Nonlocal Astroparticles in Einstein's Universe

TL;DR

This paper explores a nonlocal approach to gravitational energy in Einstein's universe, proposing that elementary particles have a radial energy density leading to a finite, nonlocal gravitational charge that integrates Machian principles into relativity.

Contribution

It introduces a nonlocal energy density model for elementary particles in Einstein's gravity, connecting Machian ideas with relativistic dynamics without relying on Newtonian mass attraction.

Findings

Elementary particles have a radial energy density of r^{-4}.

The space energy integral of an infinite particle is finite.

Nonlocal gravitational charges incorporate Machian relativity into Einstein's theory.

Abstract

Gravitational probes should maintain spatial flatness for Einsten-Infeld-Hoffmann dynamics of relativistic matter-energy. The continuous elementary source/particle in Einstein's gravitational theory is the r^{-4} radial energy density rather than the delta-operator density in empty-space gravitation. The space energy integral of such an infinite (astro)particle is finite and determines its nonlocal gravitational charge for the energy-to-energy attraction of other nonlocal (astro)particles. The non-empty flat space of the undivided material Universe is charged continuously by the world energy density of the global ensemble of overlapping radial particles. Nonlocal gravitational/inertial energy-charges incorporate Machian relativism quantitatively into Einstein's gravitation for self-contained SR-GR dynamics without references on Newton's mass-to-mass attraction.