Exact solution for the interior of a black hole

TL;DR

This paper provides an exact, regular interior solution for a black hole within the Relativistic Theory of Gravitation, matching it with the Schwarzschild exterior and addressing issues like energy regularization and finite redshift.

Contribution

It introduces an exact interior metric solution for black holes with a stiff equation of state, regularizes the energy, and maintains standard time behavior inside the horizon.

Findings

Interior solution is regular everywhere.

Energy of the black hole is finite and equals Mc^2.

Redshift at the horizon is large but finite.

Abstract

Within the Relativistic Theory of Gravitation it is shown that the equation of state $p=\rho$ holds near the center of a black hole. For the stiff equation of state $p=\rho-\rho_c$ the interior metric is solved exactly. It is matched with the Schwarzschild metric, which is deformed in a narrow range beyond the horizon. The solution is regular everywhere, with a specific shape at the origin. The gravitational redshift at the horizon remains finite but is large, $z\sim 10^{23}$$M_\odot/M$. Time keeps its standard role also in the interior. The energy of the Schwarzschild metric, shown to be minus infinity in the General Theory of Relativity, is regularized in this setup, resulting in $E=Mc^2$.