Thermal Stability, quantum topological equilibrium and an Energy-Information relation of Black holes with Quantum Hair
Abhishek Majhi · arXiv (Cornell University) · 2013
Considering the total number of the topological defects on the horizon, $N$, as an independent quantum hair, the grand canonical ensemble is studied considering Gaussian thermal fluctuations about equilibrium configurations. The finiteness conditions of the partition function lead to a stability criterion for the horizon which has an added logarithmic correction to an earlier result, as an effect of the topological defects on the horizon. Since a horizon at stable thermal equilibrium has a fixed area, additionally the chemical potential corresponding to $N$ must vanish for the horizon to reach a topological equilibrium at the quantum level. This leads to a further prediction about the energy-information relation for black holes at equilibrium from a pure quantum perspective.