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Gérard Clément

Publications and source records attributed to Gérard Clément.

At least 19 recordsLinked to original sources
arXiv2026

A wormhole with two black holes

We report on a new three-parameter stationary solution of the four-dimensional vacuum Einstein equations, which describes a Lorentzian wormhole harboring two antipodal co-rotating black holes. These are hung from one of the two spacelike infinities by two semi-infinite cosmic strings with positive or negative tension. We evaluate the Komar masses and angular momenta of the two black holes, and check that these obey the usual Smarr relation, as well as the generalized first law for a system of collinear black holes and cosmic strings. While free from Misner strings, this spacetime allows closed timelike curves within a bounded volume. The metric also admits a naked ring singularity for almost all values of the parameters.

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arXiv2026

The gravimagnetic dipole

We investigate a previously constructed stationary solution of the vacuum Einstein equations, which represents a system of two non-extreme black holes with equal masses and opposite NUT charges, connected by a Misner string with tension. For large separations, the inverse square law force measured by this tension is attractive or repulsive, according to the relative values of the masses and NUT charges. For small separations, the force is always repulsive, so that the system cannot collapse to a single black hole. For given values of the black hole masses and NUT charges, there is a unique configuration such that the Misner string is tensionless. This behaves asymptotically as the Kerr solution, but can be overspinning while remaining free from a ring singularity, thus evading the usual black hole uniqueness theorems. All double black hole and string configurations satisfy a generalized first law of black hole mechanics where the two black holes and the Misner string are treated on an equal footing.

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arXiv2024

Cotton gravity is not predictive

It is well-known that the theory of Cotton gravity proposed by Harada is trivially solved by all isotropic and homogeneous cosmologies. We show that this under-determination is more general. More precisely, the degree of arbitrariness in the solutions increases with the degree of symmetry. We give two simple examples. The first is that of static spherically symmetric solutions, which depend on an arbitrary function of the radial coordinate. The second is that of anisotropic cosmologies, which depend on an arbitrary function of time.

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arXiv2024

Spherical symmetric solutions of conformal Killing gravity: black holes, wormholes, and sourceless cosmologies

The most general set of static and spherically symmetric solutions for conformal Killing gravity coupled to Maxwell fields is presented in closed form. These solutions, depending on six parameters, include non-asymptotically flat black holes or naked singularities, non-asymptotically flat traversable wormholes, and (possibly singularity-free) closed universes. We also consider the inverse problem, showing that the most general energy-momentum tensor generating a given static spherically symmetric metric depends on three parameters. Sourceless time-dependent isotropic solutions are also given. These solutions depending on the curvature, the cosmological constant, and a new integration constant $α$, present a rich variety, including singularity-free eternal cosmologies and universes evolving symmetrically from a big bang to a big crunch within a finite lapse of time.

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arXiv2024

Mass formulas for supergravity black holes with string singularities

We extend the derivation of mass formulas for stationary axisymmetric asymptotically locally flat solutions with string singularities on the polar axis to general supergravity actions containing vector and scalar fields. It is based on the rod structure of the solutions in Weyl coordinates and is applicable to black holes with Dirac and Misner strings. The obtained formulas differ from the corresponding ones in Einstein-Maxwell theory only by summation over all independent electric charges.

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arXiv2024

Farewell to Cotton gravity

We reformulate our proof of the under-determination of Cotton gravity in terms of the Codazzi parametrization.

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arXiv2023

The first law for stationary axisymmetric multi-black hole systems

In the framework of Einstein-Maxwell theory, we consider collinear arrays of rotating electrically charged black holes connected by Misner-Dirac strings carrying gravimagnetic and magnetic fluxes. The first law of mechanics for these systems is derived. It involves as dynamical variables the areas, angular momenta and electric charges of the various Killing horizons -- black holes and Misner strings. When the gravimagnetic fluxes all vanish, the first law reduces to a form where the dynamical variables associated with the strings are the string tensions and magnetic fluxes. This form is not generically invariant under electric-magnetic duality.

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arXiv2023

Rotating traversable wormholes in Einstein-Maxwell theory

It is well-known that traversable wormhole solutions to the Einstein equations require the existence of an exotic matter source violating the null energy condition. An apparent exception is the overcharged Kerr-Newman-NUT solution of the Einstein-Maxwell equations, which has all the properties of a geodesically complete, traversable wormhole spacetime. We show that the exotic matter sourcing this consists in two counter-rotating tensionless straight cosmic strings -- the Misner-Dirac strings -- which, as expected, violate the null energy condition. The wormhole possesses an ergoregion, but no superradiance. The geodesic motion in this spacetime is briefly discussed, and the absence of closed circular null geodesics is demonstrated.

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arXiv2021

Einstein-Maxwell-Dilaton-Axion mass formulas for black holes with struts and strings

Mass formulas are obtained for stationary axisymmetric solutions of the Einstein-Maxwell dilaton-axion theory, which have a regular rod structure on the axis of symmetry. Asymptotic mass, angular momentum and charge are expressed as the sums of masses, angular momenta and charges of rods dressed with field contributions. The calculation is based on a three-dimensional sigma model representation of the stationary EMDA system and the Tomimatsu approach proposed for the Einstein-Maxwell system. Our results provide an alternative interpretation of mass formulas and thermodynamics for black holes with Dirac and Misner strings. It is also applicable to aligned multiple black holes with struts.

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arXiv2020

Nutty Kaluza-Klein dyons revisited

We extend the previous analysis of (locally) asymptotically flat solutions of Kaluza-Klein (KK) theory by assuming that the dilaton charge is an independent parameter. This corresponds to a general nondegenerate matrix of charges within the geodesic sigma model approach and comes into contact with singular solutions of the four-dimensional Einstein-scalar theory. New features of the degenerate class of solutions, which includes regular KK black holes, are also revealed. Solving the constraint equation, we find three distinct branches of the dilaton charge as a function of the other asymptotic charges, one of which contains the previously known solutions, and the other two, related by electric/magnetic duality, are new and singular. We also investigate whether a super-extreme non-rotating solution in the presence of a Newman-Unti-Tamburino (NUT) charge can become a wormhole, as is the case in Einstein-Maxwell theory. It is shown that the dilaton prevents this possibility, while non-traversable five-dimensional vacuum gravitational wormholes can exist. Finally, we analyze the geodesic structure within the chronosphere around the Misner string of Nutty KK dyons, showing that there are no closed timelike geodesics.

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arXiv2019

Balanced magnetized double black holes

We report on a two-parameter family of exact asymptotically flat stationary solutions to Einstein-Maxwell theory. These solutions are free from ring singularities in a specific parameter range. They represent systems of two non-rotating extreme black holes with opposite magnetic and NUT charges, connected by a tensionless Dirac-Misner string. For a given ADM mass of the system, the distance between the two black holes has a lower bound. We also discuss the limit in which the two constituent black holes are far apart.

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arXiv2018

Rotating magnetized black diholes

We analyze a four-parameter class of asymptotically flat magnetized solutions to the Einstein-Maxwell equations constructed by Manko et al., and show that these represent systems of two co-rotating extreme black holes with equal masses and electric charges, and opposite magnetic and NUT charges, connected by a cosmic string. We discuss several three-parameter subclasses, and determine in each case the parameter domain in which the ring singularity is absent. We find a two-parameter subclass and a one-parameter subclass where the conical singularity is also absent in the horizon co-rotating frame.

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arXiv2018

Hairy black hole solutions in a three-dimensional Galileon model

We investigate stationary rotationally symmetric solutions of a particular truncation of Horndeski theory in three dimensions, including a non-minimal scalar kinetic coupling to the curvature. After discussing the special case of a vanishing scalar charge, which includes most of the previously known solutions, we reduce the general case to an effective mechanical model in a three-dimensional target space. We analyze the possible near-horizon behaviors, and conclude that black hole solutions with degenerate horizons and constant curvature asymptotics may exist if the minimal and non-minimal scalar coupling constants have the same sign. In a special case, we find a new analytic rotating black hole solution with scalar hair and degenerate horizon. This is geodesically and causally complete, and asymptotic to the extreme BTZ metric. We also briefly discuss soliton solutions in another special case.

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arXiv2018

On the Smarr formula for rotating dyonic black holes

We revisit the derivation by Tomimatsu of the generalized Komar integrals giving the mass and angular momentum of rotating Einstein-Maxwell black holes. We show that, contrary to Tomimatsu's claim, the usual Smarr formula relating the horizon mass and angular momentum still holds in the presence of both electric and magnetic charges. The simplest case is that of dyonic Kerr-Newman black holes, for which we recover the modified Smarr formula relating the asymptotic mass and angular momentum, the difference between asymptotic and horizon masses being equal to the sum of the two Dirac string masses. Our results apply in particular to the case of dyonic dihole solutions which have been investigated recently.

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arXiv2018

Stationary double black hole without naked ring singularity

Recently double black hole vacuum and electrovacuum metrics attracted attention as exact solutions suitable for visualization of ultra-compact objects beyond the Kerr paradigm. However, many of the proposed systems are plagued with ring curvature singularities. Here we present a new simple solution of this type which is asymptotically Kerr, has zero electric and magnetic charges, but is endowed with magnetic dipole moment and electric quadrupole moment. It is manifestly free of ring singularities, and contains only a mild string-like singularity on the axis corresponding to a distributional energy-momentum tensor.Its main constituents are two extreme co-rotating black holes carrying equal electric andopposite magnetic and NUT charges.

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arXiv2018

Motion of charged particles in a NUTty Einstein-Maxwell spacetime and causality violation

We investigate the motion of electrically charged test particles in spacetimes with closed timelike curves, a subset of the black hole or wormhole Reissner-Nordström-NUT spacetimes without periodic identification of time. We show that, while in the wormhole case there are closed worldlines inside a potential well, the wordlines of initially distant charged observers moving under the action of the Lorentz force can never close or self-intersect. This means that for these observers causality is preserved, which is an instance of our weak chronology protection criterion.

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arXiv2017

A tale of two dyons

We present a one-parameter family of stationary, asymptotically flat solutions of the Einstein-Maxwell equations with only a mild singularity, which are endowed with mass, angular momentum, a dipole magnetic moment and a quadrupole electric moment. We briefly analyze the structure of this solution, which we interpret as a system of two extreme co-rotating black holes with equal masses and electric charges, and opposite magnetic and gravimagnetic charges, held apart by an electrically charged, magnetized string which also acts as a Dirac-Misner string.

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