arXiv subjects
Publications and source records attributed to Gerard Clement.
We derive all the sourceless solutions of three-dimensional conformal Killing gravity with two Killing vectors. Along with singular solutions and BTZ black holes, the stationary solutions include regular warped AdS3 black holes and wormholes.
We comment on the derivation of an analytical solution presented in arXiv:1309.1629, show that it belongs to a family of separable solutions previously constructed in arXiv:gr-qc/0109002, and question its relevance to critical collapse.
We investigate solutions of new massive gravity with two commuting Killing vectors, one of which is null, with a special emphasis on black hole solutions. Besides extreme BTZ black holes and, for a special value of the coupling constant, massless null warped black holes, we also obtain for a critical coupling a family of massive "log" black holes. These are asymptotic to the extreme BTZ black holes in the sense of log gravity.
We investigate stationary, rotationally symmetric solutions of a recently proposed three-dimensional theory of massive gravity. Along with BTZ black holes, we also obtain warped AdS_3 black holes, and (for a critical value of the cosmological constant) AdS_2 x S^1 as solutions. The entropy, mass and angular momentum of these black holes are computed.
We obtain the general static, spherically symmetric solution for the Einstein-Maxwell-dilaton system in four dimensions with a phantom coupling for the dilaton and/or the Maxwell field. This leads to new classes of black hole solutions, with single or multiple horizons. Using the geodesic equations, we analyse the corresponding Penrose diagrams revealing, in some cases, new causal structures.
Classical gravitating field theories reduced to three dimensions admit manifest gauge invariances and hidden symmetries, which together make up the invariance group G of the theory. If this group is large enough, the target space is a symmetric space G/H. New solutions may be generated by the action of invariance transformations on a seed solution. Another application is the construction of multicenter solutions from null geodesics of the target space. After a general introduction on this sigma-model approach, I will discuss the case of five-dimensional gravity, with invariace group SL(3,R), and minimal five-dimensional supergravity, with invariance group G_{2(2)}. I will also describe recent attempts at the generation of new charged rotating black rings.
The 14 Killing vectors of the target space for five-dimensional minimal supergravity reduced to three dimensions are explicitly constructed in terms of the original field variables. These vectors generate the Lie algebra of $G_2$. We also construct a symmetrical $7\times7$ matrix representative of the coset $G_{2(+2)}/((SL(2,R)\times SL(2,R))$ as a function of the same fields.
A solution generating technique is developed for D=5 minimal supergravity with two commuting Killing vectors based on the $G_2$ U-duality arising in the reduction of the theory to three dimensions. The target space of the corresponding 3-dimensional sigma-model is the coset $G_{2(2)}/(SL(2,R)\times SL(2,R))$. Its isometries constitute the set of solution generating symmetries. These include two electric and two magnetic Harrison transformations with the corresponding two pairs of gauge transformations, three $SL(2,R) S$-duality transformations, and the three gravitational scale, gauge and Ehlers transformations (altogether 14). We construct a representation of the coset in terms of $7\times 7$ matrices realizing the automorphisms of split octonions. Generating a new solution amounts to transforming the coset matrices by one-parametric subgroups of $G_{2(2)}$ and subsequently solving the dualization equations. Using this formalism we derive a new charged black ring solution with two independent parameters of rotation.
We extend the Abbott-Deser-Tekin approach to the computation of the Killing charge for a solution of topologically massive gravity (TMG) linearized around an arbitrary background. This is then applied to evaluate the mass and angular momentum of black hole solutions of TMG with non-constant curvature asymptotics. The resulting values, together with the appropriate black hole entropy, fit nicely into the first law of black hole thermodynamics.
We study dyonic solutions to the gravity-dilaton-antisymmetric form equations with the goal of identifying new $p$-brane solutions on the fluxed linear dilaton background. Starting with the generic solutions constructed by reducing the system to decoupled Liouville equations for certain values of parameters, we identify the most general solution whose singularities are hidden behind a regular event horizon, and then explore the admissible asymptotic behaviors. In addition to known asymptotically flat dyonic branes, we find two classes of asymptotically non-flat solutions which can be interpreted as describing magnetically charged branes on the electrically charged linear dilaton background (and the $S$-dual configuration of electrically charged branes on the magnetically charged background), and uncharged black branes on the dyonically charged linear dilaton background. This interpretation is shown to be consistent with the first law of thermodynamics for the new solutions.
We show that the complete static black p-brane supergravity solution with a single charge contains two and only two branches with respect to behavior at infinity in the transverse space. One branch is the standard family of asymptotically flat black branes, and another is the family of black branes which asymptotically approach the linear dilaton background with antisymmetric form flux (LDB). Such configurations were previously obtained in the near-horizon near-extreme limit of the dilatonic asymptotically flat p-branes, and used to describe the thermal phase of field theories involved in the DW/QFT dualities and the thermodynamics of little string theory in the case of the NS5-brane. Here we show by direct integration of the Einstein equations that the asymptotically LDB p-branes are indeed exact supergravity solutions, and we prove a new uniqueness theorem for static p-brane solutions satisfying cosmic censorship. In the non-dilatonic case, our general non-asymptotically flat p-branes are uncharged black branes on the background $AdS_{p+2}\times S^{D-p-2}$ supported by the form flux. We develop the general formalism of quasilocal quantities for non-asymptotically flat supergravity solutions with antisymmetric form fields, and show that our solutions satisfy the first law of theormodynamics. We also suggest a constructive procedure to derive rotating asymptotically LDB brane solutions.
We show that previously known non-asymptotically flat static black hole solutions of Einstein-Maxwell-dilaton theory may be obtained as near-horizon limits of asymptotically flat black holes. Specializing to the case of the dilaton coupling constant $α^2 = 3$, we generate from the non-asymptotically flat magnetostatic or electrostatic black holes two classes of rotating dyonic black hole solutions. The rotating dyonic black holes of the ``magnetic'' class are dimensional reductions of the five-dimensional Myers-Perry black holes relative to one of the azimuthal angles, while those of the ``electric'' class are twisted dimensional reductions of rotating dyonic Rasheed black strings. We compute the quasi-local mass and angular momentum of our rotating dyonic black holes, and show that they satisfy the first law of black hole thermodynamics, as well as a generalized Smarr formula. We also discuss the construction of non-asymptotically flat multi-extreme black hole configurations.
Critical collapse of a self-gravitating scalar field in a (2+1)-dimensional spacetime with negative cosmological constant seems to be dominated by a continuously self-similar solution of the field equations without cosmological constant. However, previous studies of linear perturbations in this background were inconclusive. We extend the continuously self-similar solutions to solutions of the field equations with negative cosmological constant, and analyse their linear perturbations. The extended solutions are characterized by a continuous parameter. A suitable choice of this parameter seems to improve the agreement with the numerical results. We also study the dynamics of the apparent horizon in the extended background.
We present new solutions to Einstein-Maxwell-dilaton-axion (EMDA) gravity in four dimensions describing black holes which asymptote to the linear dilaton background. In the non-rotating case they can be obtained as the limiting geometry of dilaton black holes. The rotating solutions (possibly endowed with a NUT parameter) are constructed using a generating technique based on the Sp(4,R) duality of the EMDA system. In a certain limit (with no event horizon present) our rotating solutions coincide with supersymmetric Israel-Wilson-Perjes type dilaton-axion solutions. In presence of an event horizon supersymmetry is broken. The temperature of the static black holes is constant, and their mass does not depend on it, so the heat capacity is zero. We investigate geodesics and wave propagation in these spacetimes and find superradiance in the rotating case. Because of the non-asymptotically flat nature of the geometry, certain modes are reflected from infinity, in particular, all superradiant modes are confined. This leads to classical instability of the rotating solutions. The non-rotating linear dilaton black holes are shown to be stable under spherical perturbations.
We perform a complete integration of the Einstein-dilaton-antisymmetric form action describing black p-branes in arbitrary dimensions assuming the transverse space to be homogeneous and possessing spherical, toroidal or hyperbolic topology. The generic solution contains eight parameters satisfying one constraint. Asymptotically flat solutions form a five-parametric subspace, while conditions of regularity of the non-degenerate event horizon further restrict this number to three, which can be related to the mass and the charge densities and the asymptotic value of the dilaton. In the case of a degenerate horizon, this number is reduced by one. Our derivation constitutes a constructive proof of the uniqueness theorem for $p$-branes with the homogeneous transverse space. No asymptotically flat solutions with toroidal or hyperbolic transverse space within the considered class are shown to exist, which result can be viewed as a demonstration of the topological censorship for p-branes. From our considerations it follows, in particular, that some previously discussed p-brane-like solutions with extra parameters do not satisfy the standard conditions of asymptotic flatness and absence of naked singularities. We also explore the same system in presence of a cosmological constant, and derive a complete analytic solution for higher-dimensional charged topological black holes, thus proving their uniqueness.
We show that an analytical continuation of the Vuorio solution to three-dimensional topologically massive gravity leads to a two-parameter family of black hole solutions, which are geodesically complete and causally regular within a certain parameter range. No observers can remain static in these spacetimes. We discuss their global structure, and evaluate their mass, angular momentum, and entropy, which satisfy a slightly modified form of the first law of thermodynamics.
We propose a new definition for the mass and angular momentum of neutral or electrically charged black holes in 2+1 gravity with two Killing vectors. These finite conserved quantities, associated with the SL(2,R) invariance of the reduced mechanical system, are shown to be identical to the quasilocal conserved quantities for an improved gravitational action corresponding to mixed boundary conditions. They obey a general Smarr-like formula and, in all cases investigated, are consistent with the first law of black hole thermodynamics. Our framework is applied to the computation of the mass and angular momentum of black hole solutions to several field-theoretical models.
We complete the list of fluxbrane solutions in classical supergravities by introducing Melvin type space-times supported by antisymmetric forms of rank $D-1$ and their pseudoscalar duals. In IIB theory these solutions belong to the same family as the seven-brane and D-instanton. In current notation, a fluxbrane supported by the D-1 form is an F0 brane, its euclidean continuation is a cylindrical background which ``interacts'' with a pointlike instanton. The general F0 brane can have a transverse space S_k times R^{(D-k-2)} with 1 <= k <= D-2. For k=1 we find the complete solution containing four parameters, three of them associated with pointlike singularities on the Melvin-type background. The S-dual to the F0 brane in ten dimensions is the F8 fluxbrane of codimension one, or F-wall, similar fluxbranes exist in any dimensions if an appropriate form field is present. F-walls contain naked singularities unless one introduces source branes. In such a way one obtains new brane-world type solutions with two bulk scalar fields. Their relation to the supersymmetric brane-worlds is discussed.