Stretched Horizon and Entropy of Superstars

TL;DR

This paper explores the microscopic origin of entropy in supergravity solutions related to superstars, establishing a phase space approach that aligns microscopic and thermodynamic entropies and examines horizon fluctuations.

Contribution

It introduces a phase space density framework for supergravity solutions, generalizes Young diagrams for mixed states, and links microscopic entropy with horizon area.

Findings

Microscopic entropy formula matches thermodynamic entropy for thermal ensembles.

Phase space densities correspond to piecewise monotonic curves generalizing Young diagrams.

Fluctuation analysis relates entropy to stretched horizon area.

Abstract

Amongst the class of supergravity solutions found by Lin, Lunin and Maldacena, we consider pure and mixed state configurations generated by phase space densities in the dual fermionic picture. A one-to-one map is constructed between the phase space densities and piecewise monotonic curves, which generalize the Young diagrams corresponding to pure states. Within the fermionic phase space picture, a microscopic formula for the entropy of mixed states is proposed. Considering thermal ensembles, agreement is found between the thermodynamic and the proposed microscopic entropies. Furthermore, we study fluctuations in thermodynamic ensembles for the superstar and compare the entropy of these ensembles with the area of stretched horizons predicted by the mean fluctuation size.