相关论文: Regge calculus: a unique tool for numerical relati…
This paper examines the behaviour of closed `lattice universes' wherein masses are distributed in a regular lattice on the Cauchy surfaces of closed vacuum universes. Such universes are approximated using a form of Regge calculus originally…
Numerical relativity has seen incredible progress in the last years, and is being applied with success to a variety of physical phenomena, from gravitational-wave research and relativistic astrophysics to cosmology and high-energy physics.…
Motivated by a recent study casting doubt on the correspondence between Regge calculus and general relativity in the continuum limit, we explore a mechanism by which the simplicial solutions can converge whilst the residual of the Regge…
Numerical relativity became a powerful tool to investigate the dynamics of binary problems with black holes or neutron stars as well as the very structure of General Relativity. Although public numerical relativity codes are available to…
With the theory of general relativity, Einstein abolished the interpretation of gravitation as a force and associated it to the curvature of spacetime. Tensorial calculus and differential geometry are the mathematical resources necessary to…
The large scale binary black hole effort in numerical relativity has led to an increasing distinction between numerical and mathematical relativity. This note discusses this situation and gives some examples of succesful interactions…
Numerical relativity is an essential tool for solving Einstein's equations of general relativity for dynamical systems characterized by high velocities and strong gravitational fields. The implementation of new algorithms that can solve…
Quantum gravity is studied in the path integral formulation applying the Regge calculus. Restricting the quadratic link lengths of the originally triangular lattice the path integral can be transformed to the partition function of a spin…
We compare different models of a quantum theory of four-dimensional lattice gravity based on Regge's original proposal. From Monte Carlo simulations we calculate two-point functions between geometrical quantities and estimate the masses of…
Understanding the predictions of general relativity for the dynamical interactions of two black holes has been a long-standing unsolved problem in theoretical physics. Black-hole mergers are monumental astrophysical events, releasing…
Numerical relativity describes a discrete initial value problem for general relativity. A choice of gauge involves slicing space-time into space-like hypersurfaces. This introduces past and future gauge relative to the hypersurface of…
The Regge Calculus approximates 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 employed in this work…
We introduce a modified Regge calculus for general relativity on a triangulated four dimensional Riemannian manifold where the fundamental variables are areas and a certain class of angles. These variables satisfy constraints which are…
We investigate quantum gravity in four dimensions using the Regge approach on triangulations of the four-torus with general, non-regular incidence matrices. We find that the simplicial lattice tends to develop spikes for vertices with low…
Any practical attempt to solve the Regge equations, these being a large system of non-linear algebraic equations, will almost certainly employ a Newton-Raphson like scheme. In such cases it is essential that efficient algorithms be used…
We revisit the Regge calculus model of the Kasner cosmology first considered by S. Lewis. One of the most highly symmetric applications of lattice gravity in the literature, Lewis' discrete model closely matched the degrees of freedom of…
The replica paradigm has emerged as a powerful tool for investigating the black hole information paradox, offering a semiclassical route to reproducing the Page curve and suggesting unitary evolution for evaporating black holes. However,…
Algebraic computing in relativity and gravitation dates back more than thirty years, but only relatively recently has hardware of sufficient power to tackle large scale calculations become commonplace. Whereas it is generally understood…
(3+1) (continuous time) Regge calculus is reduced to Hamiltonian form. The constraints are classified, classical and quantum consequences are discussed. As basic variables connection matrices and antisymmetric area tensors are used…
An important problem in analytic and geometric combinatorics is estimating the number of lattice points in a compact convex set in a Euclidean space. Such estimates have numerous applications throughout mathematics. In this note, we exhibit…