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Nathalie Deruelle

Publications and source records attributed to Nathalie Deruelle.

At least 19 recordsLinked to original sources
arXiv2018

Einstein-Gauss-Bonnet theory of gravity: The Gauss-Bonnet-Katz boundary term

We propose a boundary term to the Einstein-Gauss-Bonnet action for gravity, which is constructed as the dimensional continuation of the Chern-Weil theorem, and such that the extremization of the full action yields the equations of motion when Dirichlet boundary conditions are imposed. When translated into tensorial language, this boundary term is the generalization to this theory of the Katz boundary term and vector for general relativity. The construction allows to deal with a general background and includes the Gibbons-Hawking-Myers boundary term as a special case, when the background is taken to be a product manifold. As a first application we show that this Einstein Gauss-Bonnet Katz action yields, without any extra ingredients or regularization, the expected mass of the Boulware-Deser black hole.

gr-qc↗
arXiv2018

Chern-Weil theorem, Lovelock Lagrangians in critical dimensions and boundary terms in gravity actions

In this paper we show how to translate into tensorial language the Chern-Weil theorem for the Lorentz symmetry, which equates the difference of the Euler densities of two manifolds to the exterior derivative of a transgression form. For doing so we need to introduce an auxiliary, hybrid, manifold whose geometry we construct explicitely. This allows us to find the vector density, constructed out of spacetime quantities only, whose divergence is the exterior derivative of the transgression form. As a consequence we can show how the Einstein-Hilbert, Gauss-Bonnet and, in general, the Euler scalar densities can be written as the divergences of genuine vector densities in the critical dimensions $D=2,4$, etc. As Lovelock gravity is a dimensional continuation of Euler densities, these results are of relevance for Gauss-Bonnet and, in general, Lovelock gravity. Indeed, these vectors which can be called generalized Katz vectors ensure, in particular, a well-posed Dirichlet variational principle.

gr-qc↗
arXiv2017

Thermodynamics sheds light on black hole dynamics

We propose to unify two a priori distinct aspects of black hole physics : their thermodynamics, and their effective dynamics when they are "skeletonized" as point particles (a useful procedure when tackling, for example, their motion in a coalescing binary system). For that purpose, the Einstein- Maxwell-dilaton (EMD) theory, which contains simple examples of asympotically flat, hairy black hole solutions, will serve as a laboratory. We will find that, when reducing a black hole to a point particle endowed with its specific, scalar-field-sensitive, effective mass, one in fact describes a black hole satisfying the first law of thermodynamics, such that its global charges, and hence its entropy, remain constant. This shows that the integration constant entering the scalar-field dependent mass is its entropy.

gr-qc↗
arXiv2017

Two-body problem in Scalar-Tensor theories as a deformation of General Relativity : an Effective-One-Body approach

In this paper we address the two-body problem in massless Scalar-Tensor (ST) theories within an Effective-One-Body (EOB) framework. We focus on the first building block of the EOB approach, that is, mapping the conservative part of the two-body dynamics onto the geodesic motion of a test particle in an effective external metric. To this end, we first deduce the second post-Keplerian (2PK) Hamiltonian of the two-body problem from the known 2PK Lagrangian. We then build, by means of a canonical transformation a ST-deformation of the general relativistic EOB Hamiltonian which allows to incorporate the Scalar-Tensor (2PK) corrections to the currently best available General Relativity EOB results. This EOB-ST Hamiltonian defines a resummation of the dynamics that may provide information on the strong-field regime, in particular, the ISCO location and associated orbital frequency and can be compared to other, e.g. tidal, corrections.

gr-qc↗
arXiv2016

Einstein-Katz action, variational principle, Noether charges and the thermodynamics of AdS-black holes

In this paper we describe 4-dimensional gravity coupled to scalar and Maxwell fields by the Einstein-Katz action, that is, the covariant version of the "Gamma-Gamma $-$ Gamma-Gamma" part of the Hilbert action supplemented by the divergence of a generalized "Katz vector". We consider static solutions of Einstein's equations, parametrized by some integration constants, which describe an ensemble of asymptotically AdS black holes. Instead of the usual Dirichlet boundary conditions, which aim at singling out a specific solution within the ensemble, we impose that the variation of the action vanishes on shell for the broadest possible class of solutions. We will see that, when a long-range scalar "hair" is present, only sub-families of the solutions can obey that criterion. The Katz-Bicak-Lynden-Bell ("KBL") superpotential built on this (generalized) vector will then give straightforwardly the Noether charges associated with the spacetime symmetries (that is, in the static case, the mass). Computing the action on shell, we will see next that the solutions which obey the imposed variational principle, and with Noether charges given by the KBL superpotential, satisfy the Gibbs relation, the Katz vectors playing the role of "counterterms". Finally, we show on the specific example of dyonic black holes that the sub-class selected by our variational principle satisfies the first law of thermodynamics when their mass is defined by the KBL superpotential.

gr-qc↗
arXiv2014

Disformal Transformations, Veiled General Relativity and Mimetic Gravity

In this Note we show that Einstein's equations for gravity are generically invariant under 'disformations'. We also show that the particular subclass when this is not true yields the equations of motion of 'Mimetic Gravity'. Finally we give the 'mimetic' generalization of the Schwarzschild solution.

gr-qc↗
arXiv2012

Lorentz-violating vs ghost gravitons: the example of Weyl gravity

We show that the ghost degrees of freedom of Einstein gravity with a Weyl term can be eliminated by a simple mechanism that invokes local Lorentz symmetry breaking. We demonstrate how the mechanism works in a cosmological setting. The presence of the Weyl term forces a redefinition of the quantum vacuum state of the tensor perturbations. As a consequence the amplitude of their spectrum blows up when the Lorentz-violating scale becomes comparable to the Hubble radius. Such a behaviour is in sharp contrast to what happens in standard Weyl gravity where the gravitational ghosts smoothly damp out the spectrum of primordial gravitational waves.

gr-qc↗
arXiv2011

Nordstrom's scalar theory of gravity and the equivalence principle

Nordstrom's theory of gravity, which describes gravity by a scalar field in flat spacetime, is observationally ruled out. It is however the only theory of gravity with General Relativity to obey the strong equivalence principle. I show in this paper that this remarkable property is true beyond post-newtonian level and can be related to the existence of a 'Nordstrom-Katz' superpotential.

gr-qc↗
arXiv2010

Conformal transformations and Nordström's scalar theory of gravity

As we shall briefly recall, Nordström's theory of gravity is observationally ruled out. It is however an interesting example of non-minimal coupling of matter to gravity and of the role of conformal transformations. We show in particular that they could be useful to extend manifolds through curvature singularities.

gr-qc↗
arXiv2010

Inflation with a Weyl term, or ghosts at work

In order to assess the role of ghosts in cosmology, we study the evolution of linear cosmological perturbations during inflation when a Weyl term is added to the action. Our main result is that vector perturbations can no longer be ignored and that scalar modes diverge in the newtonian gauge but remain bounded in the comoving slicing.

gr-qc↗
arXiv2010

Conformal equivalence in classical gravity: the example of "veiled" General Relativity

In the theory of General Relativity, gravity is described by a metric which couples minimally to the fields representing matter. We consider here its "veiled" versions where the metric is conformally related to the original one and hence is no longer minimally coupled to the matter variables. We show on simple examples that observational predictions are nonetheless exactly the same as in General Relativity, with the interpretation of this "Weyl" rescaling "à la Dicke", that is, as a spacetime dependence of the inertial mass of the matter constituents.

gr-qc↗
arXiv2009

Hamiltonian formulation of f(Riemann) theories of gravity

We present a canonical formulation of gravity theories whose Lagrangian is an arbitrary function of the Riemann tensor. Our approach allows a unified treatment of various subcases and an easy identification of the degrees of freedom of the theory.

hep-th↗
arXiv2009

Various Hamiltonian formulations of f(R) gravity and their canonical relationships

Various Hamiltonian formulations of f(R) gravity can be found in the literature. Some authors follow the Ostrogradsky treatment of higher derivative theories and introduce as extra variables first order time derivatives of the metric (typically the extrinsic curvature). Some others take advantage of the conformal equivalence of f(R) theory with Einstein's gravity coupled to a scalar field and introduce as an extra variable the scalar curvature R itself, which includes second time derivatives of the metric. We show that, contrarily to some claims, these formulations are related by canonical transformations.

gr-qc↗
arXiv2009

Kerr-Schild ansatz in Einstein-Gauss-Bonnet gravity: An exact vacuum solution in five dimensions

As is well-known, Kerr-Schild metrics linearize the Einstein tensor. We shall see here that they also simplify the Gauss-Bonnet tensor, which turns out to be only quadratic in the arbitrary Kerr-Schild function f when the seed metric is maximally symmetric. This property allows us to give a simple analytical expression for its trace, when the seed metric is a five dimensional maximally symmetric spacetime in spheroidal coordinates with arbitrary parameters a and b. We also write in a (fairly) simple form the full Einstein-Gauss-Bonnet tensor (with a cosmological term) when the seed metric is flat and the oblateness parameters are equal, a=b. Armed with these results we give in a compact form the solution of the trace of the Einstein-Gauss-Bonnet field equations with a cosmological term and a different than b. We then examine whether this solution for the trace does solve the remaining field equations. We find that it does not in general, unless the Gauss-Bonnet coupling is such that the field equations have a unique maximally symmetric solution.

hep-th↗
arXiv2008

"Detuned" f(R) gravity and dark energy

In gravity theories derived from a f(R) Lagrangian, matter is usually supposed to be minimally coupled to the metric, which hence defines a ``Jordan frame.'' However, since the field equations are fourth order, gravity possesses an extra degree of freedom on top of the standard graviton, as is manifest from its equivalent description in the conformally related, Einstein, frame. We introduce explicitly this extra scalar degree of freedom in the action and couple it to matter, so that the original metric no longer defines a Jordan frame. This ``detuning'' puts f(R) gravity into a wider class of scalar--tensor theories. We argue that a ``chameleon-like'' detuning tracing the background matter density may provide purely gravitational models which account for the present acceleration of the universe and evade local gravity constraints.

gr-qc↗
arXiv2007

Junction Conditions in f(R) Theories of Gravity

Taking advantage of the conformal equivalence of f(R) theories of gravity with General Relativity coupled to a scalar field we generalize the Israel junction conditions for this class of theories by direct integration of the field equations. We suggest a specific non-minimal coupling of matter to gravity which opens the possibility of a new class of braneworld scenarios.

gr-qc↗
arXiv2006

Low energy effective gravitational equations on a Gauss-Bonnet brane

We present effective gravitational equations at low energies in a $Z_2$-symmetric braneworld with the Gauss-Bonnet term. Our derivation is based on the geometrical projection approach, and we solve iteratively the bulk geometry using the gradient expansion scheme. Although the original field equations are quite complicated due to the presence of the Gauss-Bonnet term, our final result clearly has the form of the Einstein equations plus correction terms, which is simple enough to handle. As an application, we consider homogeneous and isotropic cosmology on the brane. We also comment on the holographic interpretation of bulk gravity in the Gauss-Bonnet braneworld.

hep-th↗