Related papers: Regge calculus: a unique tool for numerical relati…
After a brief summary of the foundations of general relativity, we will concentrate on the stationary exact solutions of the Einstein and Einstein-Maxwell equations. A number of these solutions can be interpreted as black holes,…
Taking the triangle areas as independent variables in the theory of Regge calculus can lead to ambiguities in the edge lengths, which can be interpreted as discontinuities in the metric. We construct solutions to area Regge calculus using a…
Gravitational waves deliver information in exquisite detail about astrophysical phenomena, among them the collision of two black holes, a system completely invisible to the eyes of electromagnetic telescopes. Models that predict…
Regge calculus is a powerful method to approximate a continuous manifold by a simplicial lattice, keeping the connectivities of the underlying lattice fixed and taking the edge lengths as degrees of freedom. The discrete Regge model…
We discuss the applications of Gauge Theory of Gravity (GTG) within the language of geometric algebra to black holes and Hawking radiation. Applications include the Unruh effect, the Dirac and Klein-Gordon equations in several backgrounds,…
Numerical relativity is the most promising tool for theoretically modeling the inspiral and coalescence of neutron star and black hole binaries, which, in turn, are among the most promising sources of gravitational radiation for future…
A Schwarzschild type solution in Regge calculus is considered. Earlier, we considered a mechanism of loose fixing of edge lengths due to the functional integral measure arising from integration over connection in the functional integral for…
We construct initial data for a particular class of Brill wave metrics using Regge calculus, and compare the results to a corresponding continuum solution, finding excellent agreement. We then search for trapped surfaces in both sets of…
We present an overview of recent developments in numerical relativity studies of higher dimensional spacetimes with a focus on time evolutions of black-hole systems. After a brief review of the numerical techniques employed for these…
The gauge theoretical formulation of general relativity is presented. We are only concerned with local intrinsic geometry, i.e. our space-time is an open subset of a four-dimensional real vector space. Then the gauge group is the set of…
This paper aims to investigate the astrophysical applicability of the electrically and magnetically charged black hole solutions obtained in a model of nonlinear electrodynamics proposed by Kruglov (Ann. Phys. Berlin 2017, 529, 170073).…
We develop a relativistic perturbation theory for scalar clouds around rotating black holes. We first introduce a relativistic product and corresponding orthogonality relation between modes, extending a recent result for gravitational…
The Riemann scalar curvature plays a central role in Einstein's geometric theory of gravity. We describe a new geometric construction of this scalar curvature invariant at an event (vertex) in a discrete spacetime geometry. This allows one…
We consider a Schwarzschild type solution in the discrete Regge calculus formulation of general relativity quantized within the path integral approach. Earlier, we found a mechanism of a loose fixation of the background scale of Regge…
We present recent developments on numerical algorithms for computing photon and particle trajectories in the surrounding of compact objects. Strong gravity around neutron stars or black holes causes relativistic effects on the motion of…
We consider the possibility to use the areas of two-simplexes, instead of lengths of edges, as the dynamical variables of Regge calculus. We show that if the action of Regge calculus is varied with respect to the areas of two-simplexes, and…
Advances in our understanding of the origin, evolution and structure of the universe have long been driven by cosmological perturbation theory, model building and effective field theory. In this review, we introduce numerical relativity as…
We study the Regge regime of QCD as a special regime of lattice gauge theory on an asymmetric lattice. This lattice has a spacing $a_0 $ in the longitudinal direction and a spacing $a_t $ in the transversal direction. The limit…
The special theory of relativity is constructed demanding the retention of the rectilinear form of a trajectory and invariance of the wave equation under linear transformations of space and time coordinates. The usual approach to relativity…
In this paper we discuss about properties of lattices and its application in theoretical and algorithmic number theory. This result of Minkowski regarding the lattices initiated the subject of Geometry of Numbers, which uses geometry to…