6 research outputs found
Induced current and redefinition of electric and magnetic fields from non-compact Kaluza-Klein theory: An experimental signature of the fifth dimension
The field equations for gravitation and electromagnetism with sources in four
dimensions can be interpreted as arising from the vacuum Einstein equations in
five dimensions. Gauge invariance of the electromagnetic potentials leads to a
``generalized'' electromagnetic field tensor. We use the action principle to
derive the equations of motion for free electromagnetic fields in flat
spacetime, and isolate an effective electromagnetic current with a source that
is purely higher-dimensional in origin. This current provides, at least in
principle, a means of detecting extra dimensions experimentally.Comment: 6 pages; to appear in Physics Letters
An exact solution of the five-dimensional Einstein equations with four-dimensional de Sitter-like expansion
We present an exact solution to the Einstein field equations which is Ricci
and Riemann flat in five dimensions, but in four dimensions is a good model for
the early vacuum-dominated universe.Comment: 6 pages; to appear in Journal of Mathematical Physics; v2: reference
3 correcte
The Big Bang as a Phase Transition
We study a five-dimensional cosmological model, which suggests that the
universe bagan as a discontinuity in a (Higgs-type) scalar field, or
alternatively as a conventional four-dimensional phase transition.Comment: 10 pages, 2 figures; typo corrected in equation (18); 1 reference
added; version to appear in International Journal of Modern Physics
Isolated horizons in higher-dimensional Einstein-Gauss-Bonnet gravity
The isolated horizon framework was introduced in order to provide a local
description of black holes that are in equilibrium with their (possibly
dynamic) environment. Over the past several years, the framework has been
extended to include matter fields (dilaton, Yang-Mills etc) in D=4 dimensions
and cosmological constant in dimensions. In this article we present a
further extension of the framework that includes black holes in
higher-dimensional Einstein-Gauss-Bonnet (EGB) gravity. In particular, we
construct a covariant phase space for EGB gravity in arbitrary dimensions which
allows us to derive the first law. We find that the entropy of a weakly
isolated and non-rotating horizon is given by
.
In this expression is the -dimensional cross section of the
horizon with area form and Ricci scalar ,
is the -dimensional Newton constant and is the Gauss-Bonnet
parameter. This expression for the horizon entropy is in agreement with those
predicted by the Euclidean and Noether charge methods. Thus we extend the
isolated horizon framework beyond Einstein gravity.Comment: 18 pages; 1 figure; v2: 19 pages; 2 references added; v3: 19 pages;
minor corrections; 1 reference added; to appear in Classical and Quantum
Gravit
Supersymmetric isolated horizons
We construct a covariant phase space for rotating weakly isolated horizons in
Einstein-Maxwell-Chern-Simons theory in all (odd) dimensions. In
particular, we show that horizons on the corresponding phase space satisfy the
zeroth and first laws of black-hole mechanics. We show that the existence of a
Killing spinor on an isolated horizon in four dimensions (when the Chern-Simons
term is dropped) and in five dimensions requires that the induced (normal)
connection on the horizon has to vanish, and this in turn implies that the
surface gravity and rotation one-form are zero. This means that the
gravitational component of the horizon angular momentum is zero, while the
electromagnetic component (which is attributed to the bulk radiation field) is
unconstrained. It follows that an isolated horizon is supersymmetric only if it
is extremal and nonrotating. A remarkable property of these horizons is that
the Killing spinor only has to exist on the horizon itself. It does not have to
exist off the horizon. In addition, we find that the limit when the surface
gravity of the horizon goes to zero provides a topological constraint.
Specifically, the integral of the scalar curvature of the cross sections of the
horizon has to be positive when the dominant energy condition is satisfied and
the cosmological constant is zero or positive, and in particular
rules out the torus topology for supersymmetric isolated horizons (unless
) if and only if the stress-energy tensor is of the form
such that for any two null vectors and with
normalization on the horizon.Comment: 26 pages, 1 figure; v2: typos corrected, topology arguments
corrected, discussion of black rings and dipole charge added, references
added, version to appear in Classical and Quantum Gravit
Barbero-Immirzi parameter, manifold invariants and Euclidean path integrals
The Barbero-Immirzi parameter appears in the \emph{real} connection
formulation of gravity in terms of the Ashtekar variables, and gives rise to a
one-parameter quantization ambiguity in Loop Quantum Gravity. In this paper we
investigate the conditions under which will have physical effects in
Euclidean Quantum Gravity. This is done by constructing a well-defined
Euclidean path integral for the Holst action with non-zero cosmological
constant on a manifold with boundary. We find that two general conditions must
be satisfied by the spacetime manifold in order for the Holst action and its
surface integral to be non-zero: (i) the metric has to be non-diagonalizable;
(ii) the Pontryagin number of the manifold has to be non-zero. The latter is a
strong topological condition, and rules out many of the known solutions to the
Einstein field equations. This result leads us to evaluate the on-shell
first-order Holst action and corresponding Euclidean partition function on the
Taub-NUT-ADS solution. We find that shows up as a finite rotation of
the on-shell partition function which corresponds to shifts in the energy and
entropy of the NUT charge. In an appendix we also evaluate the Holst action on
the Taub-NUT and Taub-bolt solutions in flat spacetime and find that in that
case as well shows up in the energy and entropy of the NUT and bolt
charges. We also present an example whereby the Euler characteristic of the
manifold has a non-trivial effect on black-hole mergers.Comment: 18 pages; v2: references added; to appear in Classical and Quantum
Gravity; v3: typos corrected; minor revisions to match published versio