Transplanckian Dispersion Relation and Entanglement Entropy of Blackhole

Details Transplanckian Dispersion Relation and Entanglement Entropy of Blackhole Transplanckian Dispersion Relation and Entanglement Entropy of Blackhole

2003-12-12

arxiv.org/abs/hep-th/0312136v1

Fortsch.Phys. 52 (2004) 477-482

Physics

High Energy Physics

High Energy Physics - Theory

7 pages. To appear in the proceedings of 36th International Symposium Ahrenshoop on the theory of Elementary Particles: Recent

Scientific paper

10.1002/prop.200310133

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.

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