Related papers: Excision boundary conditions for the conformal met…
In this paper a new double-domain spectral method to compute binary black hole excision initial data is presented. The method solves a system of elliptic partial differential equations in the exterior of two excised spheres. At the surface…
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…
A review of the treatment of boundaries in general relativity is presented with the emphasis on application to the formulations of Einstein's equations used in numerical relativity. At present, it is known how to treat boundaries in the…
We consider accelerated black hole horizons with and without defects. These horizons appear in the $C$-metric solution to Einstein equations and in its generalization to the case where external fields are present. These solutions realize a…
We construct exact solutions to the Bianchi equations on a flat spacetime background. When the constraints are satisfied, these solutions represent in- and outgoing linearized gravitational radiation. We then consider the Bianchi equations…
We present a new scheme for constructing initial data for the Einstein field equations using the conformal thin-sandwich formulation that does not assume conformal flatness or approximate Killing vectors. This includes a method for…
We perform a statistical analysis of the binary black hole problem in the post-Newtonian approximation by systematically sampling and evolving the parameter space of initial configurations for quasi-circular inspirals. Through a principal…
The conformal method for constructing initial data for Einstein's equations is presented in both the Hamiltonian and Lagrangian picture (extrinsic curvature decomposition and conformal thin sandwich formalism, respectively), and advantages…
The Euclidean path integral for gravity is enriched by the addition of boundaries, which provide useful probes of thermodynamic properties. Common boundary conditions include Dirichlet conditions on the boundary induced metric;…
We prove that in a certain class of conformal data on an asymptotically cylindrical manifold, if the conformally decomposed Einstein constraint equations do not admit a solution, then one can always find a nontrivial solution to the limit…
The order parameter of a critical system defined in a layered parallel plate geometry subject to Neumann boundary conditions at the limiting surfaces is studied. We utilize a one-particle irreducible vertex parts framework in order to study…
The harmonic formulation of Einstein's field equations is considered, where the gauge conditions are introduced as dynamical constraints. The difference between the fully constrained approach (used in analytical approximations) and the free…
We discuss a number of topics in the area of conformally compact Einstein metrics, mostly centered around the global existence question of finding such metrics with an arbitrarily prescribed conformal infinity. The paper is partly a survey…
We consider the initial boundary value problem for free-evolution formulations of general relativity coupled to a parametrized family of coordinate conditions that includes both the moving puncture and harmonic gauges. We concentrate…
The conformal flow of metrics [2] has been used to successfully establish a special case of the Penrose inequality, which yields a lower bound for the total mass of a spacetime in terms of horizon area. Here we show how to adapt the…
I consider the initial-boundary-value-problem of nonlinear general relativistic vacuum spacetimes, which today cannot yet be evolved numerically in a satisfactory manner. Specifically, I look at gauge conditions, classifying them into gauge…
Using an approach similar to arXiv:2409.15460, we give a new proof of the nonlinear stability of de Sitter space as a solution to the Einstein vacuum equations with positive cosmological constant in $n+1$ dimensions, with $n\geq3$. Using…
The details are presented of a new evolution algorithm for the characteristic initial-boundary value problem based upon an affine parameter rather than the areal radial coordinate used in the Bondi-Sachs formulation. The advantages over the…
A compact Riemannian manifold is associated with geometric data given by the eigenvalues of various Laplacian operators on the manifold and the triple overlap integrals of the corresponding eigenmodes. This geometric data must satisfy…
In this work we describe metric-affine theories anew by making a change of field variables. A series of equivalent frameworks is presented and identifications are worked out in detail. The advantage of applying the new frameworks is that…