Constrained spin systems and KNdS black holes

Abstract

Kerr-Newman de Sitter (KNdS) spacetimes have a rich thermodynamic structure that involves multiple horizons, and so differs in key respects from asymptotically flat or AdS black holes. In this paper, we show that certain features of KNdS spacetimes can be reproduced by a constrained system of N non-interacting spins in a magnetic field. Both the KNdS and spin systems have bounded energy and entropy, a maximum of the entropy in the interior of the energy range, and a symmetry that maps lower energy states to higher energy states with the same entropy. Consequently, both systems have a temperature that can be positive or negative, where the gravitational temperature is defined analogously to that of the spins. We find that the number of spins N corresponds to 1/Λ for black holes with very small charge q and rotation parameter a, and scales like $$ \sqrt{\left({a}^2+{q}^2\right)/\Lambda} $$ a 2 + q 2 / Λ for larger values of a and q. These comparisons show that certain key features of the complex thermodynamics of KNdS spacetimes are reproduced by a simple system of noninteracting spins, suggesting that there may be a relatively simple effective description of quantum de Sitter black holes in terms of a finite dimensional Hilbert space.

Static sphere observers and geodesics in Schwarzschild-de Sitter spacetime

“…unitary holographic description of de Sitter that is correctly able to reproduce the known bulk correlators. Generalising to SdS spacetimes, which arguably should be considered as a finite energy excitation in a holographic description of de Sitter [50,51], it would be of interest to construct the relevant generalised SdS correlators in a geodesic approximation. Generalising [32], after some particular time that we identified in this work, one requires complex values for the parameter E, rendering the lengths D i complex as well, suggesting the following structure of the SdS (conjugate static sphere) correlator For D = 5, the black hole interior and exterior de Sitter temporal windows are the same T min = T max , avoiding a distinction between interior and exterior (real or complex) geodesics.…”