arXiv subjects

Robert B. Mann

Publications and source records attributed to Robert B. Mann.

At least 343 records · Page 19Linked to original sources

arXiv2008

On the Stress Tensor for Asymptotically Flat Gravity

The recent introduction of a boundary stress tensor for asymptotically flat spacetimes enabled a new construction of energy, momentum, and Lorentz charges. These charges are known to generate the asymptotic symmetries of the theory, but their explicit formulas are not identical to previous constructions in the literature. This paper corrects an earlier comparison with other approaches, including terms in the definition of the stress tensor charges that were previously overlooked. We show that these terms either vanish identically (for d > 4) or take a form that does not contribute to the conserved charges (for d=4). This verifies the earlier claim that boundary stress tensor methods for asymptotically flat spacetimes yield the same conserved charges as other approaches. We also derive some additional connections between the boundary stress tensor and the electric part of the Weyl tensor.

hep-th↗

arXiv2006

General Relativity and Quantum Mechanics: Towards a Generalization of the Lambert W Function

Herein, we present a canonical form for a natural and necessary generalization of the Lambert W function, natural in that it requires minimal mathematical definitions for this generalization, and necessary in that it provides a means of expressing solutions to a number of physical problems of fundamental nature. In particular, this generalization expresses the exact solutions for general-relativistic self-gravitating 2-body and 3-body systems in one spatial and one time dimension. It also expresses the solution to a previously unknown mathematical link between the lineal gravity problem and the Schroedinger equation.

math-ph↗

arXiv2006

Nonabelian solutions in AdS_4 and d=11 supergravity

We consider solutions of the four dimensional Einstein-Yang-Mills system with a negative cosmological constant $Λ=-3g^2$, where $g$ is the nonabelian gauge coupling constant. This theory corresponds to a consistent truncation of ${\cal N}=4$ gauged supergravity and may be uplifted to $d=11$ supergravity. A systematic study of all known solutions is presented as well as new configurations corresponding to rotating regular dyons and rotating nonabelian black holes. The thermodynamics of the static black hole solutions is also discussed. The generic EYM solutions present a nonvanishing magnetic flux at infinity and should give us information about the structure of a CFT in a background SU(2) field. We argue that the existence of these configurations violating the no hair conjecture is puzzling from the AdS/CFT point of view.

hep-th↗

arXiv2006

Note on counterterms in asymptotically flat spacetimes

We consider in more detail the covariant counterterm proposed by Mann and Marolf in asymptotically flat spacetimes. With an eye to specific practical computations using this counterterm, we present explicit expressions in general $d$ dimensions that can be used in the so-called `cylindrical cut-off' to compute the action and the associated conserved quantities for an asymptotically flat spacetime. As applications, we show how to compute the action and the conserved quantities for the NUT-charged spacetime and for the Kerr black hole in four dimensions.

hep-th↗

arXiv2006

Black hole formation in the head-on collision of ultrarelativistic charges

We study black hole formation in the head-on collision of ultrarelativistic charges. The metric of charged particles is obtained by boosting the Reissner-Nordström spacetime to the speed of light. Using the slice at the instant of collision, we study formation of the apparent horizon (AH) and derive a condition indicating that a critical value of the electric charge is necessary for formation to take place. Evaluating this condition for characteristic values at the LHC, we find that the presence of charge decreases the black hole production rate in accelerators. We comment on possible limitations of our approach.

gr-qc↗

arXiv2006

Covariant Counterterms and Conserved Charges in Asymptotically Flat Spacetimes

Recent work has shown that the addition of an appropriate covariant boundary term to the gravitational action yields a well-defined variational principle for asymptotically flat spacetimes and thus leads to a natural definition of conserved quantities at spatial infinity. Here we connect such results to other formalisms by showing explicitly i) that for spacetime dimension $d \ge 4$ the canonical form of the above-mentioned covariant action is precisely the ADM action, with the familiar ADM boundary terms and ii) that for $d=4$ the conserved quantities defined by counter-term methods agree precisely with the Ashtekar-Hansen conserved charges at spatial infinity.

gr-qc↗

arXiv2006

Black string solutions with negative cosmological constant

We present arguments for the existence of new black string solutions with negative cosmological constant. These higher-dimensional configurations have no dependence on the `compact' extra dimension, and their conformal infinity is the product of time and $S^{d-3}\times R$ or $H^{d-3}\times R$. The configurations with an event horizon topology $S^{d-2}\times S^1$ have a nontrivial, globally regular limit with zero event horizon radius. We discuss the general properties of such solutions and, using a counterterm prescription, we compute their conserved charges and discuss their thermodynamics. Upon performing a dimensional reduction we prove that the reduced action has an effective $SL(2,R)$ symmetry. This symmetry is used to construct non-trivial solutions of the Einstein-Maxwell-Dilaton system with a Liouville-type potential for the dilaton in $(d-1)$-dimensions.

hep-th↗

arXiv2006

Nuttier Bubbles

We construct new explicit solutions of general relativity from double analytic continuations of Taub-NUT spacetimes. This generalizes previous studies of 4-dimensional nutty bubbles. One 5-dimensional locally asymptotically AdS solution in particular has a special conformal boundary structure of $AdS_3\times S^1$. We compute its boundary stress tensor and relate it to the properties of the dual field theory. Interestingly enough, we also find consistent 6-dimensional bubble solutions that have only one timelike direction. The existence of such spacetimes with non-trivial topology is closely related to the existence of the Taub-NUT(-AdS) solutions with more than one NUT charge. Finally, we begin an investigation of generating new solutions from Taub-NUT spacetimes and nuttier bubbles. Using the so-called Hopf duality, we provide new explicit time-dependent backgrounds in six dimensions.

hep-th↗

arXiv2006

Holographic Renormalization of Asymptotically Flat Spacetimes

A new local, covariant ``counter-term'' is used to construct a variational principle for asymptotically flat spacetimes in any spacetime dimension $ d \ge 4$. The new counter-term makes direct contact with more familiar background subtraction procedures, but is a local algebraic function of the boundary metric and Ricci curvature. The corresponding action satisfies two important properties required for a proper treatment of semi-classical issues and, in particular, to connect with any dual non-gravitational description of asymptotically flat space. These properties are that 1) the action is finite on-shell and 2) asymptotically flat solutions are stationary points under {\it all} variations preserving asymptotic flatness; i.e., not just under variations of compact support. Our definition of asymptotic flatness is sufficiently general to allow the magentic part of the Weyl tensor to be of the same order as the electric part and thus, for d=4, to have non-vanishing NUT charge. Definitive results are demonstrated when the boundary is either a cylindrical or a hyperbolic (i.e., de Sitter space) representation of spacelike infinity ($i^0$), and partial results are provided for more general representations of $i^0$. For the cylindrical or hyperbolic representations of $i^0$, similar results are also shown to hold for both a counter-term proportional to the square-root of the boundary Ricci scalar and for a more complicated counter-term suggested previously by Kraus, Larsen, and Siebelink. Finally, we show that such actions lead, via a straightforward computation, to conserved quantities at spacelike infinity which agree with, but are more general than, the usual (e.g., ADM) results.

hep-th↗

arXiv2005

On the gravitational energy of the Kaluza Klein monopole

We use local counterterm prescriptions for asymptotically flat space to compute the action and conserved quantities in five-dimensional Kaluza-Klein theories. As an application of these prescriptions we compute the mass of the Kaluza-Klein magnetic monopole. We find consistent results with previous approaches that employ a background subtraction.

hep-th↗

arXiv2005

New Taub-NUT-Reissner-Nordström spaces in higher dimensions

We construct new charged solutions of the Einstein-Maxwell field equations with cosmological constant. These solutions describe the nut-charged generalisation of the higher dimensional Reissner-Nordström spacetimes. For a negative cosmological constant these solutions are the charged generalizations of the topological nut-charged black hole solutions in higher dimensions. Finally, we discuss the global structure of such solutions and possible applications.

hep-th↗

arXiv2005

New Multiply Nutty Spacetimes

We construct new solutions of the vacuum Einstein field equations with multiple NUT parameters, with and without cosmological constant. These solutions describe spacetimes with non-trivial topology that are asymptotically dS, AdS or flat. We also find the the multiple nut parameter extension of the inhomogeneous Einstein metrics on complex line bundles found recently by Lu, Page and Pope. We also provide a more general form of the Eguchi-Hanson solitons found by Clarkson and Mann. We discuss the global structure of such solutions and possible applications in string theory.

hep-th↗

arXiv2005

Ghost Condensation in the Brane-World

Motivated by the ghost condensate model, we study the Randall-Sundrum (RS) brane-world with an arbitrary function of the higher derivative kinetic terms, $\mathcal{P}(X)$, where $X=-(\nabla ϕ)^{2}$. The five-dimensional Einstein equations reduce to two equations of motion with a constraint between $\mathcal{P}(X)$ and the five-dimensional cosmological constant on the brane. For a static extra dimension, $\mathcal{P}(X)$ has solutions for both a negative kinetic scalar (so called {\textit{ghost}}) as well as an ordinary scalar field. However ghost condensation cannot take place. We show that small perturbations along the extra dimensional radius (the radion) can give rise to ghost condensation. This produces a radiation-dominated universe and the vanishing cosmological constant at late times but destabilizes the radion. This instability can be resolved by an inclusion of bulk matter along $y$-direction, which finally presents a possible explanation of the late-time cosmic acceleration.

hep-th↗

arXiv2005

Generation of Cosmological Seed Magnetic Fields from Inflation with Cutoff

Inflation has the potential to seed the galactic magnetic fields observed today. However, there is an obstacle to the amplification of the quantum fluctuations of the electromagnetic field during inflation: namely the conformal invariance of electromagnetic theory on a conformally flat underlying geometry. As the existence of a preferred minimal length breaks the conformal invariance of the background geometry, it is plausible that this effect could generate some electromagnetic field amplification. We show that this scenario is equivalent to endowing the photon with a large negative mass during inflation. This effective mass is negligibly small in a radiation and matter dominated universe. Depending on the value of the free parameter of the theory, we show that the seed required by the dynamo mechanism can be generated. We also show that this mechanism can produce the requisite galactic magnetic field without resorting to a dynamo mechanism.

gr-qc↗

arXiv2005

Geons with spin and charge

We construct new geon-type black holes in D>3 dimensions for Einstein's theory coupled to gauge fields. A static nondegenerate vacuum black hole has a geon quotient provided the spatial section admits a suitable discrete isometry, and an antisymmetric tensor field of rank 2 or D-2 with a pure F^2 action can be included by an appropriate (and in most cases nontrivial) choice of the field strength bundle. We find rotating geons as quotients of the Myers-Perry(-AdS) solution when D is odd and not equal to 7. For other D we show that such rotating geons, if they exist at all, cannot be continuously deformed to zero angular momentum. With a negative cosmological constant, we construct geons with angular momenta on a torus at the infinity. As an example of a nonabelian gauge field, we show that the D=4 spherically symmetric SU(2) black hole admits a geon version with a trivial gauge bundle. Various generalisations, including both black-brane geons and Yang-Mills theories with Chern-Simons terms, are briefly discussed.

gr-qc↗

arXiv2005

Breakdown of the Entropy/Area Relationship for NUT-charged Spacetimes

We demonstrate that $(D+1)$-dimensional, locally asymptotically anti-deSitter spacetimes with nonzero NUT charge generically do not respect the usual relationship between area and entropy. This result does not depend on either the existence of closed timelike curves nor on the removal of Misner string singularities, but instead is a consequence of the first law of thermodynamics.

hep-th↗

arXiv2005

A note on spherically symmetric naked singularities in general dimension

We discuss generalizations of the recent theorem by Dafermos (hep-th/0403033) forbidding a certain class of naked singularities in the spherical collapse of a scalar field. Employing techniques similar to the ones Dafermos used, we consider extending the theorem (1) to higher dimensions, (2) by including more general matter represented by a stress-energy tensor satisfying certain assumptions, and (3) by replacing the spherical geometry by a toroidal or higher genus (locally hyperbolic) one. We show that the extension to higher dimensions and a more general topology is straightforward; on the other hand, replacing the scalar field by a more general matter content forces us to shrink the class of naked singularities we are able to exclude. We then show that the most common matter theories (scalar field interacting with a non-abelian gauge field and a perfect fluid satisfying certain conditions) obey the assumptions of our weaker theorem, and we end by commenting on the applicability of our results to the five-dimensional AdS scenarii considered recently in the literature.

gr-qc↗

arXiv2004

Nut Charged Space-times and Closed Timelike Curves on the Boundary

We consider higher dimensional generalizations of the four dimensional topological Taub-NUT-AdS solutions, where the angular spheres are replaced by planes and hyperboloids. The thermodynamics of these configurations is discussed to some extent. The results we find suggest that the entropy/area relation is always violated in the presence of a NUT charge. We argue also that the conjectured AdS/CFT correspondence may teach us something about the physics in spacetimes containing closed timelike curves. To this aim, we use the observation that the boundary metric of a (D+1)-dimensional Taub-NUT-AdS solution provides a D-dimensional generalization of the known Gödel-type spacetimes.

hep-th↗