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G. W. Gibbons

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

At least 73 records · Page 4Linked to original sources
arXiv2012

What is the Shape of a Black Hole?

A brief, and certainly not exhaustive, survey is provided of some recent results and conjectures in four and higher spacetime dimensions, such as the Hoop Conjecture, relating the geometry of event horizons to dynamical quantities such as the total energy or mass of the spacetime containng the black hole. As a measure of the size of a hoop one may take Birkhoff's invariant based on sweepouts by circles or higher dimensional analogues or one may take the length of the shortest non-trivial closed geodesic. Also discussed are whether one can hear the shape of a black hole and to what extent one may associate with it a volume.

gr-qc↗
arXiv2011

The Application of Weierstrass elliptic functions to Schwarzschild Null Geodesics

In this paper we focus on analytical calculations involving null geodesics in some spherically symmetric spacetimes. We use Weierstrass elliptic functions to fully describe null geodesics in Schwarzschild spacetime and to derive analytical formulae connecting the values of radial distance at different points along the geodesic. We then study the properties of light triangles in Schwarzschild spacetime and give the expansion of the deflection angle to the second order in both $M/r_0$ and $M/b$ where $M$ is the mass of the black hole, $r_0$ the distance of closest approach of the light ray and $b$ the impact parameter. We also use the Weierstrass function formalism to analyze other more exotic cases such as Reissner-Nordstr\om null geodesics and Schwarzschild null geodesics in 4 and 6 spatial dimensions. Finally we apply Weierstrass functions to describe the null geodesics in the Ellis wormhole spacetime and give an analytic expansion of the deflection angle in $M/b$.

gr-qc↗
arXiv2011

Goryachev-Chaplygin, Kovalevskaya, and Brdička-Eardley-Nappi-Witten pp-waves spacetimes with higher rank Stäckel-Killing tensors

Hidden symmetries of the Goryachev-Chaplygin and Kovalevskaya gyrostats spacetimes, as well as the Brdička-Eardley-Nappi-Witten pp-waves are studied. We find out that these spacetimes possess higher rank Stäckel-Killing tensors and that in the case of the pp-wave spacetimes the symmetry group of the Stäckel-Killing tensors is the well-known Newton-Hooke group.

gr-qc↗
arXiv2011

The emergent nature of time and the complex numbers in quantum cosmology

The nature of time in quantum mechanics is closely related to the use of a complex, rather than say real, Hilbert space. This becomes particularly clear when considering quantum field theory in time dependent backgrounds, such as in cosmology, when the notion of positive frequency ceases to be well defined. In spacetimes lacking time orientation, i.e without the possibility of defining an arrow of time, one is forced to abandon complex quantum mechanics. One also has to face this problem in quantum cosmology. I use this to argue that this suggests that, at a fundamental level, quantum mechanics may be really real with not one, but a multitude of complex structures. I relate these ideas to other suggestions that in quantum gravity time evolution may not be unitary, possibly implemented by a super-scattering matrix, and the status of CPT.

gr-qc↗
arXiv2011

Anti-de-Sitter spacetime and its uses

This is a pedagogic account of some of the global properties of Anti-de-Sitter spacetime with a view to their application to the AdS/CFT correspondence. Particular care is taken over the distinction between Anti-de-Sitter and it's covering space. Written version of lectures given at 2nd Samos Meeting held at at Pythagoreon, Samos, Greece, 31 August - 4 September 1998 and published as Anti-de-Sitter spacetime and its uses, in Mathematical and Quantum Aspects of Relativity and Cosmology. Proceedings of the 2nd Samos Meeting on Cosmology, Geometry and Relativity, S Cotsakis and G W Gibbons eds, {\it Lecture Notes in Physics}\, {\bf 537} (2000)}

hep-th↗
arXiv2011

Supergravity vacua and solitons

This is the written version of two lectures given at the Newton Institute Euroconference on Duality and Supersymmetric Theories, Cambridge, England, 7-18 Apr 1997. It deals with the nature of supergravity vacua and black holes and black branes as solitons, focussing on my own work. While clearly dated, I believe that it contains material which remains of relevance and which is not available elsewhere

hep-th↗
arXiv2011

Topology change in classical and quantum gravity

In these two lectures I describe the difficulties one encounters when trying to construct a framework in which to describe topology change in classical general relativity where one sticks to the assumption of an everywhere non-singular Lorentzian metric and how these difficulties can be circumvented in the Euclidean approach to quantum gravity.

gr-qc↗
arXiv2011

Cosmic Baldness

We elucidate the mechanism where by gravitational fluctuations are frozen in during a period of inflation but nevertheless within the past horizon of any geodesic observer the spacetime settles down exponentially fast to the de-Sitter metric.

astro-ph.CO↗
arXiv2011

The helical phase of chiral nematic liquid crystals as the Bianchi VII(0) group manifold

We show that the optical structure of the helical phase of a chiral nematic is naturally associated with the Bianchi VII(0) group manifold, of which we give a full account. The Joets-Ribotta metric governing propagation of the extraordinary rays is invariant under the simply transitive action of the universal cover of the three dimensional Euclidean group of two dimensions. Thus extraordinary light rays are geodesics of a left-invariant metric on this Bianchi type VII(0) group. We are able to solve by separation of variables both the wave equation and the Hamilton-Jacobi equation for this metric. The former reduces to Mathieu's equation and the later to the quadrantal pendulum equation. We discuss Maxwell's equations for uniaxial optical materials where the configuration is invariant under a group action and develop a formalism to take advantage of these symmetries. The material is not assumed to be impedance matched, thus going beyond the usual scope of transformation optics. We show that for a chiral nematic in its helical phase Maxwell's equations reduce to a generalised Mathieu equation. Our results may also be relevant to helical phases of some magnetic materials and to light propagation in certain cosmological models.

gr-qc↗
arXiv2011

More about Birkhoff's Invariant and Thorne's Hoop Conjecture for Horizons

A recent precise formulation of the hoop conjecture in four spacetime dimensions is that the Birkhoff invariant $β$ (the least maximal length of any sweepout or foliation by circles) of an apparent horizon of energy $E$ and area $A$ should satisfy $β\le 4 πE$. This conjecture together with the Cosmic Censorship or Isoperimetric inequality implies that the length $\ell$ of the shortest non-trivial closed geodesic satisfies $\ell^2 \le πA$. We have tested these conjectures on the horizons of all four-charged rotating black hole solutions of ungauged supergravity theories and find that they always hold. They continue to hold in the the presence of a negative cosmological constant, and for multi-charged rotating solutions in gauged supergravity. Surprisingly, they also hold for the Ernst-Wild static black holes immersed in a magnetic field, which are asymptotic to the Melvin solution. In five spacetime dimensions we define $β$ as the least maximal area of all sweepouts of the horizon by two-dimensional tori, and find in all cases examined that $ β(g) \le \frac{16 π}{3} E$, which we conjecture holds quiet generally for apparent horizons. In even spacetime dimensions $D=2N+2$, we find that for sweepouts by the product $S^1 \times S^{D-4}$, $β$ is bounded from above by a certain dimension-dependent multiple of the energy $E$. We also find that $\ell^{D-2}$ is bounded from above by a certain dimension-dependent multiple of the horizon area $A$. Finally, we show that $\ell^{D-3}$ is bounded from above by a certain dimension-dependent multiple of the energy, for all Kerr-AdS black holes.

hep-th↗
arXiv2011

Black Hole Enthalpy and an Entropy Inequality for the Thermodynamic Volume

In a theory where the cosmological constant $Λ$ or the gauge coupling constant $g$ arises as the vacuum expectation value, its variation should be included in the first law of thermodynamics for black holes. This becomes $dE= TdS + Ω_i dJ_i + Φ_αd Q_α+ Θd Λ$, where $E$ is now the enthalpy of the spacetime, and $Θ$, the thermodynamic conjugate of $Λ$, is proportional to an effective volume $V = -\frac{16 πΘ}{D-2}$ "inside the event horizon." Here we calculate $Θ$ and $V$ for a wide variety of $D$-dimensional charged rotating asymptotically AdS black hole spacetimes, using the first law or the Smarr relation. We compare our expressions with those obtained by implementing a suggestion of Kastor, Ray and Traschen, involving Komar integrals and Killing potentials, which we construct from conformal Killing-Yano tensors. We conjecture that the volume $V$ and the horizon area $A$ satisfy the inequality $R\equiv ((D-1)V/{\cal A}_{D-2})^{1/(D-1)}\, ({\cal A}_{D-2}/A)^{1/(D-2)}\ge1$, where ${\cal A}_{D-2}$ is the volume of the unit $(D-2)$-sphere, and we show that this is obeyed for a wide variety of black holes, and saturated for Schwarzschild-AdS. Intriguingly, this inequality is the "inverse" of the isoperimetric inequality for a volume $V$ in Euclidean $(D-1)$ space bounded by a surface of area $A$, for which $R\le 1$. Our conjectured {\it Reverse Isoperimetric Inequality} can be interpreted as the statement that the entropy inside a horizon of a given "volume" $V$ is maximised for Schwarzschild-AdS. The thermodynamic definition of $V$ requires a cosmological constant (or gauge coupling constant). However, except in 7 dimensions, a smooth limit exists where $Λ$ or $g$ goes to zero, providing a definition of $V$ even for asymptotically-flat black holes.

hep-th↗
arXiv2011

The General Supersymmetric Solution of Topologically Massive Supergravity

We find the general fully non-linear solution of topologically massive supergravity admitting a Killing spinor. It is of plane-wave type, with a null Killing vector field. Conversely, we show that all solutions with a null Killing vector are supersymmetric for one or the other choice of sign for the Chern-Simons coupling constant μ. If μdoes not take the critical value μ=\pm 1, these solutions are asymptotically regular on a Poincaré patch, but do not admit a smooth global compactification with boundary S^1\times\R. In the critical case, the solutions have a logarithmic singularity on the boundary of the Poincaré patch. We derive a Nester-Witten identity, which allows us to identify the associated charges, but we conclude that the presence of the Chern-Simons term prevents us from making a statement about their positivity. The Nester-Witten procedure is applied to the BTZ black hole.

hep-th↗
arXiv2011

Non-existence of Skyrmion-Skyrmion and Skyrmion-anti-Skyrmion static equilibria

We consider classical static Skyrmion-anti-Skyrmion and Skyrmion-Skyrmion configurations, symmetric with respect to a reflection plane, or symmetric up to a $G$-parity transformation respectively. We show that the stress tensor component completely normal to the reflection plane, and hence its integral over the plane, is negative definite or positive definite respectively. Classical Skyrmions always repel classical Skyrmions and classical Skyrmions always attract classical anti-Skyrmions and thus no static equilibrium, whether stable or unstable, is possible in either case. No other symmetry assumption is made and so our results also apply to multi-Skyrmion configurations. Our results are consistent with existing analyses of Skyrmion forces at large separation, and with numerical results on Skymion-anti-Skyrmion configurations in the literature which admit a different reflection symmetry. They also hold for the massive Skyrme model. We also point out that reflection symmetric self-gravitating Skyrmions or black holes with Skyrmion hair cannot rest in symmetric equilibrium with self-gravitating anti-Skyrmions.

hep-th↗
arXiv2011

Some Spacetimes with Higher Rank Killing-Stackel Tensors

By applying the lightlike Eisenhart lift to several known examples of low-dimensional integrable systems admitting integrals of motion of higher-order in momenta, we obtain four- and higher-dimensional Lorentzian spacetimes with irreducible higher-rank Killing tensors. Such metrics, we believe, are first examples of spacetimes admitting higher-rank Killing tensors. Included in our examples is a four-dimensional supersymmetric pp-wave spacetime, whose geodesic flow is superintegrable. The Killing tensors satisfy a non-trivial Poisson-Schouten-Nijenhuis algebra. We discuss the extension to the quantum regime.

gr-qc↗
arXiv2011

The geometry of sound rays in a wind

We survey the close relationship between sound and light rays and geometry. In the case where the medium is at rest, the geometry is the classical geometry of Riemann. In the case where the medium is moving, the more general geometry known as Finsler geometry is needed. We develop these geometries ab initio, with examples, and in particular show how sound rays in a stratified atmosphere with a wind can be mapped to a problem of circles and straight lines.

gr-qc↗
arXiv2010

Kohn's Theorem, Larmor's Equivalence Principle and the Newton-Hooke Group

We consider non-relativistic electrons, each of the same charge to mass ratio, moving in an external magnetic field with an interaction potential depending only on the mutual separations, possibly confined by a harmonic trapping potential. We show that the system admits a "relativity group" which is a one-parameter family of deformations of the standard Galilei group to the Newton-Hooke group which is a Wigner-Inonu contraction of the de Sitter group. This allows a group-theoretic interpretation of Kohn's theorem and related results. Larmor's Theorem is used to show that the one-parameter family of deformations are all isomorphic. We study the "Eisenhart" or "lightlike" lift of the system, exhibiting it as a pp-wave. In the planar case, the Eisenhart lift is the Brdicka-Eardley-Nappi-Witten pp-wave solution of Einstein-Maxwell theory, which may also be regarded as a bi-invariant metric on the Cangemi-Jackiw group.

hep-th↗
arXiv2010

Universal Area Product Formulae for Rotating and Charged Black Holes in Four and Higher Dimensions

We present explicit results for the product of all horizon areas for general rotating multi-charge black holes, both in asymptotically flat and asymptotically anti-de Sitter spacetimes in four and higher dimensions. The expressions are universal, and depend only on the quantized charges, quantized angular momenta and the cosmological constant. If the latter is also quantized these universal results may provide a "looking glass" for probing the microscopics of general black holes.

hep-th↗