Unusual black-holes: about some stable (non-evaporating) extremal solutions of Einstein equations

Within a purely classical formulation of ''strong gravity'', we associated hadron constituents (and even hadrons themselves) with suitable stationary, axisymmetric solutions of certain new Einsten-type equations supposed to describe the strong field inside hadrons. As a consequence, the cosmological constant Λ and the masses M result in theory to be scaled up, and transformed into a ''hadronic constant'' and into ''strong masses'', respectively. Due to the unusual range of Λ and M values considered, we met a series of solutions of the Kerr-Newman-de Sitter (KNdS) type with so uncommon horizon properties (e.g., completely impermeable horizons), that it is worth studing them also in the case of ordinary gravity. This is the aim of the present work. 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. In the case of ordinary Einstein equations and for stable black holes of the KNdS type, we get Regge-like relations among mass M, angular momentum J, charge q and cosmological constant Λ. For instance, with the standard definitions Q2 ≡ Gq2 / (4Π ε0c4)); a ≡ J/(Mc); m ≡ GM/c2, in the case Λ = 0 in which m2 = a2 + Q2 and q is negligible we find M2 = J, where c = G = 1. When considering, for simplicity, Λ > 0 and J = 0 (and q still negligible), then we obtain m2 = 1/(9Λ). In the most general case, the condition, for instance, of ''triple coincidence'' among the three horizons yields for |Λa2/ << 1 the couple of independent relations m2 = 2/(9Λ) ; m2 = 8(a2 + Q2)/9. One of the interesting points is that - with few exceptions - all such relations (among M, J, q, Λ) lead to solutions that can be regarded as (stable) cosmological models. Worth of notice are those representing isolated worlds, bounded by a two-way impermeable horizon. (author)