Black Holes in Higher-Derivative Gravity

Extensions of Einstein gravity with higher-order derivative terms arise in string theory and other effective theories, as well as being of interest in their own right. In this paper we study static black-hole solutions in the example of Einstein gravity with additional quadratic curvature terms. A Lichnerowicz-type theorem simplifies the analysis by establishing that they must have vanishing Ricci scalar curvature. By numerical methods we then demonstrate the existence of further black-hole solutions over and above the Schwarzschild solution. We discuss some of their thermodynamic properties, and show that they obey the first law of thermodynamics.Comment: Typos corrected, discussion added, figure changed. 4 pages, 6 figure

Lichnerowicz Modes and Black Hole Families in Ricci Quadratic Gravity

A new branch of black hole solutions occurs along with the standard Schwarzschild branch in $n$-dimensional extensions of general relativity including terms quadratic in the Ricci tensor. The standard and new branches cross at a point determined by a static negative-eigenvalue eigenfunction of the Lichnerowicz operator, analogous to the Gross-Perry-Yaffe eigenfunction for the Schwarzschild solution in standard $n=4$ dimensional general relativity. This static eigenfunction has two r\^oles: both as a perturbation away from Schwarzschild along the new black-hole branch and also as a threshold unstable mode lying at the edge of a domain of Gregory-Laflamme-type instability of the Schwarzschild solution for small-radius black holes. A thermodynamic analogy with the Gubser and Mitra conjecture on the relation between quantum thermodynamic and classical dynamical instabilities leads to a suggestion that there may be a switch of stability properties between the old and new black-hole branches for small black holes with radii below the branch crossing point.Comment: 33 pages, 8 figure

Spherically Symmetric Solutions in Higher-Derivative Gravity

Extensions of Einstein gravity with quadratic curvature terms in the action arise in most effective theories of quantised gravity, including string theory. This article explores the set of static, spherically symmetric and asymptotically flat solutions of this class of theories. An important element in the analysis is the careful treatment of a Lichnerowicz-type `no-hair' theorem. From a Frobenius analysis of the asymptotic small-radius behaviour, the solution space is found to split into three asymptotic families, one of which contains the classic Schwarzschild solution. These three families are carefully analysed to determine the corresponding numbers of free parameters in each. One solution family is capable of arising from coupling to a distributional shell of matter near the origin; this family can then match on to an asymptotically flat solution at spatial infinity without encountering a horizon. Another family, with horizons, contains the Schwarzschild solution but includes also non-Schwarzschild black holes. The third family of solutions obtained from the Frobenius analysis is nonsingular and corresponds to `vacuum' solutions. In addition to the three families identified from near-origin behaviour, there are solutions that may be identified as `wormholes', which can match symmetrically on to another sheet of spacetime at finite radius.Comment: 57 pages, 6 figures; version appearing in journal; minor corrections and clarifications to v

Supersymmetric Electrovacs In Gauged Supergravities

We show that the D=6 SU(2) gauged supergravity of van Nieuwenhuizen et al, obtained by dimensional reduction of the D=7 topologically massive gauged supergravity and previously thought not to be dimensionally reducible, can be further reduced to five and four dimensions. On reduction to D=4 one recovers the special case of the SU(2)XSU(2) gauged supergravity of Freedman and Schwarz for which one of the SU(2) coupling constants vanishes. Previously known supersymmetric electrovacs of this model then imply new ground states in 7-D. We construct a supersymmetric electrovac solution of N=2 SU(2) gauged supergravity in 7-D. We also investigate the domain wall solutions of these theories and show they preserve a half of the supersymmetry.Comment: 29 pages, TeX, no figures. Introduction and conclusion rewritten. New references added. Minor changes to all section

Multiple M-wave interaction with fluxes

We present the equations of motion for multiple M0-brane (multiple M-wave or mM0) system in general eleven dimensional supergravity background. These are obtained in the frame of superembedding approach, but have a rigid structure: they can be restored from SO(1,1) x SO(9) symmetry characteristic for M0. BPS conditions for the 1/2 supersymmetric solution of these equations have the fuzzy 2-sphere solution describing M2-brane.Comment: 4 pages, no figures, RevTeX4. V2. The discussion on BPS conditions and some supersymmetric solutions is added. The explicit values of the coefficients for the interacting terms are presented. Also a couple of minor changes. V3: a small misrint corrected. Published: Phys.Rev.Lett.105 (2010) 07160

A non local unitary vector model in 3-D

We present a unified analysis of single excitation vector models in 3D. We show that there is a family of first order master actions related by duality transformations which interpolate between the different models. We use a Hamiltonian (2+1) analysis to show the equivalence of the self-dual and topologically massive models with a covariant non local model which propagates also a single massive excitation. It is shown how the non local terms appears naturally in the path integral framework.Comment: 13 pages, 1 figur

Euclidean-signature Supergravities, Dualities and Instantons

We study the Euclidean-signature supergravities that arise by compactifying D=11 supergravity or type IIB supergravity on a torus that includes the time direction. We show that the usual T-duality relation between type IIA and type IIB supergravities compactified on a spatial circle no longer holds if the reduction is performed on the time direction. Thus there are two inequivalent Euclidean-signature nine-dimensional maximal supergravities. They become equivalent upon further spatial compactification to D=8. We also show that duality symmetries of Euclidean-signature supergravities allow the harmonic functions of any single-charge or multi-charge instanton to be rescaled and shifted by constant factors. Combined with the usual diagonal dimensional reduction and oxidation procedures, this allows us to use the duality symmetries to map any single-charge or multi-charge p-brane soliton, or any intersection, into its near-horizon regime. Similar transformations can also be made on non-extremal p-branes. We also study the structures of duality multiplets of instanton and (D-3)-brane solutions.Comment: Latex, 50 pages, typos corrected and references adde

A general solution in the Newtonian limit of f(R)- gravity

We show that any analytic $f(R)$-gravity model, in the metric approach, presents a weak field limit where the standard Newtonian potential is corrected by a Yukawa-like term. This general result has never been pointed out but often derived for some particular theories. This means that only $f(R)=R$ allows to recover the standard Newton potential while this is not the case for other relativistic theories of gravity. Some considerations on the physical consequences of such a general solution are addressed.Comment: 5 page

Even-dimensional topological gravity from Chern-Simons gravity

It is shown that the topological action for gravity in 2n-dimensions can be obtained from the 2n+1-dimensional Chern-Simons gravity genuinely invariant under the Poincare group. The 2n-dimensional topological gravity is described by the dynamics of the boundary of a 2n+1-dimensional Chern-Simons gravity theory with suitable boundary conditions. The field $\phi^{a}$, which is necessary to construct this type of topological gravity in even dimensions, is identified with the coset field associated with the non-linear realizations of the Poincare group ISO(d-1,1)

The heat kernel of the compactified D=11 supermembrane with non-trivial winding

We study the quantization of the regularized hamiltonian, $H$, of the compactified D=11 supermembrane with non-trivial winding. By showing that $H$ is a relatively small perturbation of the bosonic hamiltonian, we construct a Dyson series for the heat kernel of $H$ and prove its convergence in the topology of the von Neumann-Schatten classes so that $e^{-Ht}$ is ensured to be of finite trace. The results provided have a natural interpretation in terms of the quantum mechanical model associated to regularizations of compactified supermembranes. In this direction, we discuss the validity of the Feynman path integral description of the heat kernel for D=11 supermembranes and obtain a matrix Feynman-Kac formula.Comment: 19 pages. AMS LaTeX. A whole new section was added and some other minor changes in style where mad