2,895 research outputs found
Semiclassical and Quantum Black Holes and their Evaporation, de Sitter and Anti-de Sitter Regimes, Gravitational and String Phase Transitions
An effective string theory in physically relevant cosmological and black hole
space times is reviewed. Explicit computations of the quantum string entropy,
partition function and quantum string emission by black holes (Schwarzschild,
rotating, charged, asymptotically flat, de Sitter dS and AdS space times) in
the framework of effective string theory in curved backgrounds provide an
amount of new quantum gravity results as: (i) gravitational phase transitions
appear with a distinctive universal feature: a square root branch point
singularity in any space time dimensions. This is of the type of the de Vega -
Sanchez transition for the thermal self-gravitating gas of point particles.
(ii) There are no phase transitions in AdS alone. (iii) For background,
upper bounds of the Hubble constant H are found, dictated by the quantum string
phase transition.(iv) The Hawking temperature and the Hagedorn temperature are
the same concept but in different (semiclassical and quantum) gravity regimes
respectively. (v) The last stage of black hole evaporation is a microscopic
string state with a finite string critical temperature which decays as usual
quantum strings do in non-thermal pure quantum radiation (no information
loss).(vi) New lower string bounds are given for the Kerr-Newman black hole
angular momentum and charge, which are entirely different from the upper
classical bounds. (vii) Semiclassical gravity states undergo a phase transition
into quantum string states of the same system, these states are duals of each
other in the precise sense of the usual classical-quantum (wave-particle)
duality, which is universal irrespective of any symmetry or isommetry of the
space-time and of the number or the kind of space-time dimensions.Comment: review paper, no figures. to appear in Int Jour Mod Phys
Localized energy for wave equations with degenerate trapping
Localized energy estimates have become a fundamental tool when studying wave
equations in the presence of asymptotically at background geometry. Trapped
rays necessitate a loss when compared to the estimate on Minkowski space. A
loss of regularity is a common way to incorporate such. When trapping is
sufficiently weak, a logarithmic loss of regularity suffices. Here, by studying
a warped product manifold introduced by Christianson and Wunsch, we encounter
the first explicit example of a situation where an estimate with an algebraic
loss of regularity exists and this loss is sharp. Due to the global-in-time
nature of the estimate for the wave equation, the situation is more complicated
than for the Schr\"{o}dinger equation. An initial estimate with sub-optimal
loss is first obtained, where extra care is required due to the low frequency
contributions. An improved estimate is then established using energy
functionals that are inspired by WKB analysis. Finally, it is shown that the
loss cannot be improved by any power by saturating the estimate with a
quasimode.Comment: 18 page
QFT, String Temperature and the String Phase of De Sitter Space-time
The density of mass levels \rho(m) and the critical temperature for strings
in de Sitter space-time are found. QFT and string theory in de Sitter space are
compared. A `Dual'-transform is introduced which relates classical to quantum
string lengths, and more generally, QFT and string domains. Interestingly, the
string temperature in De Sitter space turns out to be the Dual transform of the
QFT-Hawking-Gibbons temperature. The back reaction problem for strings in de
Sitter space is addressed selfconsistently in the framework of the `string
analogue' model (or thermodynamical approach), which is well suited to combine
QFT and string study.We find de Sitter space-time is a self-consistent solution
of the semiclassical Einstein equations in this framework. Two branches for the
scalar curvature R(\pm) show up: a classical, low curvature solution (-), and a
quantum high curvature solution (+), enterely sustained by the strings. There
is a maximal value for the curvature R_{\max} due to the string back reaction.
Interestingly, our Dual relation manifests itself in the back reaction
solutions: the (-) branch is a classical phase for the geometry with intrinsic
temperature given by the QFT-Hawking-Gibbons temperature.The (+) is a stringy
phase for the geometry with temperature given by the intrinsic string de Sitter
temperature. 2 + 1 dimensions are considered, but conclusions hold generically
in D dimensions.Comment: LaTex, 24 pages, no figure
The Energy-Momentum Tensor in Fulling-Rindler Vacuum
The energy density in Fulling-Rindler vacuum, which is known to be negative
"everywhere" is shown to be positive and singular on the horizons in such a
fashion as to guarantee the positivity of the total energy. The mechanism of
compensation is displayed in detail.Comment: 9 pages, ULB-TH-15/9
The Heat Kernel Expansion on a Cone and Quantum Fields Near Cosmic Strings
An asymptotic expansion of the trace of the heat kernel on a cone where the
heat coefficients have a delta function behavior at the apex is obtained. It is
used to derive the renormalized effective action and total energy of a
self-interacting quantum scalar field on the cosmic string space-time. Analogy
is pointed out with quantum theory with boundaries. The surface infinities in
the effective action are shown to appear and are removed by renormalization of
the string tension. Besides, the total renormalized energy turns out to be
finite due to cancelation of the known non-integrable divergence in the energy
density of the field with a counterterm in the bare string tension.Comment: 20 pages, JINR preprint August, 1993, E2-93-291, LATEX fil
G2 Hitchin functionals at one loop
We consider the quantization of the effective target space description of
topological M-theory in terms of the Hitchin functional whose critical points
describe seven-manifolds with G2 structure. The one-loop partition function for
this theory is calculated and an extended version of it, that is related to
generalized G2 geometry, is compared with the topological G2 string. We relate
the reduction of the effective action for the extended G2 theory to the Hitchin
functional description of the topological string in six dimensions. The
dependence of the partition functions on the choice of background G2 metric is
also determined.Comment: 58 pages, LaTeX; v2: Acknowledgments adde
Thermal Conditions for Scalar Bosons in a Curved Space Time
The conditions that allow us to consider the vacuum expectation value of the
energy-momentum tensor as a statistical average, at some particular
temperature, are given. When the mean value of created particles is stationary,
a planckian distribution for the field modes is obtained. In the massless
approximation, the temperature dependence is as that corresponding to a
radiation dominated Friedmann-like model.Comment: 14 pages (TeX manuscript
Quantum theory of massless (p,0)-forms
We describe the quantum theory of massless (p,0)-forms that satisfy a
suitable holomorphic generalization of the free Maxwell equations on Kaehler
spaces. These equations arise by first-quantizing a spinning particle with a
U(1)-extended local supersymmetry on the worldline. Dirac quantization of the
spinning particle produces a physical Hilbert space made up of (p,0)-forms that
satisfy holomorphic Maxwell equations coupled to the background Kaehler
geometry, containing in particular a charge that measures the amount of
coupling to the U(1) part of the U(d) holonomy group of the d-dimensional
Kaehler space. The relevant differential operators appearing in these equations
are a twisted exterior holomorphic derivative and its hermitian conjugate
(twisted Dolbeault operators with charge q). The particle model is used to
obtain a worldline representation of the one-loop effective action of the
(p,0)-forms. This representation allows to compute the first few heat kernel
coefficients contained in the local expansion of the effective action and to
derive duality relations between (p,0) and (d-p-2,0)-forms that include a
topological mismatch appearing at one-loop.Comment: 32 pages, 3 figure
On vacuum-vacuum amplitude and Bogoliubov coefficients
Even if the electromagnetic field does not create pairs, virtual pairs lead
to the appearance of a phase in vacuum-vacuum amplitude. This makes it
necessary to distinguish the in- and out-solutions even when it is commonly
assumed that there is only one complete set of solutions as, for example, in
the case of a constant magnetic field. Then in- and out-solutions differ only
by a phase factor which is in essence the Bogoliubov coefficient. The
propagator in terms of in- and out-states takes the same form as the one for
pair creating fields. The transition amplitude for an electron to go from an
initial in-state to out-state is equal to unity (in diagonal representation).
This is in agreement with Pauli principal: if in the field there is an electron
with given (conserved) set of quantum numbers, virtual pair cannot appear in
this state. So even the phase of transition amplitude remains unaffected by the
field. We show how one may redefine the phases of Bogoliubov coefficients in
order to express the vacuum-vacuum amplitude through them.Comment: 20pages, no figures, some typos corrected, minor improvement
One-Loop Supergravity Corrections to the Black Hole Entropy and Residual Supersymmetry
We study the one-loop corrections to the effective on-shell action of N=2
supergravity in the background of the Reissner-Nordstrom black hole. In the
extreme case the contributions from graviton, gravitino and photon to the
one-loop corrections to the entropy are shown to cancel. This gives the first
explicit example of the supersymmetric non-renormalization theorem for the
on-shell action (entropy) for BPS configurations which admit Killing spinors.
We display the residual supersymmetry of the perturbations of a general
supersymmetric theory in a bosonic BPS background.Comment: 13 Pages, LaTe
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