About Some Regge-Like Relations for (stable) Black Holes

TL;DR

This paper explores Regge-like relations for stable black holes within a modified Einstein framework incorporating a cosmological constant, revealing new relations among black hole parameters and their potential cosmological implications.

Contribution

It introduces novel Regge-like relations among black hole parameters derived from a modified Einstein theory with a cosmological constant, emphasizing stability conditions.

Findings

Stable Kerr-Newman-de Sitter solutions exhibit Regge-like relations among mass, angular momentum, charge, and Lambda.

Certain parameter choices lead to solutions interpretable as stable cosmological models.

The study highlights the importance of horizon stability in deriving black hole and cosmological relations.

Abstract

We associated, in a classical formulation of "strong gravity", hadron constituents with suitable stationary, axisymmetric solutions of some new Einstein-type equations supposed to describe the strong field inside hadrons. These new equations can be obtained by the Einstein equations with cosmological term Lambda. As a consequence, Lambda and the masses M result in our theory to be scaled up, and transformed into a "hadronic constant" and into "strong masses", respectively. Due to the unusual range of Lambda and M values considered, we met a series of solutions of the Kerr-Newman-de Sitter (hereafter KNdS) type with rather interesting properties. The requirement that those solutions be stable, i.e., that their temperature (or surface gravity) be vanishingly small, implies the coincidence of at least two of their (in general, three) horizons. Imposing the stability condition of a certain horizon does yield (once chosen the values of J, q and Lambda) mass and radius of the associated black-hole (hereafter BH). In the case of ordinary Einstein equations and for stable BHs of the KNdS type, we get in particular Regge-like (hereafter RL) relations among mass M, angular momentum J, charge q and cosmological constant Lambda; which did not receive enough attention in the previous literature. Besides, we show some particular and interesting cases of these relations. Another interesting point is that, with few exceptions, all such relations (among M, J, q, Lambda) lead to solutions that can be regarded as (stable) cosmological models.