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G W Gibbons

Publications and source records attributed to G W Gibbons.

At least 19 recordsLinked to original sources
arXiv2008

Applications of the Gauss-Bonnet theorem to gravitational lensing

In this geometrical approach to gravitational lensing theory, we apply the Gauss-Bonnet theorem to the optical metric of a lens, modelled as a static, spherically symmetric, perfect non-relativistic fluid, in the weak deflection limit. We find that the focusing of the light rays emerges here as a topological effect, and we introduce a new method to calculate the deflection angle from the Gaussian curvature of the optical metric. As examples, the Schwarzschild lens, the Plummer sphere and the singular isothermal sphere are discussed within this framework.

gr-qc↗
arXiv2002

The Maximum Tension Principle in General Relativity

I suggest that classical General Relativity in four spacetime dimensions incorporates a Principal of Maximal Tension and give arguments to show that the value of the maximal tension is $c^4 \over 4 G$. The relation of this principle to other, possibly deeper, maximal principles is discussed, in particular the relation to the tension in string theory. In that case it leads to a purely classical relation between $G$ and the classical string coupling constant $α^\prime$ and the velocity of light $c$ which does not involve Planck's constant.

hep-th↗
arXiv2001

Aspects of Born-Infeld Theory and String/M-Theory

These notes provide a hopefully pedagogic introduction to Born-Infeld theory and some of its uses in String/M-Theory from the perspective of some-one interested in spacetime geometry. Causality and the consequences of having both the open string and closed string metric are stressed. This leads to some new insighst into old problems, such as strings at finite temperature. Various strong coupling limits of both Born-Infeld and the M5-brane theories are described and their relevance for tachyon condensations are mentioned.

hep-th↗
arXiv2001

Pulse Propagation in Born-Infeld Theory, the World Volume Equivalence Principle and the Hagedorn-like Equation of State of the Chaplygin Gas

A recently proposed world-volume equivalence principal involving the Boillat, as opposed to the Einstein, metric is examined in the context of some colliding wave solutions of the Born-Infeld equations for which two plane polarized pulses pass through one another without distortion. They suffer a delay with respect to the usual Einstein metric but not with respect to the Boillat metric. Both metrics are flat in this case, and the closed string and open string causal structures are interchanged by the Legendre transformation that is used for solving the associated Monge-Ampère equation. In 1+1 dimensions the equations are known to be equivalent to the vorticity free motion of a Chaplygin gas. The latter is shown to be described by the scalar Born-Infeld equation in all dimensions and it is pointed out that the equation of state is Hagedorn-like: there is an upper bound to the pressure and temperature.

hep-th↗
arXiv2001

The metric and strong coupling limit of the M5-brane

We find the analogue of the Boillat metric of Born-Infeld theory for the M5-brane. We show that it provides the propagation cone of {\sl all} 5-brane degrees. In an arbitrary background field, this cone never lies outside the Einstein cone. An energy momentum tensor for the three-form is defined and shown to satisfy the Dominant Energy Condition. The theory is shown to be well defined for all values of the magnetic field but there is a limiting electric field strength. We consider the strong coupling limit of the M5-brane and show that the corresponding theory is conformally invariant and admits infinitely many conservation laws. On reduction to the Born-Infeld case this agrees with the work of Białnicki-Birula.

hep-th↗
arXiv1999

Holography and the Future Tube

The Future Tube $T^+_n$ of n-dimensional Minkowski spacetime may be identified with the reduced phase space or "space of motions" of a particle moving in (n+1)-dimensional Anti-de-Sitter spacetime. Both are isomorphic to a bounded homogeneous domain in ${\bf C}^{n}$ whose Shilov boundary may be identified with $n$-dimensional conformally compactified Minkowski spacetime.

hep-th↗
arXiv1999

A Bogomol`nyi equation for intersecting domain walls

We argue that the Wess-Zumino model with quartic superpotential admits static solutions in which three domain walls intersect at a junction. We derive an energy bound for such junctions and show that configurations saturating it preserve 1/4 supersymmetry.

hep-th↗
arXiv1999

Two loop and all loop finite 4-metrics

In pure Einstein theory, Ricci flat Lorentzian 4-metrics of Petrov types III or N have vanishing counter terms up to and including two loops. Moreover for pp-waves and type-N spacetimes of Kundt's class which admit a non-twisting, non expanding, null congruence all possible invariants formed from the Weyl tensor and its covariant derivatives vanish. Thus these Lorentzian metrics suffer no quantum corrections to all loop orders. By contrast for complete non-singular Riemannian metrics the two loop counter term vanishes only if the metric is flat.

hep-th↗
arXiv1998

Some Comments on Gravitational Entropy and the Inverse Mean Curvature Flow

The Geroch-Wald-Jang-Huisken-Ilmanen approach to the positive energy problem to may be extended to give a negative lower bound for the mass of asymptotically Anti-de-Sitter spacetimes containing horizons with exotic topologies having ends or infinities of the form $Σ_g \times {\Bbb R}$, in terms of the cosmological constant. We also show how the method gives a lower bound for for the mass of time-symmetric initial data sets for black holes with vectors and scalars in terms of the mass, $|Z(Q,P)|$ of the double extreme black hole with the same charges. I also give a lower bound for the area of an apparent horizon, and hence a lower bound for the entropy in terms of the same function $|Z(Q,P)|$. This shows that the so-called attractor behaviour extends beyond the static spherically symmetric case. and underscores the general importance of the function $|Z(Q,P)|$. There are hints that higher dimensional generalizations may involve the Yamabe conjectures.

hep-th↗
arXiv1998

Wrapping Branes in Space and Time

Branes may be approximated semi-classically by solutions of supergravity theories with event and Cauchy horizons. I suggest that if one wishes to avoid singularities and to capture accurately some of the properties of branes then these classical spacetimes must be identified so as to render them periodic in time.

hep-th↗
arXiv1998

Branes as BIons

A BIon may be defined as a finite energy solution of a non-linear field theory with distributional sources. By contrast a soliton is usually defined to have no sources. I show how harmonic coordinates map the exteriors of the topologically and causally non-trivial spacetimes of extreme p-branes to BIonic solutions of the Einstein equations in a topologically trivial spacetime in which the combined gravitational and matter energy momentum is located on distributional sources. As a consequence the tension of BPS p-branes is classically unrenormalized. The result holds equally for spacetimes with singularities and for those, like the M-5-brane, which are everywhere singularity free.

hep-th↗
arXiv1997

Collapsing Shells and the Isoperimetric Inequality for Black Holes

Recent results of Trudinger on Isoperimetric Inequalities for non-convex bodies are applied to the gravitational collapse of a lightlike shell of matter to form a black hole. Using some integral identities for co-dimension two surfaces in Minkowski spacetime, the area $A$ of the apparent horizon is shown to be bounded above in terms of the mass $M$ by the $16 πG^2 M^2$, which is consistent with the Cosmic Censorship Hypothesis. The results hold in four spacetime dimensions and above.

hep-th↗
arXiv1996

Master Equations and Majorana Spinors

I describe how the states of a discrete automata with p sites, each of which may be off or on, can be represented as Majorana spinors associated to a spacetime with signature (p,p). Some ideas about the quantization of such systems are discussed and the relationship to some unconventional formulations and generalizations of quantum mechanics, particularly Jordan's spinorial quantum mechanics are pointed out. A connection is made to the problem of time and the complex numbers in quantum gravity.

gr-qc↗
arXiv1996

The Sen conjecture for fundamental monopoles of distinct type

I exhibit a middle-dimensional square integrable harmonic form on the moduli space of distinct fundamental BPS monopoles of an arbitrary Lie group. This is in accord with Sen's S-duality conjecture. I also show that the moduli space has no closed or bound geodesics.

hep-th↗
arXiv1996

Tunelling with a Negative Cosmological Constant

The point of this paper is see what light new results in hyperbolic geometry may throw on gravitational entropy and whether gravitational entropy is relevant for the quantum origin of the univeres. We introduce some new gravitational instantons which mediate the birth from nothing of closed universes containing wormholes and suggest that they may contribute to the density matrix of the universe. We also discuss the connection between their gravitational action and the topological and volumetric entropies introduced in hyperbolic geometry. These coincide for hyperbolic 4-manifolds, and increase with increasing topological complexity of the four manifold. We raise the questions of whether the action also increases with the topological complexity of the initial 3-geometry, measured either by its three volume or its Matveev complexity. We point out, in distinction to the non-supergravity case, that universes with domains of negative cosmological constant separated by supergravity domain walls cannot be born from nothing. Finally we point out that our wormholes provide examples of the type of Perpetual Motion machines envisaged by Frolov and Novikov.

hep-th↗
arXiv1995

SL(2,R) Invariance of Non-Linear Electrodynamics Coupled to An Axion and a Dilaton

The most general Lagrangian for non-linear electrodynamics coupled to an axion $a$ and a dilaton $ϕ$ with $SL(2,\mbox{\elevenmsb R})$ invariant equations of motion is $$ -\half\left(\nablaϕ\right)^2 - \half e^{2ϕ}\left(\nabla a\right)^2 + \fraction{1}{4}aF_{μν}\star F^{μν} + L_{\rm inv}(g_{μν},e^{-\frac{1}{2}ϕ}F_{ρσ}) $$ where $L_{\rm inv}(g_{μν},F_{ρσ})$ is a Lagrangian whose equations of motion are invariant under electric-magnetic duality rotations. In particular there is a unique generalization of Born-Infeld theory admitting $SL(2,\mbox{\elevenmsb R})$ invariant equations of motion.

hep-th↗
arXiv1995

Electric-Magnetic Duality Rotations in Non-Linear Electrodynamics

We show that there is a function of one variable's worth of Lagrangians for a single Maxwell field coupled to gravity whose equations of motion admit electric-magnetic duality. Such Lagrangians are given by solutions of the Hamilton-Jacobi equation for timelike geodesics in Witten's two-dimensional black hole. Among them are the Born-Infeld Lagrangian which arises in open string theory. We investigate the effect of the axion and the dilaton in the open superstring case and we show that this theory loses its electric-magnetic duality invariance when one considers the higher order electromagnetic field terms. We discuss some implications for black holes in string theory and an extension to $2k$-forms in $4k$ spacetime dimensions.

hep-th↗