Papers by Andrew DeBenedictis
The General Theory of Relativity, 2012
International Journal of Geometric Methods in Modern Physics
In this paper, we introduce a new geometric/topological approach to the emerging braneworld scena... more In this paper, we introduce a new geometric/topological approach to the emerging braneworld scenario in the context of D-branes using partially negative-dimensional product (PNDP) manifolds. The working hypothesis is based on the fact that the orientability of PNDP manifolds can be arbitrary, and starting from this, we propose that gravitational interaction can derive naturally from the non-orientability. According to this hypothesis, we show that topological defects can emerge from non-orientability and they can be identified as gravitational interaction at macroscopic level. In other words, the orientability of fundamental PNDPs can be related to the appearance of curvature at low-energy scales.
Canadian Journal of Physics, Mar 1, 2009
This paper presents a brief overview on the issue of singularity resolution in loop quantum gravi... more 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. Résumé Nous présentons une brève revue portant sur la résolution du problème de singularité en gravité quantiqueà boucles, destinéeà la conférence Théorie Canada 4 tenue au Centre de Recherches Mathématiques de l'Université de Montréal (4-7 juin 2008). L'audience visée est celle de physiciens théoriques qui ne sont pas spécialistes du domaine et par conséquent, nous omettons la plupart des détails techniques.À la place, nous prsentons une brève revue de la gravité quantiqueà boucles, suivie dun survol des résultats antérieurs et présents concernant la résolution de la singularité classique du trou noir dans le cadre de la gravité quantiqueà boucles.
Springer eBooks, 2012
We shall provide here a brief review of the special theory of relativity. Since the emphasis of t... more We shall provide here a brief review of the special theory of relativity. Since the emphasis of this book is general relativity, we will state some of the results in this section without proof, for future application. For more details, the reader is referred to the references provided within this chapter.
arXiv (Cornell University), Jul 5, 2009
This paper presents a brief overview on the issue of singularity resolution in loop quantum gravi... more 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. Résumé Nous présentons une brève revue portant sur la résolution du problème de singularité en gravité quantiqueà boucles, destinéeà la conférence Théorie Canada 4 tenue au Centre de Recherches Mathématiques de l'Université de Montréal (4-7 juin 2008). L'audience visée est celle de physiciens théoriques qui ne sont pas spécialistes du domaine et par conséquent, nous omettons la plupart des détails techniques.À la place, nous prsentons une brève revue de la gravité quantiqueà boucles, suivie dun survol des résultats antérieurs et présents concernant la résolution de la singularité classique du trou noir dans le cadre de la gravité quantiqueà boucles.
arXiv (Cornell University), Feb 7, 2007
In the context of loop quantum gravity, we construct the phase-space of the isolated horizon with... more In the context of loop quantum gravity, we construct the phase-space of the isolated horizon with toroidal topology. Within the loop quantum gravity framework, this horizon is described by a torus with $N$ punctures and the dimension of the corresponding phase-space is calculated including the toroidal 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 toroidal cycles.
arXiv (Cornell University), Mar 10, 2005
In this introductory review article, we explore the special relativistic equations of particle mo... more 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.
arXiv (Cornell University), Nov 9, 1999
We calculate, in the context of higher dimensional gravity, the stress-energy tensor and Weyl ano... more 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. All results for d = 8 are new.
The General Theory of Relativity, 2012
We shall provide here a brief review of the special theory of relativity. Since the emphasis of t... more We shall provide here a brief review of the special theory of relativity. Since the emphasis of this book is general relativity, we will state some of the results in this section without proof, for future application. For more details, the reader is referred to the references provided within this chapter.
arXiv: Mathematical Physics, 2005
In this introductory review article, we explore the special relativistic equations of particle mo... more 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.
Physical Review D
In this paper we study properties that the vacuum must possess in the minimal extension to the te... more In this paper we study properties that the vacuum must possess in the minimal extension to the teleparallel equivalent of general relativity (TEGR) where the action is supplemented with a quadratic torsion term. No assumption is made about the weakness of the quadratic term although in the weak-field regime the validity of our previously derived perturbative solution is confirmed. Regarding the exact nature of the vacuum, it is found that if the center of symmetry is to be regular, the mathematical conditions on the tetrad at the isotropy point mimic those of general relativity. With respect to horizons it is found that, under very mild assumptions, a smooth horizon cannot exist unless the quadratic torsion coupling, , vanishes, which is the TEGR limit (with the Schwarzschild tetrad as its solution). This analysis is then supplemented with computational work utilizing asymptotically Schwarzschild boundary data. It is verified that in no case studied does a smooth horizon form. For > 0 naked singularities occur which break down the equations of motion before a horizon can form. For < 0 there is a limited range of where a vacuum horizon might exist but, if present, the horizon is singular. Therefore physically acceptable black hole horizons are problematic in the studied theory at least within the realm of vacuum static spherical symmetry. These results also imply that static spherical matter distributions generally must have extra restrictions on their spatial extent and stress-energy bounds so as to render the vacuum solution invalid in the singular region and make the solutions finite.
arXiv: General Relativity and Quantum Cosmology, 2017
A five-dimensional gravity theory, motivated by the brane-world picture, with Kaluza scalar $g_{5... more A five-dimensional gravity theory, motivated by the brane-world picture, with Kaluza scalar $g_{55}(r); r=\sqrt{x^2+y^2+z^2}$, is considered near the singularity (small scales where gravity is strong) and is shown to give rise to a positive contribution to the Raychaudhuri equation. This inhibits the focussing of geodesics and contributes to non - focussing of the geodesics. It is also shown that the results extend to time dependent cases such as those relevant for black hole interiors and cosmology.
Physical Review D, 2018
We consider extended covariant teleparallel (f (T)) gravity whose action is analytic in the torsi... more 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 , not surprisingly, the Bartnik-McKinnon solitons of Einstein Yang-Mills theory are recovered. However, interesting effects are discovered with the addition of terms in the action which are nonlinear in the torsion scalar, which are specifically studied 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 it is found that there exist 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.
Physical Review D, 2018
In this brief paper we study the homogeneous interiors of black holes possessing SU(2) Yang-Mills... more In this brief 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 × 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.
This paper presents a brief but comprehensive introduction to certain mathematical techniques in ... more 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. Conventions The following notation is used: The metric tensor, g µν , has a signature of +2 and g = |det (g µν)|. Semicolons denote covariant derivatives while commas represent ordinary derivatives.
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Papers by Andrew DeBenedictis