相关论文: A 3+1 perspective on null hypersurfaces and isolat…

We review in a pedagogical fashion the 3+1-split which serves to put Einstein's equations into the form of a dynamical system with constraints. We then discuss the constraint equations under the simplifying assumption of time-symmetry.…

A framework is developed in which one can write down the constraint equations on a three--dimensional hypersurface of arbitrary signature. It is then applied to isolated and dynamical horizons. The derived equations can be used to extract…

We construct the spacetime in the vicinity of a general isolated, rotating, charged black hole. The black hole is modeled as a weakly isolated horizon, and we use the characteristic initial value formulation of the Einstein equations with…

We apply the ultrarelativistic boosting procedure to map the metric of Schwarzschild-de Sitter spacetime into a metric describing de Sitter spacetime plus a shock-wave singularity located on a null hypersurface, by exploiting the picture of…

This is the second in a series of papers describing a 3+1 computational scheme for the numerical simulation of dynamic black hole spacetimes. We discuss the numerical time-evolution of a given black-hole-containing initial data slice in…

The membrane paradigm displays underlying connections between a timelike stretched horizon and a null boundary (such as a black hole horizon) and bridges the gravitational dynamics of the horizon with fluid dynamics. In this work, we…

The recently introduced Isolated Horizons (IH) formalism has become a powerful tool for realistic black hole physics. In particular, it generalizes the zeroth and first laws of black hole mechanics in terms of quasi-local quantities and…

This paper treats boundary conditions on black hole horizons for the full 3+1D Einstein equations. Following a number of authors, the apparent horizon is employed as the inner boundary on a space slice. It is emphasized that a further…

We discuss black hole spacetimes with a geometrically defined quasi-local horizon on which the curvature tensor is algebraically special relative to the alignment classification. Based on many examples and analytical results, we conjecture…

An isolated horizon (IH) is a null hypersurface at which the geometry is held fixed. This generalizes the notion of an event horizon so that the black hole is an object that is in local equilibrium with its (possibly) dynamic environment.…

With a help of a generalized Raychaudhuri equation non-expanding null surfaces are studied in arbitrarily dimensional case. The definition and basic properties of non-expanding and isolated horizons known in the literature in the 4 and 3…

We explore the possibility that spacetime horizons in 4D general relativity can be treated as manifestations of higher dimensions that induce fields on our 4D spacetime. In this paper we discuss the black hole event horizon, as an example…

There are two mathematical relativity frameworks generalizing the black hole theory: the theory of isolated horizons (IH) and the theory of near horizon geometries (NHG). We outline here and discuss the derivation of the NHG from the theory…

Using the earlier developed classical Hamiltonian framework as the point of departure, we carry out a non-perturbative quantization of the sector of general relativity, coupled to matter, admitting non-rotating isolated horizons as inner…

This work proposes a set of equations that can be used to numerically compute spacetimes containing a stationary black hole. The formalism is based on the 3+1 decomposition of General Relativity with maximal slicing and spatial harmonic…

A Hamiltonian framework is introduced to encompass non-rotating (but possibly charged) black holes that are ``isolated'' near future time-like infinity or for a finite time interval. The underlying space-times need not admit a stationary…

We present a numerical work aiming at the computation of excised initial data for black hole spacetimes in full general relativity, using Dirac gauge in the context of a constrained formalism for the Einstein equations. Introducing the…

We have developed a general method for finding apparent horizons in 3D numerical relativity. Instead of solving for the partial differential equation describing the location of the apparent horizons, we expand the closed 2D surfaces in…

The geometric trinity of gravity offers a platform in which gravity can be formulated in three analogous approaches, namely curvature, torsion and nonmetricity. In this vein, general relativity can be expressed in three dynamically…

Event and apparent horizons are key diagnostics for the presence and properties of black holes. In this article I review numerical algorithms and codes for finding event and apparent horizons in numerically-computed spacetimes, focusing on…