Black-hole event horizons-Teleology and Predictivity

TL;DR

This paper explores how the teleological boundary condition is essential for the statistical mechanics and thermodynamics of black holes, impacting properties like specific heat and viscosity within the fluid-gravity framework.

Contribution

It demonstrates that black-hole thermodynamics and horizon-fluid properties depend critically on future boundary conditions, highlighting their importance in quantum gravity and black-hole evaporation.

Findings

Negative specific heat of horizon-fluid depends on teleological boundary condition

Bulk viscosity coefficient is negative only with future boundary condition

Future boundary condition influences black-hole thermodynamics and evaporation processes

Abstract

General Relativity predicts the existence of black-holes. Access to the complete space-time manifold is required to describe the black-hole. This feature necessitates that black-hole dynamics is specified by future or teleological boundary condition. Here we demonstrate that the statistical mechanical description of black-holes, the raison d'etre behind the existence of black-hole thermodynamics, requires teleological boundary condition. Within the fluid-gravity paradigm --- Einstein's equations when projected on space-time horizons resemble Navier-Stokes equation of a fluid --- we show that the specific heat and the coefficient of bulk viscosity of the horizon-fluid are negative only if the teleological boundary condition is taken into account. We argue that in a quantum theory of gravity, the future boundary condition plays a crucial role. We briefly discuss the possible implications of this at late stages of black-hole evaporation.