1205.6814 (Matt Visser)

Area products for black hole horizons    [PDF]

Matt Visser

Area products for multi-horizon black holes often have intriguing properties, and are often independent of the mass of the black hole (depending only on various charges, angular momenta, and moduli). Such products are often formulated in terms of the areas of inner (Cauchy) horizons and event horizons, and often include the effects of unphysical "virtual'" horizons. For the Schwarzschild-de Sitter [Kottler] black hole in (3+1) dimensions it is shown by explicit exact calculation that the product of event horizon area and cosmological horizon area is not mass independent. (Including the effect of the third "virtual" horizon does not improve the situation.) Similarly, in the Reissner-Nordstrom-anti-de Sitter black hole in (3+1) dimensions the product of inner (Cauchy) horizon area and event horizon area is calculated (perturbatively), and is shown to be not mass independent. That is, the mass-independence of the product of physical horizon areas is not generic. In the generic situation, whenever the quasi-local mass m(r) is a Laurent polynomial in aerial radius, r=sqrt{A/4 pi}, there are more complicated mass-independent quantities, the elementary symmetric polynomials built up from the complete set of horizon radii (physical and virtual). Sometimes it is possible to eliminate the unphysical virtual horizons, constructing combinations of physical horizon areas that are mass independent, but they tend to be considerably more complicated than the simple products and related constructions currently mooted in the literature.

View original: http://arxiv.org/abs/1205.6814