24 research outputs found
Wightman function and stochastic gravity noise kernel in impulsive plane wave spacetimes
In this paper we study quantum field theory in impulsive plane wave
spacetimes. We first analyze the geodesics and the formation of conjugate
planes in these spacetimes. The behaviors of the world function and the van
Vleck determinant near conjugate plane are also considered. For the quantum
field, we work out the mode functions, their Bogoliubov transformations, and
the construction of the Wightman functions. By examining the Wightman function
near and on the conjugate plane, we show how the twofold and fourfold
singularity structure of the Wigthman function arise when crossing this plane.
Lastly, we come to the stochastic gravity noise kernel which is also the
correlation function of the stress energy tensor of the quantum field. Its
explicit form is given in terms of the world function and the van Vleck
determinant. We investigate its limits for small and large geodesic distances.
The leading divergent term of the noise kernel on the conjugate plane are
expressed in terms of derivatives of delta functions. Similar to that of the
Wightman functions, we also examine how the singularity structure of the noise
kernel near the lightcone changes when crossing the conjugate plane.Comment: 33 page
Domain wall space-times with a cosmological constant
We solve vacuum Einstein's field equations with the cosmological constant in
space-times admitting 3-parameter group of isometries with 2-dimensional
space-like orbits. The general exact solutions, which are represented in the
advanced and retarded null coordinates, have two arbitrary functions due to the
freedom of choosing null coordinates. In the thin-wall approximation, the
Israel's junction conditions yield one constraint equation on these two
functions in spherical, planar, and hyperbolic domain wall space-times with
reflection symmetry. The remain freedom of choosing coordinates are completely
fixed by requiring that when surface energy density of domain walls
vanishes, the metric solutions will return to some well-known solutions. It
leads us to find a planar domain wall solution, which is conformally flat, in
the de Sitter universe.Comment: 9 pages. no figur
Cosmological constant from gauge fields on extra dimensions
We present a new model of dark energy which could explain the observed
accelerated expansion of our Universe. We show that a five-dimensional
Einstein-Yang-Mills theory defined in a flat Friedmann-Robertson-Walker
universe compactified on a circle possesses degenerate vacua in four
dimensions. The present Universe could be trapped in one of these degenerate
vacua. With the natural requirement that the size of the extra dimension could
be of the GUT scale or smaller, the energy density difference between the
degenerate vacua and the true ground state can provide us with just the right
amount of dark energy to account for the observed expansion rate of our
Universe.Comment: 5 pages, minor change
Scalar field fluctuations in Schwarzschild-de Sitter space-time
We calculate quantum fluctuations of a free scalar field in the
Schwarzschild-de Sitter space-time, adopting the planar coordinates that is
pertinent to the presence of a black hole in an inflationary universe. In a
perturbation approach, doing expansion in powers of a small black hole event
horizon compared to the de Sitter cosmological horizon, we obtain time
evolution of the quantum fluctuations and then derive the scalar power
spectrum.Comment: 16 pages and 4 figures, accepted by Classical and Quantum Gravit
Graviton noise on tidal forces and geodesic congruences
In this work we continue with our recent study, using the Feynman-Vernon
worldline influence action and the Schwinger-Keldysh closed-time-path
formalism, to consider the effects of quantum noise of gravitons on the motion
of point masses. This effect can be regarded as due to a stochastic tensorial
force whose correlator is given by the graviton noise kernel associated with
the Hadamard function of the quantized gravitational field. Solving the
Langevin equation governing the motion of the separation of two masses, the
fluctuations of the separation due to the graviton noise can be obtained for
various states of the quantum field. Since this force has the stretching and
compressing effects like the tidal force, we can view it as one. We therefore
derive the expressions for, and estimate the magnitude of, this tidal force for
the cases of the Minkowski and the squeezed vacua. The influence of this force
on the evolution of the geodesic congruence through the Raychaudhuri equation
is then studied and the effects of quantum graviton noise on the shear and
rotation tensors presented.Comment: 22 page
Quasi-exactly solvable quasinormal modes
We consider quasinormal modes with complex energies from the point of view of
the theory of quasi-exactly solvable (QES) models. We demonstrate that it is
possible to find new potentials which admit exactly solvable or QES quasinormal
modes by suitable complexification of parameters defining the QES potentials.
Particularly, we obtain one QES and four exactly solvable potentials out of the
five one-dimensional QES systems based on the algebra.Comment: 3 pages, no figures. To appear in the Proceedings of the 13th
International Symposium on Particles, Strings and Cosmology (July 2-7, 2007,
Imperial College, London
Quantum Capacity and Vacuum Compressibility of Spacetime: Thermal Fields
An important yet perplexing result from work in the 90s and 00s is the
near-unity value of the ratio of fluctuations in the vacuum energy density of
quantum fields to the mean in a collection of generic spacetimes. This was done
by way of calculating the noise kernels which are the correlators of the
stress-energy tensor of quantum fields. In this paper we revisit this issue via
a quantum thermodynamics approach, by calculating two quintessential
thermodynamic quantities: the heat capacity and the quantum compressibility of
some model geometries filled with a quantum field at high and low temperatures.
This is because heat capacity at constant volume gives a measure of the
fluctuations of the energy density to the mean. When this ratio approaches or
exceeds unity, the validity of the canonical distribution is called into
question. Likewise, a system's compressibility at constant pressure is a
criterion for the validity of grand canonical ensemble. We derive the free
energy density and, from it, obtain the expressions for these two thermodynamic
quantities for thermal and quantum fields in 2d Casimir space, 2d Einstein
cylinder and 4d ( ) Einstein universe. To examine the
dependence on the dimensionality of space, for completeness, we have also
derived these thermodynamic quantities for the Einstein universes with
even-spatial dimensions: and . With this array
of spacetimes we can investigate the thermodynamic stability of quantum matter
fields in them and make some qualitative observations on the compatibility
condition for the co-existence between quantum fields and spacetimes, a
fundamental issue in the quantum and gravitation conundrum.Comment: 47 page
Semi-Analytic Techniques for Solving Quasi-Normal Modes
In this chapter, we discuss an approach to obtaining black hole quasi-normal modes known as the asymptotic iteration method, which was initially developed in mathematics as a new way to solve for eigenvalues in differential equations. Furthermore, we demonstrate that the asymptotic iteration method allows one to also solve for the radial quasi-normal modes on a variety of black hole spacetimes for a variety of perturbing fields. A specific example for Dirac fields in a general dimensional Schwarzschild black hole spacetime is given, as well as for spin-3/2 field quasi-normal modes