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Gary W. Gibbons

Publications and source records attributed to Gary W. Gibbons.

At least 37 records · Page 2Linked to original sources
arXiv2009

Gravitating Opposites Attract

Generalizing previous work by two of us, we prove the non-existence of certain stationary configurations in General Relativity having a spatial reflection symmetry across a non-compact surface disjoint from the matter region. Our results cover cases such that of two symmetrically arranged rotating bodies with anti-aligned spins in $n+1$ ($n \geq 3$) dimensions, or two symmetrically arranged static bodies with opposite charges in 3+1 dimensions. They also cover certain symmetric configurations in (3+1)-dimensional gravity coupled to a collection of scalars and abelian vector fields, such as arise in supergravity and Kaluza-Klein models. We also treat the bosonic sector of simple supergravity in 4+1 dimensions.

gr-qc↗
arXiv2009

The Bernstein Conjecture, Minimal Cones, and Critical Dimensions

Minimal surfaces and domain walls play important roles in various contexts of spacetime physics as well as material science. In this paper, we first review the Bernstein conjecture, which asserts that a plane is the only globally well defined solution of the minimal surface equation which is a single valued graph over a hyperplane in flat spaces, and its failure in higher dimensions. Then, we review how minimal cones in four- and higher-dimensional spacetimes, which are curved and even singular at the apex, may be used to provide counterexamples to the conjecture. The physical implications of these counterexamples in curved spacetimes are discussed from various points of view, ranging from classical general relativity, brane physics, and holographic models of fundamental interactions.

hep-th↗
arXiv2009

Gravitational Dual of Tachyon Condensation

We study a system of N D3-branes in which open string tachyons survive in the low energy alpha' -> 0 limit. We compute the height of the tachyon potential both in the weak and strong couplings by using N=4 super Yang-Mills and the dual AdS_5 descriptions respectively. We find an exact agreement between the two descriptions in the large N limit. This provides an example of gravitational duals of open string tachyon condensation.

hep-th↗
arXiv2009

Deformed General Relativity and Torsion

We argue that the natural framework for embedding the ideas of deformed, or doubly, special relativity (DSR) into a curved spacetime is a generalisation of Einstein-Cartan theory, considered by Stelle and West. Instead of interpreting the noncommuting "spacetime coordinates" of the Snyder algebra as endowing spacetime with a fundamentally noncommutative structure, we are led to consider a connection with torsion in this framework. This may lead to the usual ambiguities in minimal coupling. We note that observable violations of charge conservation induced by torsion should happen on a time scale of 10^3 s, which seems to rule out these modifications as a serious theory. Our considerations show, however, that the noncommutativity of translations in the Snyder algebra need not correspond to noncommutative spacetime in the usual sense.

gr-qc↗
arXiv2009

Naturalness of CP Violation in the Standard Model

We construct a natural measure on the space of CKM matrices in the standard model, assuming the fermion mass matrices are randomly selected from a distribution which fits the observed quark mass hierarchy. This measure allows us to assess the likelihood of Jarlskog's CP violation parameter J taking its observed value J $\approx$ 3 x 10^{-5}. While well below the mathematically allowed maximum, we find that this value is in fact typical, once the observed quark masses are assumed.

hep-ph↗
arXiv2009

Measures on Mixing Angles

We address the problem of the apparently very small magnitude of CP violation in the standard model, measured by the Jarlskog invariant J. In order to make statements about probabilities for certain values of J, we seek to find a natural measure on the space of Kobayashi-Maskawa matrices, the double quotient U(1)^2\SU(3)/U(1)^2. We review several possible, geometrically motivated choices of the measure, and compute expectation values for powers of J for these measures. We find that different choices of the measure generically make the observed magnitude of CP violation appear finely tuned. Since the quark masses and the mixing angles are determined by the same set of Yukawa couplings, we then do a second calculation in which we take the known quark mass hierarchy into account. We construct the simplest measure on the space of 3 x 3 Hermitian matrices which reproduces this known hierarchy. Calculating expectation values for powers of J in this second approach, we find that values of J close to the observed value are now rather likely, and there does not seem to be any fine tuning. Our results suggest that the choice of Kobayashi-Maskawa angles is closely linked to the observed mass hierarchy. We close by discussing the corresponding case of neutrinos.

hep-ph↗
arXiv2008

The Petrov and Kaigorodov-Ozsváth Solutions: Spacetime as a Group Manifold

The Petrov solution (for $Λ=0$) and the Kaigorodov-Ozsváth solution (for $Λ<0$) provide examples of vacuum solutions of the Einstein equations with simply-transitive isometry groups. We calculate the boundary stress-tensor for the Kaigorodov-Ozsváth solution in the context of the adS/CFT correspondence. By giving a matrix representation of the Killing algebra of the Petrov solution, we determine left-invariant one-forms on the group. The algebra is shown to admit a two-parameter family of linear deformations a special case of which gives the algebra of the Kaigorodov-Ozsváth solution. By applying the method of non-linear realisations to both algebras, we obtain a Lagrangian of Finsler type from the general first-order action in both cases. Interpreting the Petrov solution as the exterior solution of a rigidly rotating dust cylinder, we discuss the question of creation of CTCs by spinning up such a cylinder. We show geodesic completeness of the Petrov and Kaigorodov-Ozsváth solutions and determine the behaviour of geodesics in these spacetimes. The holonomy groups were shown to be given by the Lorentz group in both cases.

gr-qc↗
arXiv2008

Decay of Massive Dirac Hair on a Brane-World Black Hole

We investigate the intermediate and late-time behaviour of the massive Dirac spinor field in the background of static spherically symmetric brane-world black hole solutions. The intermediate asymptotic behaviour of the massive spinor field exhibits a dependence on the field's parameter mass as well as the multiple number of the wave mode. On the other hand, the late-time behaviour power law decay has a rate which is independent of those factors.

hep-th↗
arXiv2008

The Decay of Dirac Hair around a Dilaton Black Hole

The intermediate and late-time behaviour of a massive Dirac field in the background of static spherically symmetric black hole solutions is investigated. The intermediate asymptotic behaviour of a massive Dirac field depends on the mass parameter as well as the wave number of the mode, while the late time behaviour has a power law decay rate independent of both.

hep-th↗
arXiv2006

Open M5-branes

We show how, in heterotic M-theory, an M5-brane in the 11-dimensional bulk may end on an ``M9-brane'' boundary, the M5-brane boundary being a Yang monopole 4-brane. This possibility suggests various novel 5-brane configurations of heterotic M-theory, in particular a static M5-brane suspended between the two M9-brane boundaries, for which we find the asymptotic heterotic supergravity solution.

hep-th↗
arXiv2005

Properties of some five dimensional Einstein metrics

The volumes, spectra and geodesics of a recently constructed infinite family of five-dimensional inhomogeneous Einstein metrics on the two $S^3$ bundles over $S^2$ are examined. The metrics are in general of cohomogeneity one but they contain the infinite family of homogeneous metrics $T^{p,1}$. The geodesic flow is shown to be completely integrable, in fact both the Hamilton-Jacobi and the Laplace equation separate. As an application of these results, we compute the zeta function of the Laplace operator on $T^{p,1}$ for large $p$. We discuss the spectrum of the Lichnerowicz operator on symmetric transverse tracefree second rank tensor fields, with application to the stability of Freund-Rubin compactifications and generalised black holes.

hep-th↗
arXiv2004

Matrix Cosmology

Some speculative preliminary ideas relating matrix theory and cosmology are discussed.

hep-th↗
arXiv2004

On the stability of naked singularities

We study the linearised stability of the nakedly singular negative mass Schwarzschild solution against gravitational perturbations. There is a one parameter family of possible boundary conditions at the singularity. We give a precise criterion for stability depending on the boundary condition. We show that one particular boundary condition is physically preferred and show that the spacetime is stable with this boundary condition.

hep-th↗
arXiv2004

Topology and Signature Changes in Braneworlds

It has been believed that topology and signature change of the universe can only happen accompanied by singularities, in classical, or instantons, in quantum, gravity. In this note, we point out however that in the braneworld context, such an event can be understood as a classical, smooth event. We supply some explicit examples of such cases, starting from the Dirac-Born-Infeld action. Topology change of the brane universe can be realised by allowing self-intersecting branes. Signature change in a braneworld is made possible in an everywhere Lorentzian bulk spacetime. In our examples, the boundary of the signature change is a curvature singularity from the brane point of view, but nevertheless that event can be described in a completely smooth manner from the bulk point of view.

hep-th↗
arXiv2002

Uniqueness and non-uniqueness of static black holes in higher dimensions

We prove a uniqueness theorem for asymptotically flat static charged dilaton black hole solutions in higher dimensional space-times. We also construct infinitely many non-asymptotically flat regular static black holes on the same space-time manifold with the same spherical topology. An application to the uniqueness of a certain class of flat $p$-branes is also given.

hep-th↗
arXiv2001

Convex Functions and Spacetime Geometry

Convexity and convex functions play an important role in theoretical physics. To initiate a study of the possible uses of convex functions in General Relativity, we discuss the consequences of a spacetime $(M,g_{μν})$ or an initial data set $(Σ, h_{ij}, K_{ij})$ admitting a suitably defined convex function. We show how the existence of a convex function on a spacetime places restrictions on the properties of the spacetime geometry.

gr-qc↗