6,780 research outputs found
Hawking radiation without black hole entropy
In this Letter I point out that Hawking radiation is a purely kinematic
effect that is generic to Lorentzian geometries. Hawking radiation arises for
any test field on any Lorentzian geometry containing an event horizon
regardless of whether or not the Lorentzian geometry satisfies the dynamical
Einstein equations of general relativity. On the other hand, the classical laws
of black hole mechanics are intrinsically linked to the Einstein equations of
general relativity (or their perturbative extension into either semiclassical
quantum gravity or string-inspired scenarios). In particular, the laws of black
hole thermodynamics, and the identification of the entropy of a black hole with
its area, are inextricably linked with the dynamical equations satisfied by the
Lorentzian geometry: entropy is proportional to area (plus corrections) if and
only if the dynamical equations are the Einstein equations (plus corrections).
It is quite possible to have Hawking radiation occur in physical situations in
which the laws of black hole mechanics do not apply, and in situations in which
the notion of black hole entropy does not even make any sense. This observation
has important implications for any derivation of black hole entropy that seeks
to deduce black hole entropy from the Hawking radiation.Comment: Uses ReV_TeX 3.0; Five pages in two-column forma
The Semi-Classical Back Reaction to Black Hole Evaporation
The semi-classical back reaction to black hole evaporation (wherein the
renormalized energy momentum tensor is taken as source of Einstein's equations)
is analyzed in detail. It is proven that the mass of a Schwarzshild black hole
decreases according to Hawking's law where is a constant
of order one and that the particles are emitted with a thermal spectrum at
temperature .Comment: 10 pages, LATE
Signaling, Entanglement, and Quantum Evolution Beyond Cauchy Horizons
Consider a bipartite entangled system half of which falls through the event
horizon of an evaporating black hole, while the other half remains coherently
accessible to experiments in the exterior region. Beyond complete evaporation,
the evolution of the quantum state past the Cauchy horizon cannot remain
unitary, raising the questions: How can this evolution be described as a
quantum map, and how is causality preserved? What are the possible effects of
such nonstandard quantum evolution maps on the behavior of the entangled
laboratory partner? More generally, the laws of quantum evolution under extreme
conditions in remote regions (not just in evaporating black-hole interiors, but
possibly near other naked singularities and regions of extreme spacetime
structure) remain untested by observation, and might conceivably be non-unitary
or even nonlinear, raising the same questions about the evolution of entangled
states. The answers to these questions are subtle, and are linked in unexpected
ways to the fundamental laws of quantum mechanics. We show that terrestrial
experiments can be designed to probe and constrain exactly how the laws of
quantum evolution might be altered, either by black-hole evaporation, or by
other extreme processes in remote regions possibly governed by unknown physics.Comment: Combined, revised, and expanded version of quant-ph/0312160 and
hep-th/0402060; 13 pages, RevTeX, 2 eps figure
Computing the spectrum of black hole radiation in the presence of high frequency dispersion: an analytical approach
We present a method for computing the spectrum of black hole radiation of a
scalar field satisfying a wave equation with high frequency dispersion. The
method involves a combination of Laplace transform and WKB techniques for
finding approximate solutions to ordinary differential equations. The modified
wave equation is obtained by adding a higher order derivative term suppressed
by powers of a fundamental momentum scale to the ordinary wave equation.
Depending on the sign of this new term, high frequency modes propagate either
superluminally or subluminally. We show that the resulting spectrum of created
particles is thermal at the Hawking temperature, and further that the out-state
is a thermal state at the Hawking temperature, to leading order in , for
either modification.Comment: 26 pages, plain latex, 6 figures included using psfi
Trans-Planckian Tail in a Theory with a Cutoff
Trans-planckian frequencies can be mimicked outside a black-hole horizon as a
tail of an exponentially large amplitude wave that is mostly hidden behind the
horizon. The present proposal requires implementing a final state condition.
This condition involves only frequencies below the cutoff scale. It may be
interpreted as a condition on the singularity. Despite the introduction of the
cutoff, the Hawking radiation is restored for static observers. Freely falling
observers see empty space outside the horizon, but are "heated" as they cross
the horizon.Comment: 17 pages, RevTe
Black Hole Entropy: a spacetime foam approach
The spacetime foam structure is reviewed briefly (topogical fluctuations and
virtual black hole possibility; equation of state of the foam). A model of
space foam at the surface of the event horizon is introduced. The model is
applied to the calculus of the number of states of a black hole, of its entropy
and of other thermodynamical properties. A formula for the number of microholes
on the surface of the event horizon is derived. Thermodynamical properties of
the event horizon are extended to thermodynamical properties of the space. On
the basis of the previous results, the possibility of micro black holes
creation by the Unruh Effect is investigated.Comment: 23 pages, no figures, postscript file gzipped,to be published in
Classical and Quantum Gravity, July 199
When is S=A/4?
Black hole entropy and its relation to the horizon area are considered. More
precisely, the conditions and specifications that are expected to be required
for the assignment of entropy, and the consequences that these expectations
have when applied to a black hole are explored. In particular, the following
questions are addressed: When do we expect to assign an entropy?; when are
entropy and area proportional? and, what is the nature of the horizon? It is
concluded that our present understanding of black hole entropy is somewhat
incomplete, and some of the relevant issues that should be addressed in
pursuing these questions are pointed out.Comment: 14 pages, no figures. Revtex file. Manuscript edited and discussion
expanded. References added, conclusions unchanged. Version to be published in
MPL
Conservation Laws in Doubly Special Relativity
Motivated by various theoretical arguments that the Planck energy (Ep - 10^19
GeV) - should herald departures from Lorentz invariance, and the possibility of
testing these expectations in the not too distant future, two so-called "Doubly
Special Relativity" theories have been suggested -- the first by
Amelino-Camelia (DSR1) and the second by Smolin and Magueijo (DSR2). These
theories contain two fundamental scales -- the speed of light and an energy
usually taken to be Ep. The symmetry group is still the Lorentz group, but in
both cases acting nonlinearly on the energy-momentum sector. Accordingly, since
energy and momentum are no longer additive quantities, finding their values for
composite systems (and hence finding the correct conservation laws) is a
nontrivial matter. Ultimately it is these possible deviations from simple
linearly realized relativistic kinematics that provide the most promising
observational signal for empirically testing these models. Various
investigations have narrowed the conservation laws down to two possibilities
per DSR theory. We derive unique exact results for the energy-momentum of
composite systems in both DSR1 and DSR2, and indicate the general strategy for
arbitrary nonlinear realizations of the Lorentz group.Comment: V2: Extensive revisions: merged with gr-qc/0205093, new author added,
references added, discussion amplified. 4 pages, revtex4; V3: Revised in
response to referee comments; no physics changes; version to appear in
Physical Review
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