Related papers: Variational Principles in General Relativity
We present a general formalism to treat slowly rotating general relativistic superfluid neutron stars. As a first approximation, their matter content can be described in terms of a two-fluid model, where one fluid is the neutron superfluid,…
The cataclysmic observations of event GW170817, first as gravitational waves along the inspiral motion of two neutron stars, then as a short $\gamma$-ray burst, and later as a kilonova, launched the era of multimessenger astronomy, and…
We present the first results from a new method for computing spacetimes representing corotating binary black holes in circular orbits. The method is based on the assumption of exact equilibrium. It uses the standard 3+1 decomposition of…
The numerical modeling of binary neutron star mergers has become a subject of much interest in recent years. While a full and accurate model of this phenomenon would require the evolution of the equations of relativistic hydrodynamics along…
We study the global dynamics of isothermal fluids evolving in the domain of outer communication of a Schwarzschild black hole. We first formulate the initial value problem within a class of weak solutions with bounded variation (BV),…
Spacetime is foliated by spatial hypersurfaces in the 3+1 split of General Relativity. The initial value problem then consists of specifying initial data for all relevant fields on one such a spatial hypersurface. These fields are the…
A recently proposed variational approach for general relativity where, in addition to the metric tensor, two independent affine connections enter the action as dynamical variables, is revised. Field equations always reduce to the Einstein…
Most numerical models of binary stars - in particular neutron stars in compact binaries - assume the companions to be either corotational or irrotational. Either one of these assumptions leads to a significant simplification in the…
We review recent progress in the study of varying constants and attempts to explain the observed values of the fundamental physical constants. We describe the variation of $G$ in Newtonian and relativistic scalar-tensor gravity theories. We…
The initial condition problem for a binary neutron star system requires a Poisson equation solver for the velocity potential with a Neumann-like boundary condition on the surface of the star. Difficulties that arise in this boundary value…
In this paper we have examined numerically exact configurations of close binary systems composed of incompressible fluids with internal flows. Component stars of binary systems are assumed to be circularly orbiting each other but rotating…
Black hole binaries on non-eccentric orbits form an important subclass of gravitational wave sources, but it is a non-trivial issue to construct numerical initial data with minimal initial eccentricity for numerical simulations. We compute…
We propose a method of determining solutions to the constraint equations of General Relativity approximately describing binary black holes in quasi-stationary circular orbits. Black holes with arbitrary linear momenta are constructed in the…
Simulations of binary neutron stars have seen great advances in terms of physical detail and numerical quality. However, the spin of the neutron stars, one of the simplest global parameters of binaries, remains mostly unstudied. We present…
The post-Newtonian expansion appears to be a relevant tool for predicting the gravitational waveforms generated by some astrophysical systems such as binaries. In particular, inspiralling compact binaries are well-modelled by a system of…
We investigate the variational principle for the gravitational field in the presence of thin shells of completely unconstrained signature (generic shells). Such variational formulations have been given before for shells of timelike and null…
In this paper, we investigate whether Variational Principles can be associated with the Helmholtz equation subject to impedance (absorbing) boundary conditions. This model has been extensively studied in the literature from both…
These notes summarize basic concepts underlying numerical relativity and in particular the numerical modeling of black hole dynamics as a source of gravitational waves. Main topics are the 3+1 decomposition of general relativity, the…
We extend a recently developed numerical code to obtain stationary, axisymmetric solutions that describe rotating black hole spacetimes in a wide class of modified theories of gravity. The code utilizes a relaxed Newton-Raphson method to…
The variational method is a versatile tool for classical simulation of a variety of quantum systems. Great efforts have recently been devoted to its extension to quantum computing for efficiently solving static many-body problems and…