Related papers: An alternative approach to solving the Hamiltonian…
The indefinite sign of the Hamiltonian constraint means that solutions to Einstein's equations must achieve a delicate balance--often among numerically large terms that nearly cancel. If numerical errors cause a violation of the Hamiltonian…
In the harmonic description of general relativity, the principle part of Einstein's equations reduces to 10 curved space wave equations for the componenets of the space-time metric. We present theorems regarding the stability of several…
The first order corrections to the geometry of the (2+1)-dimensional black hole due to back-reaction of a massless conformal scalar field are computed. The renormalized stress energy tensor used as the source of Einstein equations is…
We construct rotating black hole solutions in Einstein-Gauss-Bonnet theory in five spacetime dimensions. These black holes are asymptotically flat, and possess a regular horizon of spherical topology and two equal-magnitude angular momenta…
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 investigate the black hole solution to (2+1)-dimensional gravity coupled to topological matter, with a vanishing cosmological constant. We calculate the total energy, angular momentum and entropy of the black hole in this model and…
We consider self-interacting scalar fields coupled to gravity. Two classes of exact solutions to Einstein's equations are obtained: the first class corresponds to the minimal coupling, the second one to the conformal coupling. One of the…
We study spherical charged black holes in the presence of a cosmological constant with corrections motivated by the theory of loop quantum gravity. The effective theory is constructed at the Hamiltonian level by introducing certain…
With the puncture method for black hole simulations, the second infinity of a wormhole geometry is compactified to a single "puncture point" on the computational grid. The region surrounding the puncture quickly evolves to a trumpet…
This work consists of two distinct parts. In the first part we present a new method for solving the initial value problem of general relativity. Given any spatial metric with a surface orthogonal Killing field and two freely specified…
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…
The hamiltonian circuit polytope is the convex hull of feasible solutions for the circuit constraint, which provides a succinct formulation of the traveling salesman and other sequencing problems. We study the polytope by establishing its…
From first principles, I present a concrete realization of Carlip's idea on the black hole entropy from the conformal field theory on the horizon in any dimension. New formulation is free of inconsistencies encountered in Carlip's. By…
We construct a black hole initial data for the Einstein equations with prescribed scalar curvature, or more precisely a piece of initial data contained inside the black hole. The constraints translate into a parabolic equation, with radius…
We analyze the excision strategy for simulating black holes. The problem is modeled by the propagation of quasi-linear waves in a 1-dimensional spatial region with timelike outer boundary, spacelike inner boundary and a horizon in between.…
We present a new algorithm for evolving orbiting black-hole binaries that does not require excision or a corotating shift. Our algorithm is based on a novel technique to handle the singular puncture conformal factor. This system, based on…
Shibata, Ury\=u and Friedman recently suggested a new decomposition of Einstein's equations that is useful for constructing initial data. In contrast to previous decompositions, the conformal metric is no longer treated as a…
To study asymptotic structures, we regularize Einstein's field equations by means of conformal transformations. The conformal factor is chosen so that it carries a dimensional scale that captures crucial asymptotic features. By choosing a…
The first step in the building of a spacetime solution of Einstein's gravitational field equations via the initial value formulation is finding a solution of the Einstein constraint equations. We recall the conformal method for constructing…
We apply the Hamiltonian formulation of teleparallel theories of gravity in 2+1 dimensions to a circularly symmetric geometry. We find a family of one-parameter black hole solutions. The BTZ solution fixes the unique free parameter of the…