arXiv subjects

G. W. Gibbons

Publications and source records attributed to G. W. Gibbons.

At least 163 records · Page 9Linked to original sources

arXiv1998

Superconducting p-branes and Extremal Black Holes

In Einstein-Maxwell theory, magnetic flux lines are `expelled' from a black hole as extremality is approached, in the sense that the component of the field strength normal to the horizon goes to zero. Thus, extremal black holes are found to exhibit the sort of `Meissner effect' which is characteristic of superconducting media. We review some of the evidence for this effect, and do present new evidence for it using recently found black hole solutions in string theory and Kaluza-Klein theory. We also present some new solutions, which arise naturally in string theory, which are non-superconducting extremal black holes. We present a nice geometrical interpretation of these effects derived by looking carefully at the higher dimensional configurations from which the lower dimensional black hole solutions are obtained. We show that other extremal solitonic objects in string theory (such as p-branes) can also display superconducting properties. In particular, we argue that the relativistic London equation will hold on the worldvolume of `light' superconducting p-branes (which are embedded in flat space), and that minimally coupled zero modes will propagate in the adS factor of the near-horizon geometries of `heavy', or gravitating, superconducting p-branes.

hep-th↗

arXiv1998

Calibrations and Intersecting Branes

We investigate the solutions of Nambu-Goto-type actions associated with calibrations. We determine the supersymmetry preserved by these solutions using the contact set of the calibration and examine their bulk interpretation as intersecting branes. We show that the supersymmetry preserved by such solutions is closely related to the spinor singlets of the subgroup $G$ of $Spin (9,1)$ or $Spin (10,1)$ that rotates the tangent spaces of the brane. We find that the supersymmetry projections of the worldvolume solutions are precisely those of the associated bulk configurations. We also investigate the supersymmetric solutions of a Born-Infeld action. We show that in some cases this problem also reduces to counting spinor singlets of a subgroup of $Spin (9,1)$ acting on the associated spinor representations. We also find new worldvolume solutions which preserve 1/8 of the supersymmetry of the bulk and give their bulk interpretation.

hep-th↗

arXiv1998

Born-Infeld-Einstein Actions?

We present some obvious physical requirements on gravitational avatars of non-linear electrodynamics and illustrate them with explicit determinantal Born-Infeld-Einstein models. A related procedure, using compensating Weyl scalars, permits us to formulate conformally invariant versions of these systems as well.

hep-th↗

arXiv1998

Wormholes on The World Volume

I describe some recent work in which classical solutions of Dirac-Born-Infeld theory may be used to throw light on some properties of M-theory. The sources of Born-Infeld theory are the ends of strings ending on the world volume. Equivalently the fundamental string may be regarded as merely a thin and extended piece of the world volume.

hep-th↗

arXiv1997

HKT and OKT Geometries on Soliton Black Hole Moduli Spaces

We consider Shiraishi's metrics on the moduli space of extreme black holes. We interpret the simplification in the pattern of N-body interactions that he observed in terms of the recent picture of black holes in four and five dimensions as composites, made up of intersecting branes. We then show that the geometry of the moduli space of a class of black holes in five and nine dimensions is hyper-Kähler with torsion, and octonionic-Kähler with torsion, respectively. For this, we examine the geometry of point particle models with extended world-line supersymmetry and show that both of the above geometries arise naturally in this context. In addition, we construct a large class of hyper-Kähler with torsion and octonionic-Kähler with torsion geometries in various dimensions. We also present a brane interpretation of our results.

hep-th↗

arXiv1997

Born-Infeld particles and Dirichlet p-branes

Born-Infeld theory admits finite energy point particle solutions with $δ$-function sources, BIons. I discuss their role in the theory of Dirichlet $p$-branes as the ends of strings intersecting the brane when the effects of gravity are ignored. There are also topologically non-trivial electrically neutral catenoidal solutions looking like two $p$-branes joined by a throat. The general solution is a non-singular deformation of the catenoid if the charge is not too large and a singular deformation of the BIon solution for charges above that limit. The intermediate solution is BPS and Coulomb-like. Performing a duality rotation we obtain monopole solutions, the BPS limit being a solution of the abelian Bogolmol'nyi equations. The situation closely resembles that of sub and super extreme black-brane solutions of the supergravity theories. I also show that certain special Lagrangian submanifolds of ${\Bbb C}^p$, $p=3,4,5$, may be regarded as supersymmetric configurations consisting of $p$-branes at angles joined by throats which are the sources of global monopoles. Vortex solutions are also exhibited.

hep-th↗

arXiv1997

Hyperkähler Manifolds and Multiply Intersecting Branes

This is a summary of the work in the author's recent paper with this title written with Jerome Gauntlett, George Papadopoulos and Paul Townsend, hep-th/9702202. We showed how to construct hyper-Kähler 8-metrics in terms of arrangements of three-dimensional hyperplanes in six-dimensional euclidean space. The slopes of the planes define two relatively prime integers $(p,q)$. Under reduction to ten dimensions and T-duality we get a geometric picture of the action of $SL(2,Z)$ on the $(NS \otimes NS,q R \otimes R)$ 5-branes of type IIB string theory. Configurations are exhibited with $3 \over 16$'th SUSY.

hep-th↗

arXiv1997

Hyper-Kahler manifolds and multiply-intersecting branes

Generalized membrane solutions of D=11 supergravity, for which the transverse space is a toric hyper-K{\" a}hler manifold, are shown to have IIB duals representing the intersection of parallel 3-branes with 5-branes whose orientations are determined by their $Sl(2;\bZ)$ charge vectors. These IIB solutions, which generically preserve 3/16 of the supersymmetry, can be further mapped to solutions of D=11 supergravity representing the intersection of parallel membranes with any number of fivebranes at arbitrary angles. Alternatively, a subclass (corresponding to non-singular D=11 solutions) can be mapped to solutions representing the intersection on a string of any number of D-5-branes at arbitrary angles, again preserving 3/16 supersymmetry, as we verify in a special case by a quaternionic extension of the analysis of Berkooz, Douglas and Leigh. We also use similar methods to find new 1/8 supersymmetric solutions of orthogonally intersecting branes.

hep-th↗

arXiv1996

HyperKähler Quotient Construction of BPS Monopole Moduli Spaces

We use the HyperKähler quotient of flat space to obtain some monopole moduli space metrics in explicit form. Using this new description, we discuss their topology, completeness and isometries. We construct the moduli space metrics in the limit when some monopoles become massless, which corresponds to non-maximal symmetry breaking of the gauge group. We also introduce a new family of HyperK"{a}hler metrics which, depending on the ``mass parameter'' being positive or negative, give rise to either the asymptotic metric on the moduli space of many SU(2) monopoles, or to previously unknown metrics. These new metrics are complete if one carries out the quotient of a non-zero level set of the moment map, but develop singularities when the zero-set is considered. These latter metrics are of relevance to the moduli spaces of vacua of three dimensional gauge theories for higher rank gauge groups. Finally, we make a few comments concerning the existence of closed or bound orbits on some of these manifolds and the integrability of the geodesic flow.

hep-th↗

arXiv1996

Nucleating Black Holes via Non-Orientable Instantons

We extend the analysis of black hole pair creation to include non- orientable instantons. We classify these instantons in terms of their fundamental symmetries and orientations. Many of these instantons admit the pin structure which corresponds to the fermions actually observed in nature, and so the natural objection that these manifolds do not admit spin structure may not be relevant. Furthermore, we analyse the thermodynamical properties of non-orientable black holes and find that in the non-extreme case, there are interesting modifications of the usual formulae for temperature and entropy.

gr-qc↗

arXiv1996

Dyson Pairs and Zero-Mass Black Holes

It has been argued by Dyson in the context of QED in flat spacetime that perturbative expansions in powers of the electric charge e cannot be convergent because if e is purely imaginary then the vacuum should be unstable to the production of charged pairs. We investigate the spontaneous production of such Dyson pairs in electrodynamics coupled to gravity. They are found to consist of pairs of zero-rest mass black holes with regular horizons. The properties of these zero rest mass black holes are discussed. We also consider ways in which a dilaton may be included and the relevance of this to recent ideas in string theory. We discuss accelerating solutions and find that, in certain circumstances, the `no strut' condition may be satisfied giving a regular solution describing a pair of zero rest mass black holes accelerating away from one another. We also study wormhole and tachyonic solutions and how they affect the stability of the vacuum.

hep-th↗

arXiv1996

Nucleation of $P$-Branes and Fundamental Strings

We construct a solution to the low-energy string equations of motion in five dimensions that describes a circular loop of fundamental string exponentially expanding in a background electric $H$-field. Euclideanising this gives an instanton for the creation of a loop of fundamental string in a background $H$-field, and we calculate the rate of nucleation. Solutions describing magnetically charged strings and $p$-branes, where the gauge field comes from Kaluza-Klein reduction on a circle, are also constructed. It is known that a magnetic flux tube in four (reduced) spacetime dimensions is unstable to the pair creation of Kaluza-Klein monopoles. We show that in $(4+p)$ dimensions, magnetic $(p+1)$ ``fluxbranes" are unstable to the nucleation of a magnetically charged spherical $p$-brane. In ten dimensions the instanton describes the nucleation of a Ramond-Ramond magnetically charged six-brane in type IIA string theory. We also find static solutions describing spherical charged $p$-branes or fundamental strings held in unstable equilibrium in appropriate background fields. Instabilities of intersecting magnetic fluxbranes are also discussed.

hep-th↗

arXiv1995

Topology and Time Reversal

In this lecture we address some topological questions connected with the existence on a general spacetime manifold of diffeomorphisms connected to the identity which reverse the time-orientation.

gr-qc↗

arXiv1995

Anti-gravitating BPS monopoles and dyons

We show that the exact static, i.e. `anti-gravitating', magnetic multi monopole solutions of the Einstein/Maxwell/dilaton-YM/Higgs equations found by Kastor, London, Traschen, and the authors, for arbitrary non-zero dilaton coupling constant $a$, are equivalent to the string theory BPS magnetic monopole solutions of Harvey and Liu when $a=\sqrt{3}$. For this value of $a$, the monopole solutions also solve the equations of five-dimensional supergravity/YM theory. We also discuss some features of the dyon solutions obtained by boosting in the fifth dimension and some features of the moduli space of anti-gravitating multi-monopoles.

hep-th↗

arXiv1995

A Judgement on Sinors

This note contains some comments on a recent paper by Friedman on two-component spinors in spacetimes which do not admit a time-orientation, and is intended to clarify the relation of the work reported in that paper to previous literature.

gr-qc↗

arXiv1995

Sphalerons and Conformally Compactified Minkowski Spacetime

Solutions to the Yang-Mills field equations which describe exploding or imploding shells of gauge field and which may serve as approximations to the exploding sphaleron are discussed. The solutions are conformally related to $SO(2)\times SO(4)$ invariant Yang-Mills solutions. The behavior of fermions in the gauge field background and higher gauge groups are also considered.

hep-ph↗

arXiv1994

Topology, Entropy and Witten Index of Dilaton Black Holes

We have found that for extreme dilaton black holes an inner boundary must be introduced in addition to the outer boundary to give an integer value to the Euler number. The resulting manifolds have (if one identifies imaginary time) topology $S^1 \times R \times S^2 $ and Euler number $χ= 0$ in contrast to the non-extreme case with $χ=2$. The entropy of extreme $U(1)$ dilaton black holes is already known to be zero. We include a review of some recent ideas due to Hawking on the Reissner-Nordström case. By regarding all extreme black holes as having an inner boundary, we conclude that the entropy of {\sl all} extreme black holes, including $[U(1)]^2$ black holes, vanishes. We discuss the relevance of this to the vanishing of quantum corrections and the idea that the functional integral for extreme holes gives a Witten Index. We have studied also the topology of ``moduli space'' of multi black holes. The quantum mechanics on black hole moduli spaces is expected to be supersymmetric despite the fact that they are not HyperKähler since the corresponding geometry has torsion unlike the BPS monopole case. Finally, we describe the possibility of extreme black hole fission for states with an energy gap. The energy released, as a proportion of the initial rest mass, during the decay of an electro-magnetic black hole is 300 times greater than that released by the fission of an ${}^{235} U$ nucleus.

hep-th↗

arXiv1994

Higher-dimensional resolution of dilatonic black hole singularities

We show that the four-dimensional extreme dilaton black hole with dilaton coupling constant $a= \sqrt{p/(p+2)}$ can be interpreted as a {\it completely non-singular}, non-dilatonic, black $p$-brane in $(4+p)$ dimensions provided that $p$ is {\it odd}. Similar results are obtained for multi-black holes and dilatonic extended objects in higher spacetime dimensions. The non-singular black $p$-brane solutions include the self-dual three brane of ten-dimensional N=2B supergravity and a multi-fivebrane solution of eleven-dimensional supergravity. In the case of a supersymmetric non-dilatonic $p$-brane solution of a supergravity theory, we show that it saturates a bound on the energy per unit $p$-volume.

hep-th↗