arXiv subjects
Publications and source records attributed to A. DeBenedictis.
Several aspects of the 4d imprint of the 5d bulk Weyl radiation are investigated within a recently proposed model solution. It is shown that the solution has a number of physically interesting properties. The constraints on the model imposed by combined measurements of rotation curve and lensing are discussed. A brief comparison with a well known scalar field model is also given.
This paper presents a brief overview on the issue of singularity resolution in loop quantum gravity presented at the Theory Canada IV conference at the Centre de Recherches Mathématiques at the Université de Montréal (June 4-7, 2008). The intended audience is theoretical physicists who are non-specialist in the field and therefore much of the technical detail is omitted here. Instead, a brief review of loop quantum gravity is presented, followed by a survey of previous and current work on results concerning the resolution of the classical black hole singularity within loop quantum gravity.
Using the improved quantization technique to the mini-superspace approximation of loop quantum gravity, we study the evolution of black holes supported by a cosmological constant. The addition of a cosmological constant allows for classical solutions with planar, cylindrical, toroidal and higher genus black holes. Here we study the quantum analog of these space-times. In all scenarios studied, the singularity present in the classical counter-part is avoided in the quantized version and is replaced by a bounce, and in the late evolution, a series of less severe bounces. Interestingly, although there are differences during the evolution between the various symmetries and topologies, the evolution on the other side of the bounce asymptotes to space-times of Nariai-type, with the exception of the planar black hole analyzed here, whose $T$-$R$=constant subspaces seem to continue expanding in the long term evolution. For the other cases, Nariai-type universes are attractors in the quantum evolution, albeit with different parameters. We study here the quantum evolution of each symmetry in detail.
In the present investigation flat rotational curves of the galaxies are considered under the framework of brane-world models where the 4d effective Einstein equation has extra terms which arise from the embedding of the 3-brane in the $5d$ bulk. It has been shown here that these long range bulk gravitational degrees of freedom can act as a mechanism to yield the observed galactic rotation curves without the need for dark matter. The present model has the advantage that the observed rotation curves result solely from well-established non-local effects of gravitation, such as dark radiation and dark pressure under a direct use of the condition of flat rotation curves and does not invoke any exotic matter field.
The possible existence of black holes has fascinated scientists at least since Michell and Laplace's proposal that a gravitating object could exist from which light could not escape. In the 20th century, in light of the general theory of relativity, it became apparent that, were such objects to exist, their structure would be far richer than originally imagined. Today, astronomical observations strongly suggest that either black holes, or objects with similar properties, not only exist but may well be abundant in our universe. In light of this, black hole research is now not only motivated by the fascinating theoretical properties such objects must possess but also as an attempt to better understand the universe around us. We review here some selected developments in black hole research, from a review of its early history to current topics in black hole physics research. Black holes have been studied at all levels; classically, semi-classically, and more recently, as an arena to test predictions of candidate theories of quantum gravity. We will review here progress and current research at all these levels as well as discuss some proposed alternatives to black holes.
In the context of loop quantum gravity, we construct the phase-space of isolated horizons with genus greater than 0. Within the loop quantum gravity framework, these horizons are described by genus g surfaces with N punctures and the dimension of the corresponding phase-space is calculated including the genus cycles as degrees of freedom. From this, the black hole entropy can be calculated by counting the microstates which correspond to a black hole of fixed area. We find that the leading term agrees with the A/4 law and that the sub-leading contribution is modified by the genus cycles.
We study the gravitational vacuum star (gravastar) configuration as proposed by other authors in a model where the interior de Sitter spacetime segment is continuously extended to the exterior Schwarzschild spacetime. The multilayered structure in previous papers is replaced by a continuous stress-energy tensor at the price of introducing anisotropy in the (fluid) model of the gravastar. Either with an ansatz for the equation of state connecting the radial $p_r$ and tangential $p_t$ pressure or with a calculated equation of state with non-homogeneous energy/fluid density, solutions are obtained which in all aspects satisfy the conditions expected for an anisotropic gravastar. Certain energy conditions have been shown to be obeyed and a polytropic equation of state has been derived. Stability of the solution with respect to possible axial perturbation is shown to hold.
In this introductory review article, we explore the special relativistic equations of particle motions and the consequent derivation of Einstein's famous formula $E=mc^2$. Next, we study the special relativistic electromagnetic field equations and generalizations of Lorentz equations of motion for charged particles. We then introduce the special relativistic gravitational field as a symmetric second order tensor field. Particle motions in the presence of static gravity are explored which could be used to study planetary dynamics, revealing perihelion shifts. Next, we investigate the system of consisting of pressureless plasmas and neutral perfect fluids coupled to the gravitational field. In that arena, we derive the relativistic Euler equation. Finally, we investigate the relativistic dynamics of a perfect fluid plasma and extensions to viscous flow and derive the relativistic Navier-Stokes equation.
We consider wormhole geometries subject to a gravitational action consisting of non-linear powers of the Ricci scalar. Specifically, wormhole throats are studied in the case where Einstein gravity is supplemented with a Ricci-squared and inverse Ricci term. In this modified theory it is found that static wormhole throats respecting the weak energy condition can exist. The analysis is done locally in the vicinity of the throat, which eliminates certain restrictions on the models introduced by considering the global topology.
The system consisting of a self gravitating perfect fluid and scalar field is considered in detail. The scalar fields considered are the quintessence and ``tachyonic'' forms which have important application in cosmology. Mathematical properties of the general system of equations are studied including the algebraic and differential identities as well as the eigenvalue structure. The Cauchy problem for both quintessence and the tachyon is presented. We discuss the initial constraint equations which must be satisfied by the initial data. A Cauchy evolution scheme is presented in the form of a Taylor series about the Cauchy surface. Finally, a simple numerical example is provided to illustrate this scheme.
A cosmology is considered driven by a stress-energy tensor consisting of a perfect fluid, an inhomogeneous pressure term (which we call a ``tachyonic dust'' for reasons which will become apparent) and a cosmological constant. The inflationary, radiation dominated and matter dominated eras are investigated in detail. In all three eras, the tachyonic pressure decreases with increasing radius of the universe and is thus minimal in the matter dominated era. The gravitational effects of the dust, however, may still strongly affect the universe at present time. In case the tachyonic pressure is positive, it enhances the overall matter {\em density} and is a candidate for dark matter. In the case where the tachyonic pressure is negative, the recent acceleration of the universe can be understood without the need for a cosmological constant. The ordinary matter, however, has positive energy density at all times. In a later section, the extension to a variable cosmological term is investigated and a specific model is put forward such that recent acceleration and future re-collapse is possible.
Einstein's spherically symmetric interior gravitational equations are investigated. Following Synge's procedure, the most general solution of the equations is furnished in case $T^{1}_{1}$ and $T^{4}_{4}$ are prescribed. The existence of a total mass function, $M(r,t)$, is rigorously proved. Under suitable restrictions on the total mass function, the Schwarzschild mass $M(r,t)=m$, implicitly defines the boundary of the spherical body as $r=B(t)$. Both Synge's junction conditions as well as the continuity of the second fundamental form are examined and solved in a general manner. The weak energy conditions for an \emph{arbitrary boost} are also considered. The most general solution of the spherically symmetric anisotropic fluid model satisfying both junction conditions is furnished. In the final section, various exotic solutions are explored using the developed scheme including gravitational instantons, interior $T$-domains and $D$-dimensional generalizations.
This paper studies wormhole solutions to Einstein gravity with an arbitrary number of time dependent compact dimensions and a matter-vacuum boundary. A new gauge is utilized which is particularly suited for studies of the wormhole throat. The solutions possess arbitrary functions which allow for the description of infinitely many wormhole systems of this type and, at the stellar boundary, the matter field is smoothly joined to vacuum. It turns out that the classical vacuum structure differs considerably from the four dimensional theory and is therefore studied in detail. The presence of the vacuum-matter boundary and extra dimensions places interesting restrictions on the wormhole. For example, in the static case, the radial size of a weak energy condition (WEC) respecting throat is restricted by the extra dimensions. There is a critical dimension, D=5, where this restriction is eliminated. In the time dependent case, one \emph{cannot} respect the WEC at the throat as the time dependence actually tends the solution towards WEC violation. This differs considerably from the static case and the four dimensional case.
We study spherically symmetric solutions to the Einstein field equations under the assumption that the space-time may possess an arbitrary number of spatial dimensions. The general solution of Synge is extended to describe systems of any dimension. Arbitrary dimension analogues of known four dimensional solutions are also presented, derived using the above scheme. Finally, we discuss the requirements for the existence of Birkhoff's theorems in space-times of arbitrary dimension with or without matter fields present. Cases are discussed where the assumptions of the theorem are considerably weakened yet the theorem still holds. We also discuss where the weakening of certain conditions may cause the theorem to fail.
Black hole interiors (the $T$-domain) are studied here in great detail. Both the {\em general} and particular $T$-domain solutions are presented including non-singular ones. Infinitely many local $T$-domain solutions may be modeled with this scheme. The duality between the $T$ and $R$ domains is presented. It is demonstrated how generally well behaved $R$-domain solutions will give rise to exotic phases of matter when collapsed inside the event horizon. However, as seen by an external observer, the field is simply that of the Schwarzschild vacuum with well behaved mass term and no evidence of this behaviour may be observed. A singularity theorem is also presented which is independent of energy conditions.
A general class of solutions is obtained which describe a spherically symmetric wormhole system. The presence of arbitrary functions allows one to describe infinitely many wormhole systems of this type. The source of the stress-energy supporting the structure consists of an anisotropic brown dwarf ``star'' which smoothly joins the vacuum and may possess an arbitrary cosmological constant. It is demonstrated how this set of solutions allows for a non-zero energy density and therefore allows positive stellar mass as well as how violations of energy conditions may be minimized. Unlike examples considered thus far, emphasis here is placed on construction by manipulating the matter field as opposed to the metric. This scheme is generally more physical than the purely geometric method. Finally, explicit examples are constructed including an example which demonstrates how multiple closed universes may be connected by such wormholes. The number of connected universes may be finite or infinite.
We calculate, in the context of higher dimensional gravity, the stress-energy tensor and Weyl anomaly associated with anti-de Sitter and anti-de Sitter black hole solutions. The boundary counter-term method is used to regularize the action and the resulting stress-energy tensor yields both the correct black hole energies as well as a vacuum energy contribution which is interpreted as a Casimir energy. This calculation is done up to d = 8 (d being the boundary dimension). We confirm some results for d < 8 as well as comment on some new results (some of which are relevant to (2,0) theory). All results for d=8 are new.
The gravitational back-reaction is calculated for the conformally invariant scalar field within a black cosmic string interior with cosmological constant. Using the perturbed metric, the gravitational effects of the quantum field are calculated. It is found that the perturbations initially strengthen the singularity. This effect is similar to the case of spherical symmetry (without cosmological constant). This indicates that the behaviour of quantum effects may be universal and not dependent on the geometry of the spacetime nor the presence of a non-zero cosmological constant.