arXiv subjects

Aimeric Colléaux

Publications and source records attributed to Aimeric Colléaux.

9 recordsLinked to original sources

arXiv2026

Rational regular black holes in non-polynomial gravity

We consider the $d\geq 4$ non-polynomial pure gravity theories defined so that their 2D reduction to spherical symmetry minimally modifies that of General Relativity at small distances. They satisfy Birkhoff theorem and admit exact black hole solutions for an arbitrary number of couplings. These solutions have a logarithmic leading correction to the entropy and a quantum-like correction to the Newtonian potential, both arising from the regularised critical order $d=2p$ theory, which is related in even dimensions to the Euler characteristic of the 2D orbit space. These black holes can be made regular, without the need for infinite towers of corrections, using invariants of any order $p>d/2$. In even dimensions, their smoothness is linear in the number of corrections and does not require fine-tuning. We construct a class of theories admitting as unique (massless) vacuum an extremal black hole deformation of (A)dS$_4$ or M$_4$ with vanishing entropy, so that Nernst's third law of thermodynamics is satisfied without discontinuity in the entropy. We show that a Maxwell field does not disrupt the regularity of the metric, and that simple non-minimal couplings in the action enable to regularise the electric field. Considering infinite towers of corrections, we construct quasi-regular black holes with one horizon as well as regular (A)dS-core ones with a near-extremal inner horizon for any mass. When charged, these two types of black holes prevent or tame the mass inflation provided the mass and charge satisfy an inequality of the form $M > α\ell + βQ^2 / \ell$, where $α$ and $β$ are numerical factors depending on the specific model, while $\ell$ is the length scale controlling the high-energy corrections. The quasi-regular black holes are sufficient to resolve the Coulomb singularity without the need for non-minimal couplings.

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arXiv2026

Quasi-topological gravity for 4-dimensional Taub-NUT, near-horizon extreme Kerr, and swirling symmetries

We classify 4-dimensional gravitational theories with integrability properties analogous to quasi-topological gravity, but for metrics with the symmetries of spherical, hyperbolic, and planar Schwarzschild and Taub-NUT solutions, their double-Wick-rotated counterparts - the B-metrics, the near-horizon extreme Kerr, and the swirling universe - and the Eguchi-Hanson instanton. These are the symmetries that allow consistent reductions (principle of symmetric criticality) with 4 Killing vectors and 3-dimensional orbits. Considering theories depending only on the Riemann tensor, we show that, for these metrics, only those with third-order equations (second-order after trivial integration) can be analytic in the Riemann tensor. We show that there is a unique theory with first-order field equations (algebraic after trivial integration, with the same integrability as general relativity) at each order in curvature and construct regular static black holes from infinite towers of these high-energy corrections to general relativity. For these theories, we obtain closed-form solutions for all the symmetries listed above, which we analyze to ensure they have a clear physical interpretation.

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arXiv2025

Double Wick rotations between symmetries of Taub-NUT, near-horizon extreme Kerr, and swirling spacetimes

We explicitly show that certain 4-dimensional infinitesimal group actions with 3-dimensional orbits are related by double Wick rotations. In particular, starting with the symmetries of the spherical/hyperbolic/planar Taub-NUT spacetimes, one can obtain symmetries of the near-horizon extreme Kerr (NHEK) geometry or swirling universe by complex analytic continuations of coordinates. Similarly, the static spherical/hyperbolic/planar symmetries (i.e., symmetries of the Schwarzschild spacetime and other A-metrics) are mapped to symmetries of the B-metrics (or Melvin spacetime). All these mappings are theory-independent -- they constitute relations among symmetries themselves, and, hence among the classes of symmetry-invariant metrics and electromagnetic field strengths, rather than among specific solutions. Consequently, finding, e.g., vacuum Taub-NUT-type solutions in a given gravitational theory automatically yields vacuum NHEK- or swirling-type solutions of that theory, with a possible extension to the electromagnetic case.

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arXiv2025

Degenerate higher-order Maxwell-Einstein theories

We classify higher-order Maxwell-Einstein theories linear in the curvature tensor and quadratic in the derivatives of the electromagnetic field strength whose kinetic matrices are degenerate. This provides a generalisation of quadratic degenerate higher-order scalar-tensor theories for a U(1) gauge field. After establishing a classification of the independent Lagrangians, we obtain all the theories with at most third order field equations involving only second order derivatives of the metric, thus generalising Horndeski's quadratic theory for a gauge field. Some of these are shown to be conformally invariant. We then classify degenerate non-minimally coupled interactions, obtaining all conformally invariant ones. Finally, we investigate the effect of U(1)-preserving disformal transformations on these degenerate Lagrangians. The ``mimetic" singular transformations are obtained and new ghost-free degenerate theories are generated.

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arXiv2024

Degenerate Higher-Order Maxwell Theories in Flat Space-Time

We consider, in Minkowski spacetime, higher-order Maxwell Lagrangians with terms quadratic in the derivatives of the field strength tensor, and study their degrees of freedom. Using a 3+1 decomposition of these Lagrangians, we extract the kinetic matrix for the components of the electric field, corresponding to second time derivatives of the gauge field. If the kinetic matrix is invertible, the theory admits five degrees of freedom, namely the usual two polarisations of a photon plus three extra degrees of freedom which are shown to be Ostrogradski ghosts. We also classify the cases where the kinetic matrix is non-invertible and, using analogous simple models, we argue that, even though the degeneracy conditions reduce the number of degrees of freedom, it does not seem possible to fully eliminate all potential Ostrogradski ghosts.

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arXiv2024

Classification of generalised higher-order Einstein-Maxwell Lagrangians

We classify all higher-order generalised Einstein-Maxwell Lagrangians that include terms linear in the curvature tensor and quadratic in the derivatives of the electromagnetic field strength tensor. Using redundancies due to the Bianchi identities, dimensionally dependent identities and boundary terms, we show that a general Lagrangian of this form can always be reduced to a linear combination of only 21 terms, with coefficients that are arbitrary functions of the two scalar invariants derived from the field strength. We give an explicit choice of basis where these 21 terms include 3 terms linear in the Riemann tensor and 18 terms quadratic in the derivatives of the field strength.

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arXiv2020

Dimensional aspects of Lovelock-Lanczos gravity

There has recently been an increasing interest in regularizations of Lovelock-Lanczos gravity (LLG) in four dimensions, in which dimensional poles and possibly counter-terms are introduced to compensate the vanishing of the Lovelock field equations in critical and lower dimensions. In this paper, we review and extend some of these results. We first find a class of LLG theories whose perturbative expansion around a given (A)dS vacuum can be regularized up to arbitrary order, the simplest one being close to Lovelock gravities with a unique vacuum. If well-defined, these models might be interpreted as effective field theories of gravitons in four dimensions, or might be combined with other regularization approaches. Among those, we establish the general procedure to obtain $4$D covariant and background independent regularizations from metric transformations. In the conformal (and critical) case, we generalize previous results obtained for the Gauss-Bonnet theory to the full Lovelock series. Similarly, the regularization of Gauss-Bonnet gravity from the breaking of $4$D-covariance down to $3$D is generalized to arbitrary curvature order, seemingly resulting in new Minimally Modified gravities propagating solely the two degrees of freedom of the graviton. Finally, we present general results regarding the minisuperspace regularization of specific sectors of LLG. Non-perturbative (in curvature) regularized theories admitting non-singular black holes as well as non-singular past-dS$_4$ and cyclic closed cosmologies are found. We conclude with the non-uniqueness of these background regularizations by finding inequivalent regularizations of the Bianchi I sector of Lovelock-Lanczos gravity in four dimensions.

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arXiv2017

Non-polynomial Lagrangian approach to Regular Black Holes

We present a review on Lagrangian models admitting spherically symmetric regular black holes, and cosmological bounce solutions. Non-linear electrodynamics, non-polynomial gravity, and fluid approaches are explained in details. They consist respectively in a gauge invariant generalization of the Maxwell Lagrangian, in modifications of the Einstein-Hilbert action via non-polynomial curvature invariants, and finally in the reconstruction of density profiles able to cure the central singularity of black holes. The non-polynomial gravity curvature invariants have the special property to be second order and polynomial in the metric field, in spherically symmetric spacetimes. Along the way, other models and results are discussed, and some general properties that regular black holes should satisfy are mentioned. A covariant Sakharov criterion for the absence of singularities in dynamical spherically symmetric spacetimes is also proposed and checked for some examples of such regular metric fields.

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arXiv2015

Modified Gravity Models Admitting Second Order Equations of Motion

The aim of this paper is to find higher order geometrical corrections to the Einstein-Hilbert action that can lead to only second order equations of motion. The metric formalism is used, and static spherically symmetric and Friedmann-Lemaître space-times are considered, in four dimensions. The FKWC-basis are introduced in order to consider all the possible invariant scalars, and both polynomial and non-polynomial gravities are investigated.

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