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 $\mathbb{E}_{3}$ where the potential is singular but invariant under the continuous inhomogeneous orthogonal group $\mathcal{I}O(3)$. 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 $\mathcal{I}O(3)$ 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 $\mathcal{I}O(3)$. (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 $\mathcal{I}O(3)$, 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 $R\times S^{2}$. Beyond the bounce the magnitude of the Yang-Mills electric field asymptotically grows monotonically. This results in an ever expanding $R$ 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 f(T)f(T)-Yang-Mills theory

We consider extended covariant teleparallel $(f(T))$ gravity whose action is analytic in the torsion scalar and which is sourced by an $su(2)$ valued Yang-Mills field. Specifically, we search for regular solutions to the coupled $f(T)$ Yang-Mills system. For $f(T)=T$ 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 $F(T)$ gravity via the variational principle. The analysis is valid for both the traditional form of $F(T)$ 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 $4\pi$. 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