KNdS Black Holes and Spin Systems

It is known that the interplay of black hole and cosmological horizons introduces distinctive thermodynamic behavior in deSitter black holes. In this talk, we present a study of the thermodynamic behavior of rotating, charged black holes with positive cosmological constant, also known as Kerr-Newman-deSitter (KNdS) black holes. We employ the use of the ‘area product’ parameter, X, first introduced by McInerney, Satishchandranan, and Traschen to replace the mass m, and we write all thermodynamic quantities as algebraic functions of X. Using X allows us to show that there is a Schottky peak in some regions of the black hole parameter space for KNdS black holes, as was previously shown for the Schwarzschild-deSitter (SdS) case by Traschen et al. A Schottky peak, or Schottky anomaly, is defined as an effect where the heat capacity of a system has a peak, and is considered as an anomaly because it is usual for the heat capacity to either increase or stay constant with temperature. For example, a Schottky anomaly is present in a two-state spin system in a magnetic field. Finally, we will describe future goals we have set to explore models for understanding the underlying quantum degrees of freedom of KNdS black holes.