7 research outputs found
The information paradox: A pedagogical introduction
The black hole information paradox is a very poorly understood problem. It is
often believed that Hawking's argument is not precisely formulated, and a more
careful accounting of naturally occurring quantum corrections will allow the
radiation process to become unitary. We show that such is not the case, by
proving that small corrections to the leading order Hawking computation cannot
remove the entanglement between the radiation and the hole. We formulate
Hawking's argument as a `theorem': assuming `traditional' physics at the
horizon and usual assumptions of locality we will be forced into mixed states
or remnants. We also argue that one cannot explain away the problem by invoking
AdS/CFT duality. We conclude with recent results on the quantum physics of
black holes which show the the interior of black holes have a `fuzzball'
structure. This nontrivial structure of microstates resolves the information
paradox, and gives a qualitative picture of how classical intuition can break
down in black hole physics.Comment: 38 pages, 7 figures, Latex (Expanded form of lectures given at CERN
for the RTN Winter School, Feb 09), typo correcte
A bound on the entropy of supergravity?
We determine, in two independent ways, the number of BPS quantum states
arising from supergravity degrees of freedom in a system with fixed total D4D0
charge. First, we count states generated by quantizing the spacetime degrees of
freedom of 'entropyless' multicentered solutions consisting of anti-D0-branes
bound to a D6-anti-D6 pair. Second, we determine the number of free
supergravity excitations of the corresponding AdS_3 geometry with the same
total charge. We find that, although these two approaches yield a priori
different sets of states, the leading degeneracies in a large charge expansion
are equal to each other and that, furthermore, the number of such states is
parametrically smaller than that arising from the D4D0 black hole's entropy.
This strongly suggests that supergravity alone is not sufficient to capture all
degrees of freedom of large supersymmetric black holes. Comparing the free
supergravity calculation to that of the D6-anti-D6-D0 system we find that the
bound on the free spectrum imposed by the stringy exclusion principle (a
unitarity bound in the dual CFT) seems to be captured in the dynamics of the
fully interacting but classcial supergravity equations of motion.Comment: 33 pages, 5 figure
Black Holes as Effective Geometries
Gravitational entropy arises in string theory via coarse graining over an
underlying space of microstates. In this review we would like to address the
question of how the classical black hole geometry itself arises as an effective
or approximate description of a pure state, in a closed string theory, which
semiclassical observers are unable to distinguish from the "naive" geometry. In
cases with enough supersymmetry it has been possible to explicitly construct
these microstates in spacetime, and understand how coarse-graining of
non-singular, horizon-free objects can lead to an effective description as an
extremal black hole. We discuss how these results arise for examples in Type II
string theory on AdS_5 x S^5 and on AdS_3 x S^3 x T^4 that preserve 16 and 8
supercharges respectively. For such a picture of black holes as effective
geometries to extend to cases with finite horizon area the scale of quantum
effects in gravity would have to extend well beyond the vicinity of the
singularities in the effective theory. By studying examples in M-theory on
AdS_3 x S^2 x CY that preserve 4 supersymmetries we show how this can happen.Comment: Review based on lectures of JdB at CERN RTN Winter School and of VB
at PIMS Summer School. 68 pages. Added reference
Quantizing N=2 Multicenter Solutions
N=2 supergravity in four dimensions, or equivalently N=1 supergravity in five
dimensions, has an interesting set of BPS solutions that each correspond to a
number of charged centers. This set contains black holes, black rings and their
bound states, as well as many smooth solutions. Moduli spaces of such solutions
carry a natural symplectic form which we determine, and which allows us to
study their quantization. By counting the resulting wavefunctions we come to an
independent derivation of some of the wall-crossing formulae. Knowledge of the
explicit form of these wavefunctions allows us to find quantum resolutions to
some apparent classical paradoxes such as solutions with barely bound centers
and those with an infinitely deep throat. We show that quantum effects seem to
cap off the throat at a finite depth and we give an estimate for the
corresponding mass gap in the dual CFT. This is an interesting example of a
system where quantum effects cannot be neglected at macroscopic scales even
though the curvature is everywhere small.Comment: 49 pages + appendice
Turbulence and Holography
We examine the interplay between recent advances in quantum gravity and the
problem of turbulence. In particular, we argue that in the gravitational
context the phenomenon of turbulence is intimately related to the properties of
spacetime foam. In this framework we discuss the relation of turbulence and
holography and the interpretation of the Kolmogorov scaling in the quantum
gravitational setting.Comment: 19 pages, LaTeX; version 2: reference adde