509 research outputs found
Conformal Scalar Propagation on the Schwarzschild Black-Hole Geometry
The vacuum activity generated by the curvature of the Schwarzschild
black-hole geometry close to the event horizon is studied for the case of a
massless, conformal scalar field. The associated approximation to the unknown,
exact propagator in the Hartle-Hawking vacuum state for small values of the
radial coordinate above results in an analytic expression which
manifestly features its dependence on the background space-time geometry. This
approximation to the Hartle-Hawking scalar propagator on the Schwarzschild
black-hole geometry is, for that matter, distinct from all other. It is shown
that the stated approximation is valid for physical distances which range from
the event horizon to values which are orders of magnitude above the scale
within which quantum and backreaction effects are comparatively pronounced. An
expression is obtained for the renormalised in the
Hartle-Hawking vacuum state which reproduces the established results on the
event horizon and in that segment of the exterior geometry within which the
approximation is valid. In contrast to previous results the stated expression
has the superior feature of being entirely analytic. The effect of the
manifold's causal structure to scalar propagation is also studied.Comment: 34 pages, 2 figures. Published on line on October 16, 2009 and due to
appear in print in Gen.Rel.Gra
Vacuum polarization in two-dimensional static spacetimes and dimensional reduction
We obtain an analytic approximation for the effective action of a quantum
scalar field in a general static two-dimensional spacetime. We apply this to
the dilaton gravity model resulting from the spherical reduction of a massive,
non-minimally coupled scalar field in the four-dimensional Schwarzschild
geometry. Careful analysis near the event horizon shows the resulting
two-dimensional system to be regular in the Hartle-Hawking state for general
values of the field mass, coupling, and angular momentum, while at spatial
infinity it reduces to a thermal gas at the black-hole temperature.Comment: REVTeX 4, 23 pages. Accepted by PRD. Minor modifications from
original versio
Energy-Momentum Tensor of Particles Created in an Expanding Universe
We present a general formulation of the time-dependent initial value problem
for a quantum scalar field of arbitrary mass and curvature coupling in a FRW
cosmological model. We introduce an adiabatic number basis which has the virtue
that the divergent parts of the quantum expectation value of the
energy-momentum tensor are isolated in the vacuum piece of , and
may be removed using adiabatic subtraction. The resulting renormalized
is conserved, independent of the cutoff, and has a physically transparent,
quasiclassical form in terms of the average number of created adiabatic
`particles'. By analyzing the evolution of the adiabatic particle number in de
Sitter spacetime we exhibit the time structure of the particle creation
process, which can be understood in terms of the time at which different
momentum scales enter the horizon. A numerical scheme to compute as a
function of time with arbitrary adiabatic initial states (not necessarily de
Sitter invariant) is described. For minimally coupled, massless fields, at late
times the renormalized goes asymptotically to the de Sitter invariant
state previously found by Allen and Folacci, and not to the zero mass limit of
the Bunch-Davies vacuum. If the mass m and the curvature coupling xi differ
from zero, but satisfy m^2+xi R=0, the energy density and pressure of the
scalar field grow linearly in cosmic time demonstrating that, at least in this
case, backreaction effects become significant and cannot be neglected in de
Sitter spacetime.Comment: 28 pages, Revtex, 11 embedded .ps figure
Some general properties of the renormalized stress-energy tensor for static quantum states on (n+1)-dimensional spherically symmetric black holes
We study the renormalized stress-energy tensor (RSET) for static quantum
states on (n+1)-dimensional, static, spherically symmetric black holes. By
solving the conservation equations, we are able to write the stress-energy
tensor in terms of a single unknown function of the radial co-ordinate, plus
two arbitrary constants. Conditions for the stress-energy tensor to be regular
at event horizons (including the extremal and ``ultra-extremal'' cases) are
then derived using generalized Kruskal-like co-ordinates. These results should
be useful for future calculations of the RSET for static quantum states on
spherically symmetric black hole geometries in any number of space-time
dimensions.Comment: 9 pages, no figures, RevTeX4, references added, accepted for
publication in General Relativity and Gravitatio
Method to compute the stress-energy tensor for the massless spin 1/2 field in a general static spherically symmetric spacetime
A method for computing the stress-energy tensor for the quantized, massless,
spin 1/2 field in a general static spherically symmetric spacetime is
presented. The field can be in a zero temperature state or a non-zero
temperature thermal state. An expression for the full renormalized
stress-energy tensor is derived. It consists of a sum of two tensors both of
which are conserved. One tensor is written in terms of the modes of the
quantized field and has zero trace. In most cases it must be computed
numerically. The other tensor does not explicitly depend on the modes and has a
trace equal to the trace anomaly. It can be used as an analytic approximation
for the stress-energy tensor and is equivalent to other approximations that
have been made for the stress-energy tensor of the massless spin 1/2 field in
static spherically symmetric spacetimes.Comment: 34 pages, no figure
The Dimensional-Reduction Anomaly in Spherically Symmetric Spacetimes
In D-dimensional spacetimes which can be foliated by n-dimensional
homogeneous subspaces, a quantum field can be decomposed in terms of modes on
the subspaces, reducing the system to a collection of (D-n)-dimensional fields.
This allows one to write bare D-dimensional field quantities like the Green
function and the effective action as sums of their (D-n)-dimensional
counterparts in the dimensionally reduced theory. It has been shown, however,
that renormalization breaks this relationship between the original and
dimensionally reduced theories, an effect called the dimensional-reduction
anomaly. We examine the dimensional-reduction anomaly for the important case of
spherically symmetric spaces.Comment: LaTeX, 19 pages, 2 figures. v2: calculations simplified, references
adde
Analytical approximation of the stress-energy tensor of a quantized scalar field in static spherically symmetric spacetimes
Analytical approximations for and of a
quantized scalar field in static spherically symmetric spacetimes are obtained.
The field is assumed to be both massive and massless, with an arbitrary
coupling to the scalar curvature, and in a zero temperature vacuum state.
The expressions for and are divided into
low- and high-frequency parts. The contributions of the high-frequency modes to
these quantities are calculated for an arbitrary quantum state. As an example,
the low-frequency contributions to and are
calculated in asymptotically flat spacetimes in a quantum state corresponding
to the Minkowski vacuum (Boulware quantum state). The limits of the
applicability of these approximations are discussed.Comment: revtex4, 17 pages; v2: three 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
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