As another illustration of the application of stochastic gravity we now consider the backreaction and
fluctuations in black hole spacetimes. Backreaction refers to the quantum effects of matter fields such as
vacuum polarization, quantum fluctuations and particle creation on the spacetime structure and
dynamics. Studying the dynamics of quantum fields in a fixed background spacetime, Hawking
found that black holes emit thermal radiation with a temperature inversely proportional to
their mass [156, 213, 294, 358]. When the backreaction of the quantum fields on the spacetime
dynamics is included, one expects that the mass of the black hole decreases as thermal radiation at
higher and higher temperatures is emitted. The reduction of the mass of a black hole due to
particle creation is often referred to as the black hole ‘evaporation’ process. Backreaction of
Hawking radiation [9, 18
, 142, 166
, 167
, 380
, 381
, 382
] could alter the evolution of the background
spacetime and change the nature of its end state, more drastically so for Planck-size black
holes.
Backreaction is a technically challenging but conceptually rewarding problem. Progress is slow in this
long standing problem, but it cannot be ignored because existing results from test-field approximations or
semiclassical analysis are not trustworthy when backreaction becomes strong enough as to alter the
structure and dynamics of the background spacetime. At the least one needs to know how strong the
backreaction effects are, and under what circumstances the existing predictions make sense. Without an
exact quantum solution of the black-hole-plus-quantum-field system or at least a full backreaction
consideration including the intrinsic and induced effects of metric fluctuations, much of the long speculation
on the end-state of black hole collapse – remnants, naked singularity, baby universe formation or complete
evaporation (see, e.g., [12, 47, 130, 168, 184, 250, 306, 318, 319, 375, 376]) – and the information loss
issue [157, 158, 160, 286] (see, e.g., [288, 307] for an overview and recent results from quantum
information [40, 333]) will remain speculation and puzzles. This issue also enters into the extension of the
well-known black-hole thermodynamics [23, 25, 26, 171, 172, 214, 224, 253, 254, 337, 342, 346, 363, 364] to
nonequilibrium conditions [105] and can lead to new inferences on the microscopic structure of spacetime
and the true nature of Einstein’s equations [216] from the viewpoint of general relativity as
geometro-hydrodynamics and gravity as emergent phenomena. (See the non-traditional views of
Volovik [356, 357]and Hu [185, 186, 190
] on spacetime structure, Wen [139, 240, 372, 373] on quantum
order, Seiberg [326], Horowitz and Polchinsky [173] on emergent gravity, Herzog on the hydrodynamics
of M-theory [164] and the seminal work of Unruh and Jacobson [215, 351] leading to analog
gravity [15, 16, 320].)
http://www.livingreviews.org/lrr-2008-3 | ![]() This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 2.0 Germany License. Problems/comments to |