Transplanckian Dispersion Relation and Entanglement Entropy of Blackhole

TL;DR

This paper demonstrates that implementing a transplanckian dispersion relation in quantum field theory near black hole horizons renders the entanglement entropy UV finite, offering insights into quantum gravity effects.

Contribution

It introduces a general transplanckian dispersion relation to resolve UV divergences in black hole entanglement entropy calculations.

Findings

Entanglement entropy becomes UV finite with the dispersion relation.

Modified dispersion relations are consistent with string theory.

Minimal length scale leads to bounded high-energy modes.

Abstract

The quantum correction to the entanglement entropy of the event horizon is plagued by the UV divergence due to the infinitely blue-shifted near horizon modes. The resolution of this UV divergence provides an excellent window to a better understanding and control of the quantum gravity effects. We claim that the key to resolve this UV puzzle is the transplanckian dispersion relation. We calculate the entanglement entropy using a very general type of transplanckian dispersion relation such that high energy modes above a certain scale are cutoff, and show that the entropy is rendered UV finite. We argue that modified dispersion relation is a generic feature of string theory, and this boundedness nature of the dispersion relation is a general consequence of the existence of a minimal distance in string theory.