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Marc Mars

Publications and source records attributed to Marc Mars.

At least 73 records · Page 4Linked to original sources
arXiv2007

Accelerating expansion and change of signature

We show that some types of sudden singularities admit a natural explanation in terms of regular changes of signature on brane-worlds in AdS$_{5}$. The present accelerated expansion of the Universe and its possible ending at a sudden singularity may therefore simply be an indication that our braneworld is about to change its Lorentzian signature to an Euclidean one, while remaining fully regular. An explicit example of this behaviour satisfying the weak and strong energy conditions is presented.

gr-qc↗
arXiv2007

Is the accelerated expansion evidence of a forthcoming change of signature on the brane?

We show that regular changes of signature on brane-worlds in AdS bulks may account for some types of the recently fashionable sudden singularities. Therefore, the possibility that the Universe seems to approach a future sudden singularity at an accelerated rate of expansion might simply be an indication that our braneworld is about to change from Lorentzian to Euclidean signature. Both the brane and the bulk remain fully regular everywhere. We present a model in which the weak and strong energy conditions hold on the brane, in contrast with the standard cosmologies leading to the analogous kinematical behaviour (that is, with a diverging Hubble factor).

gr-qc↗
arXiv2007

On marginally outer trapped surfaces in stationary and static spacetimes

In this paper we prove that for any spacelike hypersurface containing an untrapped barrier in a stationary spacetime satisfying the null energy condition, any marginally outer trapped surface cannot lie in the exterior region where the stationary Killing vector is timelike. In the static case we prove that any marginally outer trapped surface cannot penetrate into the exterior region where the static Killing vector is timelike. In fact, we prove these result at an initial data level, without even assuming existence of a spacetime. The proof relies on a powerful theorem by Andersson and Metzger on existence of an outermost marginally outer trapped surface.

gr-qc↗
arXiv2007

Lorentzian and signature changing branes

General hypersurface layers are considered in order to describe brane-worlds and shell cosmologies. No restriction is placed on the causal character of the hypersurface which may thus have internal changes of signature. Strengthening the results in our previous letter [1], we confirm that a good, regular and consistent description of signature change is achieved in these brane/shells scenarios, while keeping the hypersurface and the bulk completely regular. Our formalism allows for a unified description of the traditional timelike branes/shells together with the signature-changing, or pure null, ones. This allows for a detailed comparison of the results in both situations. An application to the case of hypersurface layers in static bulks is presented, leading to the general Robertson-Walker geometry on the layer --with a possible signature change. Explicit examples on anti de Sitter bulks are then studied. The permitted behaviours in different settings ($Z_{2}$-mirror branes, asymmetric shells, signature-changing branes) are analysed in detail. We show in particular that (i) in asymmetric shells there is an upper bound for the energy density, and (ii) that the energy density within the brane vanishes when approaching a change of signature. The description of a signature change as a `singularity' seen from within the brane is considered. We also find new relations between the fundamental constants in the brane/shell, its tension, and the cosmological and gravitational constants of the bulk, independently of the existence or not of a change of signature.

hep-th↗
arXiv2007

Stability of marginally outer trapped surfaces and existence of marginally outer trapped tubes

The present work extends our short communication Phys. Rev. Lett. 95, 111102 (2005). For smooth marginally outer trapped surfaces (MOTS) in a smooth spacetime we define stability with respect to variations along arbitrary vectors v normal to the MOTS. After giving some introductory material about linear non self-adjoint elliptic operators, we introduce the stability operator L_v and we characterize stable MOTS in terms of sign conditions on the principal eigenvalue of L_v. The main result shows that given a strictly stable MOTS S contained in one leaf of a given reference foliation in a spacetime, there is an open marginally outer trapped tube (MOTT), adapted to the reference foliation, which contains S. We give conditions under which the MOTT can be completed. Finally, we show that under standard energy conditions on the spacetime, the MOTT must be either locally achronal, spacelike or null.

gr-qc↗
arXiv2007

Linear perturbations of matched spacetimes: the gauge problem and background symmetries

We present a critical review about the study of linear perturbations of matched spacetimes including gauge problems. We analyse the freedom introduced in the perturbed matching by the presence of background symmetries and revisit the particular case of spherically symmetry in n-dimensions. This analysis includes settings with boundary layers such as brane world models and shell cosmologies.

gr-qc↗
arXiv2006

Stationary axisymmetric exteriors for perturbations of isolated bodies in general relativity, to second order

Perturbed stationary axisymmetric isolated bodies, e.g. stars, represented by a matter-filled interior and an asymptotically flat vacuum exterior joined at a surface where the Darmois matching conditions are satisfied, are considered. The initial state is assumed to be static. The perturbations of the matching conditions are derived and used as boundary conditions for the perturbed Ernst equations in the exterior region. The perturbations are calculated to second order. The boundary conditions are overdetermined: necessary and sufficient conditions for their compatibility are derived. The special case of perturbations of spherical bodies is given in detail.

gr-qc↗
arXiv2006

Generalized inverse mean curvature flows in spacetime

Motivated by the conjectured Penrose inequality and by the work of Hawking, Geroch, Huisken and Ilmanen in the null and the Riemannian case, we examine necessary conditions on flows of two-surfaces in spacetime under which the Hawking quasilocal mass is monotone. We focus on a subclass of such flows which we call uniformly expanding, which can be considered for null as well as for spacelike directions. In the null case, local existence of the flow is guaranteed. In the spacelike case, the uniformly expanding condition leaves a 1-parameter freedom, but for the whole family, the embedding functions satisfy a forward-backward parabolic system for which local existence does not hold in general. Nevertheless, we have obtained a generalization of the weak (distributional) formulation of this class of flows, generalizing the corresponding step of Huisken and Ilmanen's proof of the Riemannian Penrose inequality.

gr-qc↗
arXiv2005

First and Second Order Perturbations of Hypersurfaces

In this paper we find the first and second order perturbations of the induced metric and the extrinsic curvature of a non-degenerate hypersurface $Σ$ in a spacetime $(M,g)$, when the metric $g$ is perturbed arbitrarily to second order and the hypersurface itself is allowed to change perturbatively (i.e. to move within spacetime) also to second order. The results are fully general and hold in arbitrary dimensions and signature. An application of these results for the perturbed matching theory between spacetimes is presented.

gr-qc↗
arXiv2005

Local existence of dynamical and trapping horizons

Given a spacelike foliation of a spacetime and a marginally outer trapped surface S on some initial leaf, we prove that under a suitable stability condition S is contained in a ``horizon'', i.e. a smooth 3-surface foliated by marginally outer trapped slices which lie in the leaves of the given foliation. We also show that under rather weak energy conditions this horizon must be either achronal or spacelike everywhere. Furthermore, we discuss the relation between ``bounding'' and ``stability'' properties of marginally outer trapped surfaces.

gr-qc↗
arXiv2003

Trapped surfaces and symmetries

We prove that strictly stationary spacetimes cannot contain closed trapped nor marginally trapped surfaces. The result is purely geometric and holds in arbitrary dimension. Other results concerning the interplay between (generalized) symmetries and trapped submanifolds are also presented.

gr-qc↗
arXiv2002

On the Penrose Inequality

We summarize results on the Penrose inequality bounding the ADM-mass or the Bondi mass in terms of the area of an outermost apparent horizon for asymptotically flat initial data of Einstein's equations. We first recall the proof, due to Geroch and to Jang and Wald, of monotonicity of the Geroch-Hawking mass under a smooth inverse mean curvature flow for data with non-negative Ricci scalar, which leads to a Penrose inequality if the apparent horizon is a minimal surface.We then sketch a proof of the Penrose inequality of Malec, Mars and Simon which holds for general horizons and for data satisfying the dominant energy condition, but imposes (in addition to smooth inverse mean curvature flow) suitable restrictions on the data on a spacelike surface. These conditions can, however, at least locally be fulfilled by a suitable choice of the initial surface in a given spacetime. Remarkably, they are also (formally) identical to ones employed earlier by Hayward in order to define a 2+1 foliation on null surfaces, with respect to which the Hawking mass is again monotonic.

gr-qc↗
arXiv2002

On uniqueness of static Einstein-Maxwell-dilaton black holes

We prove uniqueness of static, asymptotically flat spacetimes with non-degenerate black holes for three special cases of Einstein-Maxwell-dilaton theory: For the coupling ``$α= 1$'' (which is the low energy limit of string theory) on the one hand, and for vanishing magnetic or vanishing electric field (but arbitrary coupling) on the other hand. Our work generalizes in a natural, but non-trivial way the uniqueness result obtained by Masood-ul-Alam who requires both $α= 1$ and absence of magnetic fields, as well as relations between the mass and the charges. Moreover, we simplify Masood-ul-Alam's proof as we do not require any non-trivial extensions of Witten's positive mass theorem. We also obtain partial results on the uniqueness problem for general harmonic maps.

gr-qc↗
arXiv2002

Axially symmetric Einstein-Straus models

The existence of static and axially symmetric regions in a Friedman-Lemaitre cosmology is investigated under the only assumption that the cosmic time and the static time match properly on the boundary hypersurface. It turns out that the most general form for the static region is a two-sphere with arbitrarily changing radius which moves along the axis of symmetry in a determined way. The geometry of the interior region is completely determined in terms of background objects. When any of the most widely used energy-momentum contents for the interior region is imposed, both the interior geometry and the shape of the static region must become exactly spherically symmetric. This shows that the Einstein-Straus model, which is the generally accepted answer for the null influence of the cosmic expansion on the local physics, is not a robust model and it is rather an exceptional and isolated situation. Hence, its suitability for solving the interplay between cosmic expansion and local physics is doubtful and more adequate models should be investigated.

gr-qc↗
arXiv2002

G_2 Perfect-Fluid Cosmologies with a proper conformal Killing vector

We study the Einstein field equations for spacetimes admitting a maximal two-dimensional abelian group of isometries acting orthogonally transitively on spacelike surfaces and, in addition, with at least one conformal Killing vector. The three-dimensional conformal group is restricted to the case when the two-dimensional abelian isometry subalgebra is an ideal and it is also assumed to act on non-null hypersurfaces (both, spacelike and timelike cases are studied). We consider both, diagonal and non-diagonal metrics and find all the perfect-fluid solutions under these assumptions (except those already known). We find four families of solutions, each one containing arbitrary parameters for which no differential equations remain to be integrated. We write the line-elements in a simplified form and perform a detailed study for each of these solutions, giving the kinematical quantities of the fluid velocity vector, the energy-density and pressure, values of the parameters for which the energy conditions are fulfilled everywhere, the Petrov type, the singularities in the spacetimes and the Friedmann-Lemaitre-Robertson-Walker metrics contained in each family.

gr-qc↗
arXiv2002

On the Penrose Inequality for general horizons

For asymptotically flat initial data of Einstein's equations satisfying an energy condition, we show that the Penrose inequality holds between the ADM mass and the area of an outermost apparent horizon, if the data are restricted suitably. We prove this by generalizing Geroch's proof of monotonicity of the Hawking mass under a smooth inverse mean curvature flow, for data with non-negative Ricci scalar. Unlike Geroch we need not confine ourselves to minimal surfaces as horizons. Modulo smoothness issues we also show that our restrictions on the data can locally be fulfilled by a suitable choice of the initial surface in a given spacetime.

gr-qc↗
arXiv2002

Stationary and Axisymmetric Perfect Fluids with one Conformal Killing Vector

We study the stationary and axisymmetric non-convective differentially rotating perfect-fluid solutions of Einstein's field equations admitting one conformal symmetry. We analyse the two inequivalent Lie algebras not exhaustively considered in Mars and Senovilla, 1994, and show that the general solution for each Lie algebra depends on one arbitrary function of one of the coordinates while a set of three ordinary differential equations for four unknowns remains to be solved. The conformal Killing vector of these solutions is necessarily homothetic. We summarize in a table all the possible solutions for all the allowed Lie algebras and also add a corrigendum to an erroneous statement in the paper quated above concerning the differentially rotating character of one of the solutions presented

gr-qc↗