6 research outputs found
Wilsonian Approach to Fluid/Gravity Duality
The problem of gravitational fluctuations confined inside a finite cutoff at
radius outside the horizon in a general class of black hole geometries
is considered. Consistent boundary conditions at both the cutoff surface and
the horizon are found and the resulting modes analyzed. For general cutoff
the dispersion relation is shown at long wavelengths to be that of a
linearized Navier-Stokes fluid living on the cutoff surface. A cutoff-dependent
line-integral formula for the diffusion constant is derived. The
dependence on is interpreted as renormalization group (RG) flow in the
fluid. Taking the cutoff to infinity in an asymptotically AdS context, the
formula for reproduces as a special case well-known results derived
using AdS/CFT. Taking the cutoff to the horizon, the effective speed of sound
goes to infinity, the fluid becomes incompressible and the Navier-Stokes
dispersion relation becomes exact. The resulting universal formula for the
diffusion constant reproduces old results from the membrane
paradigm. Hence the old membrane paradigm results and new AdS/CFT results are
related by RG flow. RG flow-invariance of the viscosity to entropy ratio is shown to follow from the first law of thermodynamics together with
isentropy of radial evolution in classical gravity. The ratio is expected to
run when quantum gravitational corrections are included.Comment: 34 pages, harvmac, clarified boundary conditio
The entropy of black holes: a primer
After recalling the definition of black holes, and reviewing their energetics
and their classical thermodynamics, one expounds the conjecture of Bekenstein,
attributing an entropy to black holes, and the calculation by Hawking of the
semi-classical radiation spectrum of a black hole, involving a thermal
(Planckian) factor. One then discusses the attempts to interpret the black-hole
entropy as the logarithm of the number of quantum micro-states of a macroscopic
black hole, with particular emphasis on results obtained within string theory.
After mentioning the (technically cleaner, but conceptually more intricate)
case of supersymmetric (BPS) black holes and the corresponding counting of the
degeneracy of Dirichlet-brane systems, one discusses in some detail the
``correspondence'' between massive string states and non-supersymmetric
Schwarzschild black holes.Comment: 51 pages, 4 figures, talk given at the "Poincare seminar" (Paris, 6
December 2003), to appear in Poincare Seminar 2003 (Birkhauser