3,936 research outputs found
Red-shifts near black holes
A simple ordinary differential equation is derived governing the red-shifts
of wave-fronts propagating through a non-stationary spherically symmetric
space-time. Approach to an event horizon corresponds to approach to a fixed
point; in general, the phase portrait of the equation illuminates the
qualitative features of the geometry. In particular, the asymptotics of the
red-shift as a horizon is approached, a critical ingredient of Hawking's
prediction of radiation from black holes, are easily brought out. This
asympotic behavior has elements in common with the universal behavior near
phase transitions in statistical physics. The validity of the Unruh vacuum for
the Hawking process can be understood in terms of this universality. The
concept of surface gravity is extended to to non-stationary spherically
symmetric black holes. Finally, it is shown that in the non-stationary case,
Hawking's predicted flux of radiation from a black hole would be modified.Comment: 20 pages, plain Tex, IOP macros, 4 eps figures, accepted by CQ
Generalized entropy and Noether charge
We find an expression for the generalized gravitational entropy of Hawking in
terms of Noether charge. As an example, the entropy of the Taub-Bolt spacetime
is calculated.Comment: 6 pages, revtex, reference correcte
Quantum Coherence and Closed Timelike Curves
Various calculations of the matrix have shown that it seems to be non
unitary for interacting fields when there are closed timelike curves. It is
argued that this is because there is loss of quantum coherence caused by the
fact that part of the quantum state circulates on the closed timelike curves
and is not measured at infinity. A prescription is given for calculating the
superscattering matrix on space times whose parameters can be
analytically continued to obtain a Euclidean metric. It is illustrated by a
discussion of a spacetime in with two disks in flat space are identified. If
the disks have an imaginary time separation, this corresponds to a heat bath.
An external field interacting with the heat bath will lose quantum coherence.
One can then analytically continue to an almost real separation of the disks.
This will give closed timelike curves but one will still get loss of quantum
coherence.Comment: 13 page
Mass and charge fluctuations and black hole entropy
The effects of thermal fluctuations of the mass (horizon area) and electric
charge, on the entropy of non-rotating charged {\it macroscopic} black holes,
are analyzed using a grand canonical ensemble. Restricting to Gaussian
fluctuations around equilibrium, and assuming a power law type of relation
between the black hole mass, charge and horizon area, characterized by two real
positive indices, the grand canonical entropy is shown to acquire a logarithmic
correction with a positive coefficient proportional to the sum of the indices.
However, the root mean squared fluctuations of mass and charge relative to the
mean values of these quantities turn out to be independent of the details of
the assumed mass-area relation. We also comment on possible cancellation
between log (area) corrections arising due to {\it fixed area} quantum
spacetime fluctuations and that due to thermal fluctuations of the area and
other quantities.Comment: 8 pages revtex, no figure
Misner String Entropy
I show that gravitational entropy can be ascribed to spacetimes containing
Misner strings (the gravitational analogues of Dirac strings), even in the
absence of any other event horizon (or bolt) structures. This result follows
from an extension of proposals for evaluating the stress-energy of a
gravitational system which are motivated by the AdS/CFT correspondence.Comment: revtex, 5 pages, references added, typo correcte
Comment on "Absence of trapped surfaces and singularities in cylindrical collapse"
Recently, the gravitational collapse of an infinite cylindrical thin shell of
matter in an otherwise empty spacetime with two hypersurface orthogonal Killing
vectors was studied by Gon\c{c}alves [Phys. Rev. {\bf D65}, 084045 (2002).]. By
using three "alternative" criteria for trapped surfaces, the author claimed to
have shown that {\em they can never form either outside or on the shell,
regardingless of the matter content for the shell, except at asymptotical
future null infinite}.
Following Penrose's original idea, we first define trapped surfaces in
cylindrical spacetimes in terms of the expansions of null directions orthogonal
to the surfaces, and then show that the first criterion used by Gon\c{c}alves
is incorrect. We also show that his analysis of non-existence of trapped
surfaces in vacuum is incomplete. To confirm our claim, we present an example
that is a solution to the vacuum Einstein field equations and satisfies all the
regular conditions imposed by Gon\c{c}alves. After extending the solution to
the whole spacetime, we show explicitly that trapped surfaces exist in the
extended region.Comment: latex, 2 figures, the last version to appear in Phys. Rev.
Can Extremal Black Holes Have Non-Zero Entropy ?
We give several pieces of evidence to show that extremal black holes cannot
be obtained as limits of non-extremal black holes. We review arguments in the
literature showing that the entropy of extremal black holes is zero, while that
of near-extremal ones obey the Bekenstein-Hawking formula. However, from the
counting of degeneracy of quantum (BPS) states of string theory the entropy of
extremal stringy black holes obeys the area law. An attempt is made to
reconcile these arguments.Comment: 18 pages, RevTEX; last section modified, version to appear in Mod.
Phys. Lett.
Entropy of Rotating Misner String Spacetimes
Using a boundary counterterm prescription motivated by the AdS/CFT
conjecture, I evaluate the energy, entropy and angular momentum of the class of
Kerr-NUT/bolt-AdS spacetimes. As in the non-rotating case, when the NUT charge
is nonzero the entropy is no longer equal to one-quarter of the area due to the
presence of the Misner string. When the cosmological constant is also non-zero,
the entropy is bounded from above.Comment: Revtex, 9 pages, 3 figure
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