821 research outputs found
Focusing and the Holographic Hypothesis
The ``screen mapping" introduced by Susskind to implement 't Hooft's
holographic hypothesis is studied. For a single screen time, there are an
infinite number of images of a black hole event horizon, almost all of which
have smaller area on the screen than the horizon area. This is consistent with
the focusing equation because of the existence of focal points. However, the
{\it boundary} of the past (or future) of the screen obeys the area theorem,
and so always gives an expanding map to the screen, as required by the
holographic hypothesis. These considerations are illustrated with several
axisymmetric static black hole spacetimes.Comment: 8 pages, plain latex, 5 figures included using psfi
Finite temperature mobility of a particle coupled to a fermion environment
We study numerically the finite temperature and frequency mobility of a
particle coupled by a local interaction to a system of spinless fermions in one
dimension. We find that when the model is integrable (particle mass equal to
the mass of fermions) the static mobility diverges. Further, an enhanced
mobility is observed over a finite parameter range away from the integrable
point. We present a novel analysis of the finite temperature static mobility
based on a random matrix theory description of the many-body Hamiltonian.Comment: 11 pages (RevTeX), 5 Postscript files, compressed using uufile
Does backreaction enforce the averaged null energy condition in semiclassical gravity?
The expected stress-energy tensor of quantum fields generically
violates the local positive energy conditions of general relativity. However,
may satisfy some nonlocal conditions such as the averaged null energy
condition (ANEC), which would rule out traversable wormholes. Although ANEC
holds in Minkowski spacetime, it can be violated in curved spacetimes if one is
allowed to choose the spacetime and quantum state arbitrarily, without
imposition of the semiclassical Einstein equation G_{ab} = 8 \pi . In
this paper we investigate whether ANEC holds for solutions to this equation, by
studying a free, massless scalar field with arbitrary curvature coupling in
perturbation theory to second order about the flat spacetime/vacuum solution.
We "reduce the order" of the perturbation equations to eliminate spurious
solutions, and consider the limit in which the lengthscales determined by the
incoming state are much larger than the Planck length. We also need to assume
that incoming classical gravitational radiation does not dominate the first
order metric perturbation. We find that although the ANEC integral can be
negative, if we average the ANEC integral transverse to the geodesic with a
suitable Planck scale smearing function, then a strictly positive result is
obtained in all cases except for the flat spacetime/vacuum solution. This
result suggests --- in agreement with conclusions drawn by Ford and Roman from
entirely independent arguments --- that if traversable wormholes do exist as
solutions to the semiclassical equations, they cannot be macroscopic but must
be ``Planck scale''. A large portion of our paper is devoted to the analysis of
general issues concerning the nature of the semiclassical Einstein equation and
of prescriptions for extracting physically relevant solutions.Comment: 54 pages, 3 figures, uses revtex macros and epsf.tex, to appear in
Phys Rev D. A new appendix has been added showing consistency of our results
with recent results of Visser [gr-qc/9604008]. Some corrections were made to
Appendix A, and several other minor changes to the body of the paper also
were mad
Bubbles on Manifolds with a U(1) Isometry
We investigate the construction of five-dimensional, three-charge
supergravity solutions that only have a rotational U(1) isometry. We show that
such solutions can be obtained as warped compactifications with a singular
ambi-polar hyper-Kahler base space and singular warp factors. We show that the
complete solution is regular around the critical surface of the ambi-polar
base. We illustrate this by presenting the explicit form of the most general
supersymmetric solutions that can be obtained from an Atiyah-Hitchin base space
and its ambi-polar generalizations. We make a parallel analysis using an
ambi-polar generalization of the Eguchi-Hanson base space metric. We also show
how the bubbling procedure applied to the ambi-polar Eguchi-Hanson metric can
convert it to a global AdS_2xS^3 compactification.Comment: 33 pages, 5 figures, LaTeX; references adde
Noise Kernel and Stress Energy Bi-Tensor of Quantum Fields in Hot Flat Space and Gaussian Approximation in the Optical Schwarzschild Metric
Continuing our investigation of the regularization of the noise kernel in
curved spacetimes [N. G. Phillips and B. L. Hu, Phys. Rev. D {\bf 63}, 104001
(2001)] we adopt the modified point separation scheme for the class of optical
spacetimes using the Gaussian approximation for the Green functions a la
Bekenstein-Parker-Page. In the first example we derive the regularized noise
kernel for a thermal field in flat space. It is useful for black hole
nucleation considerations. In the second example of an optical Schwarzschild
spacetime we obtain a finite expression for the noise kernel at the horizon and
recover the hot flat space result at infinity. Knowledge of the noise kernel is
essential for studying issues related to black hole horizon fluctuations and
Hawking radiation backreaction. We show that the Gaussian approximated Green
function which works surprisingly well for the stress tensor at the
Schwarzschild horizon produces significant error in the noise kernel there. We
identify the failure as occurring at the fourth covariant derivative order.Comment: 21 pages, RevTeX
Black Rings in Taub-NUT and D0-D6 interactions
We analyze the dynamics of neutral black rings in Taub-NUT spaces and their
relation to systems of D0 and D6 branes in the supergravity approximation. We
employ several recent techniques, both perturbative and exact, to construct
solutions in which thermal excitations of the D0-branes can be turned on or
off, and the D6-brane can have -fluxes turned on or off in its worldvolume.
By explicit calculation of the interaction energy between the D0 and D6 branes,
we can study equilibrium configurations and their stability. We find that
although D0 and D6 branes (in the absence of fields, and at zero
temperature) repeal each other at non-zero separation, as they get together
they go over continuosly to an unstable bound state of an extremal singular
Kaluza-Klein black hole. We also find that, for -fields larger than a
critical value, or sufficiently large thermal excitation, the D0 and D6 branes
form stable bound states. The bound states with thermally excited D0 branes are
black rings in Taub-NUT, and we provide an analysis of their phase diagram.Comment: 50 pages, 8 figures; v3: minor changes and references added; v4:
improved figs. 7 and 8, matches with published versio
Linear Response, Validity of Semi-Classical Gravity, and the Stability of Flat Space
A quantitative test for the validity of the semi-classical approximation in
gravity is given. The criterion proposed is that solutions to the
semi-classical Einstein equations should be stable to linearized perturbations,
in the sense that no gauge invariant perturbation should become unbounded in
time. A self-consistent linear response analysis of these perturbations, based
upon an invariant effective action principle, necessarily involves metric
fluctuations about the mean semi-classical geometry, and brings in the
two-point correlation function of the quantum energy-momentum tensor in a
natural way. This linear response equation contains no state dependent
divergences and requires no new renormalization counterterms beyond those
required in the leading order semi-classical approximation. The general linear
response criterion is applied to the specific example of a scalar field with
arbitrary mass and curvature coupling in the vacuum state of Minkowski
spacetime. The spectral representation of the vacuum polarization function is
computed in n dimensional Minkowski spacetime, and used to show that the flat
space solution to the semi-classical Einstein equations for n=4 is stable to
all perturbations on distance scales much larger than the Planck length.Comment: 22 pages: This is a significantly expanded version of gr-qc/0204083,
with two additional sections and two new appendices giving a complete,
explicit example of the semi-classical stability criterion proposed in the
previous pape
Tensor reduction of two-loop vacuum diagrams and projectors for expanding three-point functions
Explicit general formulae for the tensor reduction of two-loop massive vacuum
diagrams are presented. The problem of calculating the corresponding
coefficients is shown to be equivalent to the problem of constructing
differential operators (projectors) extracting the coefficients of the momentum
expansion of massive scalar three-point functions (with any number of loops),
so the solution to the latter problem is also given.Comment: 13 pages, plain latex, no figure
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