Thermodynamics of horizons in a globally regular spherically symmetric spacetime

Abstract

We address the question of thermodynamics of horizons in a globally regular spherically symmetric spacetime which is asymptotically de Sitter as r → 0 and as r → ∞. A source term in the Einstein equations smoothly connects two de Sitter vacua with different values of the cosmological constant and corresponds to an anisotropic vacuum fluid defined by symmetry of its stress-energy tensor, which is invariant under radial boosts. In the most general case, the spacetime has three horizons, an internal one, ra, which is a cosmological horizon for an observer in the R-region 0 ≤ r ≤ ra; the horizon rb > ra which is the boundary of the T-region ra < r < rb seen as a black or white hole by an observer in the R-region rb < r < rc, where rc is his cosmological horizon. We present a detailed analysis of the thermodynamics of horizons using the Padmanabhan approach relevant to the case of non-zero pressures.