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Gérard Clément

Publications and source records attributed to Gérard Clément.

At least 37 records · Page 2Linked to original sources
arXiv2016

Chern-Simons dilaton black holes in 2+1 dimensions

We construct rotating magnetic solutions to the three-dimensional Einstein-Maxwell-Chern-Simons-dilaton theory with a Liouville potential. These include a class of black hole solutions which generalize the warped AdS black holes. The regular black holes belong to two disjoint sectors. The first sector includes black holes which have a positive mass and are co-rotating, while the black holes of the second sector have a negative mass and are counter-rotating. We also show that a particular, non-black hole, subfamily of our three-dimensional solutions may be uplifted to new regular non-asymptotically flat solutions of five-dimensional Einstein-Maxwell-Chern-Simons theory.

gr-qc↗
arXiv2016

NUT wormholes

We show that supercritically charged black holes with NUT provide a new setting for traversable wormholes. This does not require exotic matter, a price being the Misner string singularities. Without assuming time periodicity to make Misner strings unobservable, we show that, contrary to expectations, geodesics do not stop there. Moreover, since there is no central singularity the space-time turns out to be geodesically complete. Another unpleasant feature of spacetimes with NUTs is the presence of regions where the azimuthal angle $φ$ becomes timelike, signalling the appearance of closed timelike curves (CTCs). We show that among them there are no closed timelike or null geodesics, so the freely falling observers should not encounter causality violations. Considering worldlines of charged particles, we find that, although these can become closed in the vicinity of the wormhole throat for large enough charge-to-mass ratio, the non-causal orbits are still disconnected from the distant zones. All these findings support our feeling that wormholes with NUTs deserve to be taken seriously. Integrating the geodesic equations completely, we demonstrate the existence of timelike and null geodesics connecting two asymptotic regions of the wormhole, such that the tidal forces in the throat are reasonably small. We discuss bounds on the NUT charge which follow from the Schwinger pair creation and ionization thresholds and speculate that such NUT wormholes could be present in some galactic centers.

hep-th↗
arXiv2015

Axisymmetric multiwormholes revisited

The construction of stationary axisymmetric multiwormhole solutions to gravitating field theories admitting toroidal reductions to three-dimensional gravitating sigma models is reviewed. We show that, as in the multi-black hole case, strut singularities always appear in this construction, except for very special configurations with an odd number of centers. We also review the analytical continuation of the multicenter solution across the $n$ cuts associated with the wormhole mouths. The resulting Riemann manifold has $2^n$ sheets interconnected by $2^{n-1}n$ wormholes. We find that the maximally extended multicenter solution can never be asymptotically locally flat in all the Riemann sheets.

gr-qc↗
arXiv2015

Rehabilitating space-times with NUTs

We revisit the Taub-NUT solution of the Einstein equations without time periodicity condition, showing that the Misner string is still fully transparent for geodesics. In this case, analytic continuation can be carried out through both horizons leading to a Hausdorff spacetime without a central singularity, and thus geodesically complete. Furthermore, we show that, in spite of the presence of a region containing closed time-like curves, there are no closed causal {\em geodesics}. Thus, some longstanding obstructions to accept the Taub-NUT solution as physically relevant are removed.

hep-th↗
arXiv2015

A scenario for critical scalar field collapse in $AdS_3$

We present a family of exact solutions, depending on two parameters $α$ and $b$ (related to the scalar field strength), to the three-dimensional Einstein-scalar field equations with negative cosmological constant $Λ$. For $b=0$ these solutions reduce to the static BTZ family of vacuum solutions, with mass $M = -α$. For $b\neq0$, the solutions become dynamical and develop a strong spacelike central singularity. The $α<0$ solutions are black-hole like, with a global structure topologically similar to that of the BTZ black holes, and a finite effective mass. We show that the near-singularity behavior of the solutions with $α>0$ agrees qualitatively with that observed in numerical simulations of subcritical collapse. We analyze the linear perturbations of the threshold solution, $α=0$, in the $Λ=0$ approximation, and find that it has only one unstable growing mode, which qualifies it as a candidate critical solution for scalar field collapse.

gr-qc↗
arXiv2014

Quantized rotating Taub-bolt instantons

We argue that previously suggested metrics for rotating Taub-bolt instantons do not satisfy all the necessary regularity conditions, and we present a family of new regular rotating Taub-bolts labelled by an odd integer $k$. There are two types of rotating bolt solutions. The first infinite sequence starts with non-rotating Taub-NUT with positive mass $M_k=N$ for $a=0$ and goes to $(k-2)N$ for $|a|\to \infty$ (or $N$ for $k=1$), where $a$ is the rotation parameter. For the second sequence of rotating Page bolts, the masses $M_k$ go through the value $M_k=5N/4$ for $a=0$ and asymptote to $(k+2)N$ for $|a|\to \infty$.

hep-th↗
arXiv2014

Bertotti-Robinson and soliton string solutions of $D=5$ minimal supergravity

We report on a series of new solutions to five-dimensional minimal supergravity. Our method applies to space-times with two commuting Killing symmetries and consists in combining dimensional reduction on two-spaces of constant curvature with reduction on a two-torus. The first gives rise to various generalized Bertotti-Robinson solutions supported by electric and magnetic fluxes, which presumably describe the near-horizon regions of black holes and black rings (strings). The second provides generating techniques based on U-duality of the corresponding three-dimensional sigma model. We identify duality transformations relating the above solutions to asymptotically flat ones and obtain new globally regular dyonic solitons. Some new extremal asymptotically flat multi-center solutions are constructed too. We also show that geodesic solutions of three-dimensional sigma models passing through the same target space point generically split into disjoint classes which cannot be related by the isotropy subgroup of U-duality.

hep-th↗
arXiv2014

Bertotti-Robinson solutions in five--dimensional quadratic gravity

We construct new solutions of five-dimensional quadratic gravity as direct products of a constant curvature two-surface with a solution of three-dimensional new massive gravity with constant scalar curvature. These solutions could represent near-horizon limits of five-dimensional asymptotically flat black strings or black rings. A number of these non-asymptotically flat solutions are themselves black strings or rings. A by-product of our analysis is the construction of new solutions of four-dimensional quadratic gravity obtained by toroidal reduction of the five-dimensional solutions with flat transverse space. These again include black strings or rings, and an $AdS_2\times T^2$ solution of $f(R)$ gravity for a specific relation between the model parameters.

gr-qc↗
arXiv2013

Bertotti-Robinson solutions of D=5 Einstein-Maxwell-Chern-Simons-Lambda theory

We present a series of new solutions in five-dimensional Einstein-Maxwell-Chern-Simons theory with an arbitrary Chern-Simons coupling $γ$ and a cosmological constant $Λ$. For general $γ$ and $Λ$ we give various generalizations of the Bertotti-Robinson solutions supported by electric and magnetic fluxes, some of which presumably describe the near-horizon regions of black strings or black rings. Among them there is a solution which could apply to the horizon of a topological AdS black ring in gauged minimal supergravity. Others are horizonless and geodesically complete. We also construct extremal asymptotically flat multi-string solutions for $Λ=0$ and arbitrary $γ$.

gr-qc↗
arXiv2013

New coset matrix for D=6 self-dual supergravity

Toroidal reduction of minimal six-dimensional supergravity, minimal five-dimensional supergravity and four-dimensional Einstein-Maxwell gravity to three dimensions gives rise to a sequence of cosets $O(4,3)/(O(4)\times O(3))\supset G_{2(2)}/(SU(2)\times SU(2))\supset SU(2,1)/S(U(2)\times U(1))$ which are invariant subspaces of each other. The known matrix representations of these cosets, however, are not suitable to realize these embeddings which could be useful for solution generation. We construct a new representation of the largest coset in terms of $7\times 7$ real symmetric matrices and show how to select invariant subspaces corresponding to lower cosets by algebraic constraints. The new matrix representative may be also directly applied to minimal five-dimensional supergravity. Due to full O(4,3) covariance it is simpler than the one derived by us previously for the coset $G_{2(2)}/(SU(2)\times SU(2))$.

hep-th↗
arXiv2013

Oxidation of D=3 cosets and Bonnor dualities in $D\leq 6$

Bonnor's map in General Relativity is duality between (dimensionally reduced) vacuum gravity and static truncation of electro-vacuum theory. It was used as a tool to generate an exact solution of electro-vacuum from some vacuum solution. It can be expected that similar dualities will be useful for solution generation in higher-dimensional theories too. Here we study such maps within a class of theories in dimensions $D\leq 6$ using oxidation of D=3 cosets and consistent truncation of the corresponding theories. Our class includes those theories whose D=3 symmetries are subgroups of $G=O(5,4)$. It contains six-dimensional minimal supergravity, five-dimensional minimal and $U(1)^3$ supergravities and a number of four-dimensional theories which attracted attention recently in the search of exact solutions. We give explicit reduction/truncation formulas relating different theories in dimensions $D=4, 5, 6$ in terms of metrics and matter fields and discuss various alternative duality chains between them.

hep-th↗
arXiv2011

Relativité générale: solutions exactes stationnaires

After a brief summary of the foundations of general relativity, we will concentrate on the stationary exact solutions of the Einstein and Einstein-Maxwell equations. A number of these solutions can be interpreted as black holes, corresponding to a special spacetime geometry. Then, we will show that the reformulation of the stationary Einstein-Maxwell equations as a gravitating sigma model provides us with a powerful tool to generate new solutions.

gr-qc↗
arXiv2011

All extremal instantons in Einstein-Maxwell-dilaton-axion theory

We construct explicitly all extremal instanton solutions to $\mathcal{N}=4,\, D=4$ supergravity truncated to one vector field (Einstein-Maxwell-dilaton-axion (EMDA) theory). These correspond to null geodesics of the target space of the sigma-model $G/H=Sp(4,\mathbb{R})/GL(2,\mathbb{R})$ obtained by compactification of four-dimensional Euclidean EMDA on a circle. They satisfy a no-force condition in terms of the asymptotic charges and part of them (corresponding to nilpotent orbits of the $Sp(4,\mathbb{R})$ U-duality) are presumably supersymmetric. The space of finite action solutions is found to be unexpectedly large and includes, besides the Euclidean versions of known Lorentzian solutions, a number of new asymptotically locally flat (ALF) instantons endowed with electric, magnetic, dilaton and axion charges. We also describe new classes of charged asymptotically locally Euclidean (ALE) instantons as well as some exceptional solutions. Our classification scheme is based on the algebraic classification of matrix generators according to their rank, according to the nature of the charge vectors and according to the number of independent harmonic functions with unequal charges. Besides the nilpotent orbits of $G$, we find solutions which satisfy the asymptotic no-force condition, but are not supersymmetric. The renormalized on-shell action for instantons is calculated using the method of matched background subtraction.

hep-th↗
arXiv2011

Phantom Black Holes and Sigma Models

We construct static multicenter solutions of phantom Einstein-Maxwell-dilaton theory from null geodesics of the target space, leading to regular black holes without spatial symmetry for certain discrete values of the dilaton coupling constant. We also discuss the three-dimensional gravitating sigma models obtained by reduction of phantom Einstein-Maxwell, phantom Kaluza-Klein and phantom Einstein-Maxwell-dilaton-axion theories. In each case, we generate by group transformations phantom charged black hole solutions from a neutral seed.

hep-th↗
arXiv1998

Spinning ring wormholes: a classical model for elementary particles?

Static horizonless solutions to the Einstein--Maxwell field equations, with only a circular cosmic string singularity, are extended to exact rotating asymptotically flat solutions. The possible interpretation of these field configurations as spinning elementary particles or as macroscopic rotating cosmic rings is discussed.

gr-qc↗
arXiv1998

Self--gravitating cosmic rings

The classical Einstein--Maxwell field equations admit static horizonless wormhole solutions with only a circular cosmic string singularity. We show how to extend these static solutions to exact rotating asymptotically flat solutions. For a suitable range of parameter values, these solutions describe charged or neutral rotating closed cosmic strings, with a perimeter of the order of their Schwarzschild radius.

gr-qc↗
arXiv1996

Stationary BPS solutions to dilaton-axion gravity

Stationary four-dimensional BPS solutions to gravity coupled bosonic theories admitting a three-dimensional sigma-model representation on coset spaces are interpreted as null geodesics of the target manifold equipped with a certain number of harmonic maps. For asymptotically flat (or Taub-NUT) space-times such geodesics can be directly parametrized in terms of charges saturating the Bogomol'nyi-Gibbons-Hull bound, and classified according to the structure of related coset matrices. We investigate in detail the ``dilaton-axion gravity'' with one vector field, and show that in the space of BPS solutions an $SO(1,2) \times SO(2)$ classical symmetry is acting. Within the present formalism the most general multicenter (IWP/Taub-NUT dyon) solutions are derived in a simple way. We also discover a large new class of asymptotically flat solutions for which the dilaton and axion charges are constrained only by the BPS bound. The string metrics for these solutions are generically regular. Both the IWP class and the new class contain massless solutions.

hep-th↗