Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2007-03-26
Phys.Rev.D76:024006,2007
Physics
High Energy Physics
High Energy Physics - Theory
31 pages, 2 figures; v2: improvements to the presentation, typos fixed, reference added, version published in PRD
Scientific paper
10.1103/PhysRevD.76.024006
We compute the black hole horizon entanglement entropy S_E for a massless scalar field, first with a hard cutoff and then with high frequency dispersion, both imposed in a frame that falls freely across the horizon. Using WKB methods, we find that S_E is finite for a hard cutoff or super-luminal dispersion, because the mode oscillations do not diverge at the horizon and the contribution of high transverse momenta is cut off by the angular momentum barrier. For sub-luminal dispersion the entropy depends on the behavior at arbitrarily high transverse momenta. In all cases it scales with the horizon area. For the hard cutoff it is linear in the cutoff, rather than quadratic. This discrepancy from the familiar result arises from the difference between the free-fall frame and the static frame in which a cutoff is usually imposed. In the super-luminal case the entropy scales with a fractional power of the cutoff that depends on the index of the dispersion relation. Implications for the possible relation between regularized entanglement entropy and the Bekenstein-Hawking entropy are discussed.
Jacobson Ted
Parentani Renaud
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