40 research outputs found
Dynamical N-body Equlibrium in Circular Dilaton Gravity
We obtain a new exact equilibrium solution to the N-body problem in a
one-dimensional relativistic self-gravitating system. It corresponds to an
expanding/contracting spacetime of a circle with N bodies at equal proper
separations from one another around the circle. Our methods are
straightforwardly generalizable to other dilatonic theories of gravity, and
provide a new class of solutions to further the study of (relativistic)
one-dimensional self-gravitating systems.Comment: 4 pages, latex, reference added, minor changes in wordin
Chaos in an Exact Relativistic 3-body Self-Gravitating System
We consider the problem of three body motion for a relativistic
one-dimensional self-gravitating system. After describing the canonical
decomposition of the action, we find an exact expression for the 3-body
Hamiltonian, implicitly determined in terms of the four coordinate and momentum
degrees of freedom in the system. Non-relativistically these degrees of freedom
can be rewritten in terms of a single particle moving in a two-dimensional
hexagonal well. We find the exact relativistic generalization of this
potential, along with its post-Newtonian approximation. We then specialize to
the equal mass case and numerically solve the equations of motion that follow
from the Hamiltonian. Working in hexagonal-well coordinates, we obtaining
orbits in both the hexagonal and 3-body representations of the system, and plot
the Poincare sections as a function of the relativistic energy parameter . We find two broad categories of periodic and quasi-periodic motions that we
refer to as the annulus and pretzel patterns, as well as a set of chaotic
motions that appear in the region of phase-space between these two types.
Despite the high degree of non-linearity in the relativistic system, we find
that the the global structure of its phase space remains qualitatively the same
as its non-relativisitic counterpart for all values of that we could
study. However the relativistic system has a weaker symmetry and so its
Poincare section develops an asymmetric distortion that increases with
increasing . For the post-Newtonian system we find that it experiences a
KAM breakdown for : above which the near integrable regions
degenerate into chaos.Comment: latex, 65 pages, 36 figures, high-resolution figures available upon
reques
Tunnelling, Temperature and Taub-NUT Black Holes
We investigate quantum tunnelling methods for calculating black hole
temperature, specifically the null geodesic method of Parikh and Wilczek and
the Hamilton-Jacobi Ansatz method of Angheben et al. We consider application of
these methods to a broad class of spacetimes with event horizons, inlcuding
Rindler and non-static spacetimes such as Kerr-Newman and Taub-NUT. We obtain a
general form for the temperature of Taub-NUT-Ads black holes that is
commensurate with other methods. We examine the limitations of these methods
for extremal black holes, taking the extremal Reissner-Nordstrom spacetime as a
case in point.Comment: 22 pages, 3 figures; added references, fixed figures, added comments
to extremal section, added footnot
Hawking radiation of Dirac particles via tunneling from Kerr black hole
We investigated Dirac Particles' Hawking radiation from event horizon of Kerr
black hole in terms of the tunneling formalism. Applying WKB approximation to
the general covariant Dirac equation in Kerr spacetime background, we obtain
the tunneling probability for fermions and Hawking temperature of Kerr black
hole. The result obtained by taking the fermion tunneling into account is
consistent with the previous literatures.Comment: 7 pages, no figures, to appear in CQ
Fermions tunnelling from the charged dilatonic black holes
Kerner and Mann's recent work shows that, for an uncharged and non-rotating
black hole, its Hawking temperature can be exactly derived by fermions
tunnelling from its horizons. In this paper, our main work is to improve the
analysis to deal with charged fermion tunnelling from the general dilatonic
black holes, specifically including the charged, spherically symmetric
dilatonic black hole, the rotating Einstein-Maxwell-Dilaton-Axion (EMDA) black
hole and the rotating Kaluza-Klein (KK) black hole. As a result, the correct
Hawking temperatures are well recovered by charged fermions tunnelling from
these black holes.Comment: 16 pages, revised version to appear in Class. Quant. Gra
Fermions Tunnelling from Black Holes
We investigate the tunnelling of spin 1/2 particles through event horizons.
We first apply the tunnelling method to Rindler spacetime and obtain the Unruh
temperature. We then apply fermion tunnelling to a general non-rotating black
hole metric and show that the Hawking temperature is recovered.Comment: 22 pages, v2: added references, v3: fixed minor typos, v4: added a
new section applying fermion tunnelling method to Kruskal-Szekers
coordinates, fixed minor typo, and added references, v5: modified
introduction and conclusion, fixed typo
Hawking Temperature in Taub-NUT (A)dS spaces via the Generalized Uncertainty Principle
Using the extended forms of the Heisenberg uncertainty principle from string
theory and the quantum gravity theory, we drived Hawking temperature of a
Taub-Nut-(A)dS black hole. In spite of their distinctive natures such as
asymptotically locally flat and breakdown of the area theorem of the horizon
for the black holes, we show that the corrections to Hawking temperature by the
generalized versions of the the Heisenberg uncertainty principle increases like
the Schwarzschild-(A)dS black hole and give the reason why the Taub-Nut-(A)dS
metric may have AdS/CFT dual picture.Comment: version published in General Relativity and Gravitatio
Boundary Conditions, Energies and Gravitational Heat in General Relativity (a Classical Analysis)
The variation of the energy for a gravitational system is directly defined
from the Hamiltonian field equations of General Relativity. When the variation
of the energy is written in a covariant form it splits into two (covariant)
contributions: one of them is the Komar energy, while the other is the
so-called covariant ADM correction term. When specific boundary conditions are
analyzed one sees that the Komar energy is related to the gravitational heat
while the ADM correction term plays the role of the Helmholtz free energy.
These properties allow to establish, inside a classical geometric framework, a
formal analogy between gravitation and the laws governing the evolution of a
thermodynamic system. The analogy applies to stationary spacetimes admitting
multiple causal horizons as well as to AdS Taub-bolt solutions.Comment: Latex file, 31 pages; one reference and two comments added, misprints
correcte
Tunnelling Methods and Hawking's radiation: achievements and prospects
The aim of this work is to review the tunnelling method as an alternative
description of the quantum radiation from black holes and cosmological
horizons. The method is first formulated and discussed for the case of
stationary black holes, then a foundation is provided in terms of analytic
continuation throughout complex space-time. The two principal implementations
of the tunnelling approach, which are the null geodesic method and the
Hamilton-Jacobi method, are shown to be equivalent in the stationary case. The
Hamilton-Jacobi method is then extended to cover spherically symmetric
dynamical black holes, cosmological horizons and naked singularities. Prospects
and achievements are discussed in the conclusions.Comment: Topical Review commissioned and accepted for publication by
"Classical and Quantum Gravity". 101 pages; 6 figure
Unruh--DeWitt detectors in spherically symmetric dynamical space-times
In the present paper, Unruh--DeWitt detectors are used in order to
investigate the issue of temperature associated with a spherically symmetric
dynamical space-times. Firstly, we review the semi-classical tunneling method,
then we introduce the Unruh--DeWitt detector approach. We show that for the
generic static black hole case and the FRW de Sitter case, making use of
peculiar Kodama trajectories, semiclassical and quantum field theoretic
techniques give the same standard and well known thermal interpretation, with
an associated temperature, corrected by appropriate Tolman factors. For a FRW
space-time interpolating de Sitter space with the Einstein--de Sitter universe
(that is a more realistic situation in the frame of CDM cosmologies),
we show that the detector response splits into a de Sitter contribution plus a
fluctuating term containing no trace of Boltzmann-like factors, but rather
describing the way thermal equilibrium is reached in the late time limit. As a
consequence, and unlike the case of black holes, the identification of the
dynamical surface gravity of a cosmological trapping horizon as an effective
temperature parameter seems lost, at least for our co-moving simplified
detectors. The possibility remains that a detector performing a proper motion
along a Kodama trajectory may register something more, in which case the
horizon surface gravity would be associated more likely to vacuum correlations
than to particle creation.Comment: 19 pages, to appear on IJTP. arXiv admin note: substantial text
overlap with arXiv:1101.525