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.
Rudmin, Joseph D.
"An Isotropic Metric,"
Virginia Journal of Science: Vol. 58
, Article 4.
Available at: https://digitalcommons.odu.edu/vjs/vol58/iss1/4