Steven Willison

Lovelock black holes with maximally symmetric horizons

We investigate some properties of n( ≥ 4)-dimensional spacetimes having symmetries corresponding to the isometries of an (n − 2)-dimensional maximally symmetric space in Lovelock gravity under the null or dominant energy condition. The well-posedness of the generalized Misner–Sharp quasi-local mass proposed in the past study is shown. Using this quasi-local mass, we clarify the basic properties of the dynamical black holes defined by a future outer trapping horizon under certain assumptions on the Lovelock coupling constants. The C2 vacuum solutions are classified into four types: (i) Schwarzschild–Tangherlini-type solution; (ii) Nariai-type solution; (iii) special degenerate vacuum solution; and (iv) exceptional vacuum solution. The conditions for the realization of the last two solutions are clarified. The Schwarzschild–Tangherlini-type solution is studied in detail. We prove the first law of black-hole thermodynamics and present the expressions for the heat capacity and the free energy.

Three-dimensional supergravity reloaded

The locally supersymmetric extension of the most general gravity theory in three dimensions leading to first-order field equations for the vielbein and the spin connection is constructed. Apart from the Einstein–Hilbert term with cosmological constant, the gravitational sector contains the Lorentz–Chern–Simons form and a term involving the torsion each with arbitrary couplings. The supersymmetric extension is carried out for vanishing and negative effective cosmological constant, and it is shown that the action can be written as a Chern–Simons theory for the supersymmetric extension of the Poincare and AdS groups, respectively. Here we introduce a duality map between different gravity theories that greatly simplifies the construction. This map relies on the different ways to make geometry emerge from a single gauge potential. The extension for gravitini is also performed.

Some exact solutions with torsion in 5D Einstein-Gauss-Bonnet gravity

Exact solutions with torsion in Einstein-Gauss-Bonnet gravity are derived. These solutions have a cross product structure of two constant curvature manifolds. The equations of motion give a relation for the coupling constants of the theory in order to have solutions with nontrivial torsion. This relation is not the Chern-Simons combination. One of the solutions has an AdS 2 X S 3 structure and is so the purely gravitational analogue of the Bertotti-Robinson space-time where the torsion can be seen as the dual of the covariantly constant electromagnetic field.

The Universe as a topological defect

Four-dimensional Einsteins general relativity is shown to arise from a gauge theory for the conformal group, SO(4,2). The theory is constructed from a topological dimensional reduction of the six-dimensional Euler density integrated over a manifold with a four-dimensional topological defect. The resulting action is a four-dimensional theory defined by a gauged Wess-Zumino-Witten term. An ansatz is found which reduces the full set of field equations to those of Einsteins general relativity. When the same ansatz is replaced in the action, the gauged WZW term reduces to the Einstein-Hilbert action. Furthermore, the unique coupling constant in the action can be shown to take integer values if the fields are allowed to be analytically continued to complex values.

General relativity from a gauged Wess-Zumino-Witten term

In this paper two things are done. First it is shown how a four-dimensional gauged Wess-Zumino-Witten term arises from the five-dimensional Einstein-Hilbert plus Gauss-Bonnet Lagrangian with a special choice of the coefficients. Second, the way in which the equations of motion of four-dimensional General Relativity arise is exhibited.

General relativity with small cosmological constant from spontaneous compactification of Lovelock theory in vacuum

It is shown that Einstein gravity in four dimensions with small cosmological constant and small extra dimensions can be obtained by spontaneous compactification of Lovelock gravity in vacuum. Assuming that the extra dimensions are compact spaces of constant curvature, general relativity is recovered within a certain class of Lovelock theories possessing necessarily cubic or higher order terms in curvature. This bounds the higher dimension to at least 7. Remarkably, the effective gauge coupling and Newton constant in four dimensions are not proportional to the gravitational constant in higher dimensions, but are shifted with respect to their standard values. This effect opens up new scenarios where a maximally symmetric solution in higher dimensions could decay into the compactified spacetime either by tunneling or through a gravitational analog of ghost condensation. Indeed, this is what occurs requiring both the extra dimensions and the four-dimensional cosmological constant to be small.

Local well-posedness in Lovelock gravity

It has long been known that Lovelock gravity, being of Cauchy–Kowalevskaya type, admits a well defined initial value problem for analytic data. However, this does not address the physically important issues of continuous dependence of the solution on the data and the domain of dependence property. In this note, we fill this gap in our understanding of the (local) dynamics of the theory. We show that, by a known mathematical trick, the fully nonlinear harmonic-gauge-reduced Lovelock field equations can be made equivalent to a quasilinear PDE system. Due to this equivalence, an analysis of the principal symbol, as has appeared in recent works by other authors, is sufficient to decide the issue of local well-posedness of perturbations about a given background.

Gauged Wess-Zumino-Witten models for space-time groups and gravitational actions

In this paper we investigate gauged Wess-Zumino-Witten models for space-time groups as gravitational theories, following the trend of recent work by Anabalon, Willison and Zanelli. We discuss the field equations in any dimension and study in detail the simplest case of two space-time dimensions and gauge group SO(2,1). For this model we study black hole solutions and we calculate their mass and entropy which resulted in a null value for both.

Intersecting hypersurfaces in AdS and Lovelock gravity

Colliding and intersecting hypersurfaces filled with matter (membranes) are studied in the Lovelock higher order curvature theory of gravity. Lovelock terms couple hypersurfaces of different dimensionalities, extending the range of possible intersection configurations. We restrict the study to constant curvature membranes in constant curvature anti-de Sitter (AdS) and dS background and consider their general intersections. This illustrates some key features which make the theory different from the Einstein gravity. Higher co-dimension membranes may lie at the intersection of co-dimension one hypersurfaces in Lovelock gravity; the hypersurfaces are located at the discontinuities of the first derivative of the metric, and they need not carry matter. The example of colliding membranes shows that general solutions can only be supported by (spacelike) matter at the collision surface, thus naturally conflicting with the dominant energy condition (DEC). The imposition of the DEC gives selection rules on the type...

Lovelock gravity and Weyl's tube formula

In four space-time dimensions, there are good theoretical reasons for believing that general relativity is the correct geometrical theory of gravity, at least at the classical level. If one admits the possibility of extra space-time dimensions, what would we expect classical gravity to be like? It is often stated that the most natural generalization is Lovelocks theory, which shares many physical properties with general relativity. But there are also key differences and problems. A potentially serious problem is the breakdown of determinism, which can occur when the matrix of coefficients of second time derivatives of the metric degenerates. This can be avoided by imposing inequalities on the curvature. Here it is argued that such inequalities occur naturally if the Lovelock action is obtained from Weyls formulas for the volume and surface area of a tube. Part of the purpose of this article is to give a treatment of the Weyl tube formula in terminology familiar to relativists and to give an appropriate (straightforward) generalization to a tube embedded in Minkowski space.