Discrete and finite Genral Relativity

TL;DR

This paper develops a discrete, finite formalism of General Relativity using localized pointlike fields, deriving classical solutions like Schwarzschild metric through averaging, offering a novel approach to gravity.

Contribution

It introduces a discrete, localized field formalism for General Relativity and derives classical solutions via an averaging process, providing a new perspective on gravitational interactions.

Findings

Derived a finite, singularity-free point-like field called 'classical graviton'

Recovered Einstein's continuous formalism through averaging

Obtained Schwarzschild metric by imposing spherical symmetry

Abstract

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 finite, singularity-free, point-like field that we associate to a ``classical graviton". The standard Einstein's continuous formalism is retrieved by means of an averaging process, and its continuous solutions are determined by the chosen imposed symetry. The Schwarzschild metric is obtained by the imposition of spherical symmetry on the averaged field.