Boltzmannian state counting for black hole entropy in Causal Set Theory

Abstract

This paper presents the first numerical study of black hole thermodynamics in Causal Set Theory, focusing on the entropy of a Schwarzschild black hole as embodied in the distribution of proposed horizon molecules. To simulate causal sets we created a highly parallelized computational framework in \texttt{C++} which allowed for the generation of causal sets with over a million points, the largest causal sets in a non-conformally flat spacetime to date. Our results confirm that the horizon molecules model is consistent with the Bekenstein-Hawking formula up to a dimensionless constant that can be interpreted as the fundamental discreteness scale in the order of a Planck length. Furthermore, the molecules are found to straddle the horizon of the black hole to within a few Planck lengths, indicating that entropy lives on the surface of the black hole. Finally, possible implications for the information paradox are drawn. In particular, we show how the horizon molecules model could yield a finite black hole temperature cut-off or even prevent full black hole evaporation.