“Regge-like” relations for stable (non-evaporating) black holes
Tóm tắt
Within a purely classical formulation of “strong gravity,” we associated hadron constituents (and even hadrons themselves) with suitable stationary, axisymmetric solutions of certain new Einsteintype equations supposed to describe the strong field inside hadrons. Such equations are nothing but Einstein equations—with cosmological term—suitably scaled down. As a consequence, the cosmological constant Λ and the massesM 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 Λ andM values considered, we met a series of solutions of the Kerr-Newman-de Sitter (KNdS) type with rather interesting properties: aim of the present work is putting forth such results, while “translating” them into the more popular language of ordinary gravity. The requirement that those solutions be stable, i.e., that their temperature (or surface gravity) bevanishingly 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 ofJ, q and Λ) mass and radius of the associated black hole. In the case of ordinary Einstein equations and for stable blackholes of the KNdS type, we get in particular Regge-like relations among massM, angular momentumJ, chargeq and cosmological constant Λ; which did not receive enough attention in the previous literature. For instance, with the standard definitionsQ
2 = Gq2/(4πε
0
c
4), a ≡ J/(Mc), m ≡GM/c
2, in the case Λ=0 in whichm
2=a2+Q2 and ifq is negligible, we findm
2=J. When considering, for simplicity, Λ>0 andJ=0 (andq still negligible), then we obtainm
2 = 1/(9Λ). In the most general case, the condition, for instance, of “triple coincidence” among the three horizons yields for ¦Λa
2¦<< 1 the couple of independent relationsm
2 = 2/(9Λ) andm
2 = 8(a
2 + Q2. Another interesting point is that—with few exceptions—all such relations (amongM, J, q, Λ) lead to solutions that can be regarded as (stable) cosmological models.
Tài liệu tham khảo
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