The stretched horizon and black hole complementarity

Abstract

Three postulates asserting the validity of conventional quantum theory, semiclassical general relativity, and the statistical basis for thermodynamics are introduced as a foundation for the study of blackhole evolution. We explain how these postulates may be implemented in a "stretched horizon" or membrane description of the black hole, appropriate to a distant observer. The technical analysis is illustrated in the simplified context of ( 1 + 1 )-dimensional dilaton gravity. Our postulates imply that the dissipative properties of the stretched horizon arise from a course graining of microphysical degrees of freedom that the horizon must possess. A principle of black-hole complementarity is advocated. The overall viewpiont is similar to that poineered by 't Hooft but the detailed implementation is different.PACS number(s): 04.60. +n, 97.60.Lf

Holographic discreteness of inflationary perturbations

“…The black hole entropy derived from thermodynamic reasoning appears to be complete, in the sense that it includes all possible degrees of freedom of mass-energy that make up the hole. If we insist that black holes are quantum mechanical objects that obey unitary evolution, they must somehow encode all the information counted in this entropy, then radiate it to spatial infinity as Hawking quanta as they evaporate [32][33][34][35]. Such considerations led 't Hooft and Susskind to propose [36,37] a "holographic principle" [38] for any physical system: the total entropy S within any surface is bounded by one quarter of the area A of the surface in Planck units.…”

Black hole entropy from near-horizon microstates

“…The idea that the black hole entropy should be accounted for by microstates near the black hole horizon has great appeal and a long history [1][2][3][4][5][6][7][8][9]. One reason for this is that a demonstration that the horizon has of order one degree of freedom per Planck area would provide a statistical explanation of the area formula for the entropy.…”

On 't Hooft's S-matrix Ansatz for quantum black holes

“…Similar considerations hold in the case of the stretched horizon picture [17], though one has in this case a different set up. One is indeed interpreting the horizon as a 2 + 1 dimensional membrane embedded in spacetime (more precisely a timelike hyper-surface).…”

“…We point out then where we believe the analogy fails and list arguments which suggest to interpret the horizon as a fluctuating membrane, in agreement with standard proposals [17], [18]. We finally use an analogy with two dimensional electrostatic to interpret again (2.16) this time from a stringy perspective.…”