An Isotropic Metric

TL;DR

This paper introduces an isotropic metric for black holes and a refined vacuum condition that distinguish matter and gravitational energy densities, proposing a slight modification to Einstein's equations to resolve inconsistencies between electromagnetism and gravity.

Contribution

It presents a new isotropic metric and vacuum condition that clarify energy density calculations and suggest a modification to Einstein's equations for better consistency.

Findings

Distinct terms for matter and gravitational energy densities

Resolution of electromagnetism-gravity inconsistency

Proposed modification to Einstein's equations

Abstract

An isotropic metric for a black hole and a better vacuum condition \nabla^2 V_G =0 are presented which yield distinct terms for the energy densities of ordinary matter and gravitational fields in the Einstein tensor (G^44 =-g^2 (2\nabla^2 V_G +(\nabla V_G)^2)) This model resolves an inconsistency between electromagnetism and gravity in the calculation of field energy. Resolution of this inconsistency suggests a slight modification of the Einstein equation to gG^\mu\nu = 8\pi G T^\mu\nu.