Thermodynamics of entanglement in Schwarzschild spacetime

TL;DR

This paper explores the thermodynamics of entanglement in Schwarzschild spacetime, revealing that entanglement energy near the horizon behaves similarly to black hole thermodynamics, suggesting entanglement as a microscopic origin.

Contribution

It extends previous work to curved spacetime, showing entanglement energy's proportionality to boundary area and its thermodynamic structure akin to black holes.

Findings

Entanglement energy near the horizon is proportional to boundary area.

Entanglement thermodynamics mirrors black hole thermodynamics.

Red-shift effect explains the energy behavior.

Abstract

Extending the analysis in our previous paper, we construct the entanglement thermodynamics for a massless scalar field on the Schwarzschild spacetime. Contrary to the flat case, the entanglement energy $E_{ent}$ turns out to be proportional to area radius of the boundary if it is near the horizon. This peculiar behavior of $E_{ent}$ can be understood by the red-shift effect caused by the curved background. Combined with the behavior of the entanglement entropy, this result yields, quite surprisingly, the entanglement thermodynamics of the same structure as the black hole thermodynamics. On the basis of these results, we discuss the relevance of the concept of entanglement as the microscopic origin of the black hole thermodynamics.