55 research outputs found
Thermodynamics and Evaporation of Closed Black Cosmic Strings
Both the canonical and microcanonical ensembles are utilized to study the
thermodynamic and evaporation properties of a closed black cosmic string whose
spacetime is asymptotically anti deSitter. There are similarities and
differences to the Schwarzschild-anti deSitter and 2+1 BTZ black hole
solutions. It is found that there exist regimes of black string/thermal
radiation equilibrium as well as stable remnant regimes. The relevance to black
hole evaporation is discussed.Comment: 10 pages with AMS packages. 1 figur
Anisotropic Structures and Wormholes with Loop Quantum Gravity Holonomy Corrections
Anisotropic spherically symmetric systems are studied in the connection and
densitized triad variables used in loop quantum gravity. The material source is
an anisotropic fluid, which is arguably the most commonly used source term in
anisotropic studies within general relativity. The gravitational+anisotropic
fluid constraints are derived and analyzed and then quantum gravity inspired
holonomy replacements are performed. The quantum properties of the fluid are
dictated by the modified constraint equations. Particular attention is paid to
wormhole throats, as they provide a simplistic model of the structures thought
to be ubiquitous in the quantum gravity space-time foam at high energy scales.
In comparison to the purely classical theory, the quantum corrections act to
increase the energy density of the fluid, which indicates that they may lessen
the energy condition violation present in the classical theory. Related to
this, in principle it would be possible to have scenarios where the classical
solution yields everywhere negative (with a zero at the throat) fluid energy
density but the corresponding quantum corrected theory possesses only small
regions of negative energy density or even everywhere non-negative energy
density.Comment: 20 pages, 6 figures. New version has updated references, minor
corrections and more comments regarding the interpretation of the results.
Accepted for publication in Physical Review
Integration in General Relativity
This paper presents a brief but comprehensive introduction to certain
mathematical techniques in General Relativity. Familiar mathematical procedures
are investigated taking into account the complications of introducing a non
trivial space-time geometry. This transcript should be of use to the beginning
student and assumes only very basic familiarity with tensor analysis and modern
notation. This paper will also be of use to gravitational physicists as a quick
reference.Comment: 8 pages (expect updates with additions
Discrete Phase Space: Quantum mechanics and non-singular potential functions
The three-dimensional potential equation, motivated by representations of
quantum mechanics, is investigated in four different scenarios: (i) In the
usual Euclidean space where the potential is singular but
invariant under the continuous inhomogeneous orthogonal group
. The invariance under the translation subgroup is compared to
the corresponding unitary transformation in the Schr\"{o}dinger representation
of quantum mechanics. This scenario is well known but serves as a reference
point for the other scenarios. (ii) Next, the discrete potential equation as a
partial difference equation in a three-dimensional lattice space is studied. In
this arena the potential is non-singular but invariance under
is broken. This is the usual picture of lattice theories and numerical
approximations. (iii) Next we study the six-dimensional continuous phase space.
Here a phase space representation of quantum mechanics is utilized. The
resulting potential is singular but possesses invariance under
. (iv) Finally, the potential is derived from the discrete
phase space representation of quantum mechanics, which is shown to be an
\emph{exact} representation of quantum mechanics. The potential function here
is both non-singular and possesses invariance under , and this
is proved via the unitary transformations of quantum mechanics in this
representation.Comment: 17 pages, 3 figure
Loop Quantum Corrected Einstein Yang-Mills Black Holes
In this paper we study the homogeneous interiors of black holes possessing
SU(2) Yang-Mills fields subject to corrections inspired by loop quantum
gravity. The systems studied possess both magnetic and induced electric
Yang-Mills fields. We consider the system of equations both with and without
Wilson loop corrections to the Yang-Mills potential. The structure of the
Yang-Mills Hamiltonian along with the restriction to homogeneity allows for an
anomaly free effective quantization. In particular we study the bounce which
replaces the classical singularity and the behavior of the Yang-Mills fields in
the quantum corrected interior, which possesses topology .
Beyond the bounce the magnitude of the Yang-Mills electric field asymptotically
grows monotonically. This results in an ever expanding sector even though
the two-sphere volume is asymptotically constant. The results are similar with
and without Wilson loop corrections on the Yang-Mills potential.Comment: 11 pages, 5 figures. Updated version contains clarifications and
several new references. Accepted for publication in Physical Review
Regular solutions in -Yang-Mills theory
We consider extended covariant teleparallel gravity whose action is
analytic in the torsion scalar and which is sourced by an valued
Yang-Mills field. Specifically, we search for regular solutions to the coupled
Yang-Mills system. For we, not surprisingly, recover the
Bartnik-McKinnon solitons of Einstein Yang-Mills theory. However, interesting
effects are discovered with the addition of terms in the action which are
nonlinear in the torsion scalar, which we specifically study up to cubic order.
With the addition of the nonlinear terms the number of regular solutions
becomes finite. As well, beyond critical values of the coupling constants we
find that there exist \emph{no} regular solutions. These behaviors are
asymmetric with respect to the sign of the nonlinear coupling constants and the
elimination of regular solutions turns out to be extremely sensitive to the
presence of the cubic coupling. It may be possible, therefore, that with
sufficiently high powers of torsion in the action, there may be no regular
Yang-Mills static solutions.Comment: 12 pages, 8 figures. v2: Typographical errors corrected. Accepted for
publication in Physical Review
Junction Conditions for F(T) Gravity from a Variational Principle
We derive a general set of acceptable junction conditions for gravity
via the variational principle. The analysis is valid for both the traditional
form of gravity theory as well as the more recently introduced Lorentz
covariant theory of Kr\v{s}\v{s}\'ak and Saridakis. We find that the general
junction conditions derived, when applied to simple cases such as highly
symmetric static or time dependent geometries (such as spherical symmetry)
imply both the Synge junction conditions as well as the
Israel-Sen-Lanczos-Darmois junction conditions of General Relativity. In more
complicated scenarios the junction conditions derived do not generally imply
the well-known junction conditions of General Relativity. However, the
junctions conditions of de la Cruz-Dombriz, Dunsby, and S\'aez-G\'omez make up
an interesting subset of this more general case.Comment: 14 pages, 1 figure. Updated version contains clarification on the
role of the spin connection and a number of added references. Matches version
accepted for publication in Phys. Rev.
Shape minimization problems in liquid crystals
We consider a class of liquid crystal free-boundary problems for which both
the equilibrium shape and internal configuration of a system must
simultaneously be determined, for example in films with air- or fluid-liquid
crystal interfaces and elastomers. We develop a finite element algorithm to
solve such problems with dynamic mesh control, achieved by supplementing the
free energy with an auxiliary functional that promotes mesh quality and is
minimized in the null space of the energy. We apply this algorithm to a
flexible capacitor, as well as to determine the shape of liquid crystal
tactoids as a function of the surface tension and elastic constants. These are
compared with theoretical predictions and experimental observations of tactoids
from the literature.Comment: 9 pages, 7 figure
Topology and Volume Effects in Quantum Gravity: Wheeler-DeWitt Theory
We consider the quantization of space-times which can possess different
topologies within a symmetry reduced version of Wheeler-DeWitt theory. The
quantum states are defined from a natural decomposition as an outer-product of
a topological state, dictating the topology of the two-surfaces of the
space-time, and a geometric state, which controls the geometry and is comprised
of solutions to the Wheeler-DeWitt constraints. Within this symmetry reduced
theory an eigenvalue equation is derived for the two-volume of spacetime, which
for spherical topology is fixed to a value of . However, for the other
topologies it is found that the spectrum can be \emph{discrete} and hence the
universe, if in one of these other topological states, may only possess certain
possible values for the two-volume, whereas classically all values are allowed.
We analyze this result in the context of pure gravity (black holes).Comment: 15 pages, 5 figures. New version has some clarifications and minor
typographical corrections. Updated version also includes a short appendix on
the geometry and topology of the sub-spaces. Matches version accepted for
publication in Classical and Quantum Gravit
Non-commutative black holes of various genera in the connection formalism
We consider black hole interiors of arbitrary genus number within the
paradigm of non-commutative geometry. The study is performed in two ways: One
way is a simple smearing of a matter distribution within the black hole. The
resulting structure is often known in the literature as a "model inspired by
non-commutative geometry". The second method involves a more fundamental
approach, in which the Hamiltonian formalism is utilized and a non-trivial
Poisson bracket is introduced between the configuration degrees of freedom, as
well as between the canonical momentum degrees of freedom. This is done in
terms of connection variables instead of the more common ADM variables.
Connection variables are utilized here since non-commutative effects are
usually inspired from the quantum theory, and it is the connection variables
that are used in some of the more promising modern theories of quantum gravity.
We find that in the first study, the singularity of the black holes can easily
be removed. In the second study, we find that introducing a non-trivial bracket
between the connections (the configuration variables) may delay the
singularity, but not necessarily eliminate it. However, by introducing a
non-trivial bracket between the densitized triads (the canonical momentum
variables) the singularity can generally be removed. In some cases, new
horizons also appear due to the non-commutativity.Comment: 14 pages. Version 2 has included extra references, and some
typographical corrections. Matches version accepted for publication in
Physical Review
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