Related papers: Area Regge calculus and continuum limit
We study a continuous-time random walk on $\mathbb{Z}^d$ in an environment of random conductances taking values in $(0,\infty)$. For a static environment, we extend the quenched local limit theorem to the case of a general speed measure,…
While there has been some advance in the use of Regge calculus as a tool in numerical relativity, the main progress in Regge calculus recently has been in quantum gravity. After a brief discussion of this progress, attention is focussed on…
This article explores the structure theory of compatible generalized derivations of finite-dimensional $\omega$-Lie algebras over a field $\mathbb{K}$. We prove that any compatible quasiderivation of an $\omega$-Lie algebra can be embedded…
In this article, we generalize some frequently used metrical notions such as: completeness, closedness, continuity, g-continuity and compatibility to relation-theoretic setting and utilize these relatively weaker notions to prove results on…
The theory of measurement is employed to elucidate the physical basis of general relativity. For measurements involving phenomena with intrinsic length or time scales, such scales must in general be negligible compared to the (translational…
A general covariant extension of Einstein's field equations is considered with a view to Numerical Relativity applications. The basic variables are taken to be the metric tensor and an additional four-vector. The extended field equations,…
We establish generalized Gaussian bounds and local limit theorems with Gaussian-type error for the convolution powers of certain complex-valued functions on $\mathbb{Z}^d$. These global space-times estimates/error, which are sharp in…
In this paper, we present a series of techniques to describe General Relativity using Geometric Algebra (GA). We emphasize the physical interpretation of quantities and provide a step-by-step guide for performing calculations. In doing so,…
Taking a hint from Dirac's large number hypothesis, we note the existence of cosmologically combined conservation laws that work to cosmologically long time. We thus modify Einstein's theory of general relativity with fixed gravitation…
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…
We derive a generalized deviation equation -- analogous to the well-known geodesic deviation equation -- for test bodies in General Relativity. Our result encompasses and generalizes previous extensions of the standard geodesic deviation…
We present a new scheme of defining invariant observables for general relativistic systems. The scheme is based on the introduction of an observer which endowes the construction with a straightforward physical interpretation. The…
We show the point-wise definiteness and some other properties of the energy-momentum tensor for a certain class of Euler-Lagrange equations under quite general conditions.
We use the framework of generalized entanglement wedges to revisit the connected wedge theorem (CWT). This construction identifies an entanglement wedge associated for any bulk region and allows us to rephrase the CWT in terms of the…
We develop a framework to derive consistency constraints on gravitational Regge amplitudes based on the finite energy sum rules (FESRs), which directly connect gravitational Regge amplitudes at a finite ultraviolet scale with infrared…
It is well-known that the equations for a simple fluid can be cast into what is called their Lagrange formulation. We introduce a notion of a generalized Lagrange formulation, which is applicable to a wide variety of systems of partial…
We develop the General Theory of Relativity in a formalism with extended causality that describes physical interaction through discrete, transversal and localized pointlike fields. The homogeneous field equations are then solved for a…
The central limit theorem for convex bodies says that with high probability the marginal of an isotropic log-concave distribution along a random direction is close to a Gaussian, with the quantitative difference determined asymptotically by…
This article presents detailed discussions and calculations of the recent paper "Quantum Regge calculus of Einstein-Cartan theory" in Phys. Lett. B682 (2009) 300. The Euclidean space-time is discretized by a four-dimensional simplicial…
In this paper, we propose a generalization of the Riemann curvature tensor on manifolds (of dimension two or higher) endowed with a Regge metric. Specifically, while all components of the metric tensor are assumed to be smooth within…