Deviation from the First Law of Thermodynamics for Particle-like Quantum Kerr-de Sitter Black Holes

Abstract

The goal of this paper is to extend the particle-like quantization scheme presented in Pacheco and Silk (2020), to extremal Kerr-de Sitter black holes in four spacetime dimensions, thereby obtaining various quantized parameters, like the black hole mass and angular momentum, consistent with existing results, in the proper limits. Moreover, we show numerically, that for such extremal quantum black holes, there is a root mean square deviation from the First Law of black hole thermodynamics, of the order $\mathcal{O}(\Lambda^{0.45 \pm 0.01})$, where $\Lambda$ denotes the Cosmological Constant.