On eternal black holes and some interior solutions

TL;DR

This paper introduces two new exact solutions to Einstein's equations for eternal black holes with stiff matter, expanding the known solutions from four to six, and confirms a relativistic mass equivalence principle.

Contribution

The authors derive two novel solutions for eternal black holes, including a rotating one, and confirm a generalized mass equivalence principle.

Findings

Expanded the set of eternal black hole solutions from four to six.

Derived the Kerr interior solution.

Validated a relativistic generalization of the mass equivalence principle.

Abstract

In this article we deduce two new exact solutions of Einstein's equations for eternal black holes, now related to stiff matter, one `static' and another rotating (stationary like the Kerr one), thus the number of these eternal solutions grows from four to six. Dealing with these static and rotating solutions we automatically rehabilitate the practically forgotten Sommerfeld-Lenz approach to the deduction of our results for the satisfaction of Einstein's equations, e.g., in these rotating cases. At the same time, we come to the confirmation of our new relativistic generalization of the inertial/gravitational mass equivalence principle, as well as to obtention of the Kerr interior solution.