The Holographic Interpretation of Hawking Radiation

Holography gives us a tool to view the Hawking effect from a new, classical perspective. In the context of Randall-Sundrum braneworld models, we show that the basic features of four-dimensional evaporating solutions are nicely translated into classical five-dimensional language. This includes the dual bulk description of particles tunneling through the horizon. Honorable Mention in the Gravity Research Foundation Essay Competition, 2007 [email protected] [email protected] The problem of understanding why and how black holes emit particles is not an easy one. It is intriguing that the motivation that led to the discovery of Hawking radiation came from classical considerations, namely the analogy between the laws of black hole mechanics and the laws of thermodynamics. However, already on dimensional grounds one realizes that in order to construct a quantity with the dimensions of an entropy starting from the area of the event horizon AH, quantum mechanics needs to enter into the game. Indeed, the only possibility is S ∼ kBAH/APl, where APl is Planck area and kB Boltzmann’s constant. This, in turn, implies that the black hole temperature T is O(~) and, correctly, vanishes in the classical limit. The actual derivation of particles emission by black holes [1] requires the quantization of matter fields in the dynamical background describing the formation of a black hole via gravitational collapse. This is the crucial feature allowing the initial vacuum state of our radiation fields to be detected, by asymptotic observers in the future asymptotic region at late times, as a mixed thermal state at the Hawking temperature (for a Schwarzschild black hole of mass M and with c = G = 1) TH = ~ 8πMkB . (1) A visual mechanism useful to understand the reason for the quantum instability of the Schwarzschild spacetime was first proposed in [2]. Creation of particle-antiparticle virtual pairs in the near horizon region may be such that the negative-energy antiparticle is absorbed by the black hole, leaving its positiveenergy partner free to escape to infinity. Estimates for this process indicate that