ of the extrinsic curvature tensor. The Hamiltonian equations hereby become hyperbolic. We study this new…
Algebraic quantization has been applied on the class of globally hyperbolic spacetime for many decades, leading to remarkable results. Nonetheless, the presence of a boundary calls for a separate treatment, since, in general, it breaks…
It has recently been demonstrated (Class. Quantum Grav. 31, 085010, 2014) that the conformally invariant wave equation on a Minkowski background can be solved with a fully pseudospectral numerical method. In particular, it is possible to…
In a recent seminal paper \cite{D-H-R} of Dafermos, Holzegel and Rodnianski the linear stability of the Schwarzschild family of black hole solutions to the Einstein vacuum equations was established by imposing a double null gauge. In this…
In this paper, we prove the nonlinear stability in exponential time of Minkowki space-time with a translation space-like Killing field. In the presence of such a symmetry, the 3 + 1 vacuum Einstein equations reduce to the 2 + 1 Einstein…
Utilizing various gauges of the radial coordinate, we give a General Relativistic (GR) description of static spherically symmetric spacetimes with a massive point source and vacuum outside this singularity. We show that in GR there exists a…
The resolution of the nonlinear stability of black holes as solutions to the Einstein equations relies crucially on imposing the right geometric gauge conditions. In the vacuum case, the use of Generally Covariant Modulated (GCM) spheres…
We model pseudo-Finsler geometries, with pseudo-Euclidean signatures of metrics, for two classes of four dimensional nonholonomic manifolds: a) tangent bundles with two dimensional base manifolds and b) pseudo-Riemannian/ Einstein…
We study the Lorentzian Calder\'on problem, where the objective is to determine a globally hyperbolic Lorentzian metric up to a boundary fixing diffeomorphism from boundary measurements given by the hyperbolic Dirichlet-to-Neumann map. This…
It is shown that a spacetime with collisionless matter evolving from data on a compact Cauchy surface with hyperbolic symmetry can be globally covered by compact hypersurfaces on which the mean curvature is constant and by compact…
We present numerical solutions of several spacetimes of physical interest, including binary black hole mergers, in shift-symmetric Einstein-scalar-Gauss-Bonnet (ESGB) gravity, and describe our methods for solving the full equations of…
Hyperboloidal slices are spacelike slices that reach future null infinity. Their asymptotic behaviour is different from Cauchy slices, which are traditionally used in numerical relativity simulations. This work uses free evolution of the…
We investigate the ultrarelativistic boost of a Schwarzschild black hole immersed in an external electromagnetic field, described by an exact solution of the Einstein-Maxwell equations found by Ernst (the ``Schwarzschild-Melvin'' metric).…
In this paper, we prove the existence of global in time small data solutions of semilinear Klein-Gordon equations in space-time with a static Schwarzschild radius in the expanding universe.
We discuss the initial value problem for the Einstein equations in Hitchin's generalised geometry for the case of closed divergence (which correspond to the equations of motion in the bosonic part of the NS-NS sector in type II…
It has been recently shown in [Phys. Rev. Lett. 125 (2020) 041302] that microstate counting carried out for quantum states residing on the horizon of a black hole leads to a correction of the form $\exp(-A/4l_p^2)$ in the Bekenstein-Hawking…
We give a short proof of asymptotic completeness and global existence for the cubic Nonlinear Klein-Gordon equation in one dimension. Our approach to dealing with the long range behavior of the asymptotic solution is by reducing it, in…