arXiv subjects

José M. M. Senovilla

Publications and source records attributed to José M. M. Senovilla.

At least 19 recordsLinked to original sources

arXiv2026

Study of gravitational radiation at $\mathscr{J}$ for the general type-D Einstein-Maxwell solution with cosmological constant

We characterize the gravitational radiation present in the general Plebański-Demiański type~D solution with cosmological constant $Λ$ of any sign. We show that radiation escapes towards infinity if and only if the acceleration parameter is non-zero. We calculate the Cotton-York tensor and the boundary stress-energy tensor at infinity for negative $Λ$, and for positive $Λ$ the $D$ tensor that complements initial or final data at $\mathscr{J}$. In addition, we recast a recent parametrization of this family of metrics into a new form by a simple homothety, correctly identifying $Λ$, and study the existence and regularity of the possible axes of symmetry, searching for a relation between deficit angles and radiation. We also identify the branch of general non-radiating solutions with non-vanishing Cotton-York tensor at $ \mathscr{J} $.

gr-qc↗

arXiv2026

Asymptotic Gravitational Radiation of Photon Rockets with $Λ$: Point, String, and Sheet Sources

We study the existence of gravitational radiation at infinity for pure-radiation Robinson-Trautman metrics with one spacelike Killing vector and a cosmological constant $Λ$ of arbitrary sign. These metrics describe "photon rockets" with point, string, and sheet sources moving through spacetime while emitting null radiation. For $Λ\neq 0$, we use criteria for the existence of gravitational radiation based on the asymptotic super-Poynting vector. For point sources, we extend to $Λ\neq 0$ the known $Λ=0$ result that the Kinnersley rocket is the only rocket without gravitational radiation. However, for string and sheet sources, new possibilities without gravitational radiation arise. For $Λ>0$, we show that the vanishing of the canonical asymptotic super-Poynting vector---computed with respect to the unit normal to scri---exactly characterizes the absence of radiation. On the other hand, for $Λ<0$, we show that the appropriate criterion is the vanishing of the components normal to scri of the asymptotic super-Poynting vectors associated with any unit timelike vector tangent to scri or, equivalently, the proportionality between the Cotton-York tensor and the holographic stress tensor at scri. In particular, we provide explicit examples of metrics for which the Cotton-York and holographic stress tensors commute, yet gravitational radiation is present because the two tensors are not proportional. We also determine the principal null directions (PNDs) of the rescaled Weyl tensor at scri for both signs of $Λ$ and relate their geometry relative to the normal to scri to the tensorial criteria for gravitational radiation.

gr-qc↗

arXiv2026

Junction Conditions for General Gravitational Theories

The junction conditions for general theories of gravity based on actions that depend on arbitrary functions of the curvature scalar invariants (including differential invariants) are obtained using the distributional formalism. In case of the existence of thin shells, a general expression for the shell energy-momentum tensor is presented. Generalized Israel equations are also obtained. The conditions for a proper matching, without shells, are derived. The main results are: (i) shells arise if the $m$th-covariant derivative of the Riemann tensor is continuous at the matching hypersurface, where $m$ is the maximum order of differentiation appearing in the Lagrangian density; (ii) a proper junction without thin shells requires further that the $(m+1)$-th derivative be also continuous, (iii) theories with $m=0$ that are quadratic in the scalar curvature invariants are special and unique for they allow for discontinuities of the Riemann tensor resulting in the existence of thin shells and {\em gravitational double layers} and (iv) General Relativity and $F(R)$ theories are extraordinary theories that admit shells of curvature (i.e. impulsive gravitational waves) because other theories require the absence of jumps of the second fundamental form across the matching hypersurface. For proper junctions, the continuity across the matching hypersurface of the normal components of the energy-momentum tensor is proven to be a {\em universal} property, independently of the field equations, thereby providing important necessary conditions for any matching in any gravitational theory. All results are derived for a minimal coupling with the matter, but the strategy would be analogous for more general couplings.

gr-qc↗

arXiv2026

Gravitational waves in Cubic Metric-Affine Gravity

We derive new exact gravitational wave solutions with dynamical torsion and nonmetricity tensors in the framework of cubic Metric-Affine Gravity (MAG). For this purpose, we consider the full algebraic classification of the gravitational field in general metric-affine geometries and impose a set of Type N conditions on the field strength tensors that implement the kinetics of torsion and nonmetricity in a particular cubic MAG model, recently considered to eliminate ghostly instabilities from the vector and axial sectors of the theory. The new solutions represent pp-waves characterised by a metric function that includes the dynamical contributions of the torsion and nonmetricity tensors provided by the field equations of the model. In particular, these quantities induce a scalar polarisation mode in the gravitational-wave spectrum, thus offering a distinctive phenomenological signature beyond the ordinary tensor polarisation modes of General Relativity.

gr-qc↗

arXiv2026

New bounds for the area of MOTS and generalized ultra-massive spacetimes

Bounds for the area of general closed marginally trapped surfaces (MTSs) are presented. They do not require any stability condition, and are determined by a constant that depends on a particular component of the Einstein tensor on the surface and another constant that governs the (in)stability of the MTS. When stability is imposed, the area bounds are refined. These bounds are realized in spacetimes exhibiting interesting generic properties: they possess marginally trapped tubes foliated by marginally trapped topological spheres containing a distinguished round sphere $\bar S$ with constant Gaussian curvature that saturates the area bound. This distinguished surface separates two distinct regions of the marginally trapped tubes: a dynamical horizon and a timelike membrane. The particular case where there is a positive cosmological constant leads to the well-known universal bound $4π/ Λ$ for spatially stable MTSs, and to the recently introduced `ultra-massive spacetimes'. These spacetimes are more extreme than black holes, as there is no event horizon and the entire exterior region undergoes unavoidable collapse. In this paper similar behaviour is found for non-positive $Λ$ if the energy-momentum content is powerful enough. The results may have implications for binary mergers and on accreting very compact objects.

gr-qc↗

arXiv2026

On the regularity of deformed extremal horizons

It has recently been argued that extremal black holes can act as amplifiers of new physics, due to horizon instabilities that enhance the effects of ultraviolet corrections. In this paper, we revisit some of these claims and investigate the viability of a class of non-spherical extremal black holes. In particular, we revisit the regularity of perturbed extremal Reissner--Nordström AdS black holes showing that, while some certain components of the scalar stress energy tensor diverge, the backreaction remains finite. We also study geodesic completeness, identifying a simple geometric constraint which, if satisfied, ensures that null geodesics cross the horizon smoothly. This analysis suggests the existence of a broad class of spacetimes with regular non-spherical horizons.

gr-qc↗

arXiv2025

Gravitational radiation at infinity with negative cosmological constant and AdS$_4$ holography

The covariant characterization of the existence of gravitational radiation traversing infinity $\mathscr{J}$ in the presence of a negative cosmological constant is presented. It is coherent and consistent with the previous characterizations put forward for the cases of non-negative cosmological constant, relying on the properties of the asymptotic super-Poynting vector; or in more transparent terms, based on the intrinsic properties of the flux of tidal energy at infinity. The proposed characterization is fully satisfactory, it can be covariantly typified in terms of boundary data at infinity, and it can also be categorized according to the geometric properties of the rescaled Weyl tensor at $\mathscr{J}$. The cases with no incoming radiation entering from (or no outgoing radiation escaping at) $\mathscr{J}$ can similarly be determined in terms of the boundary data or geometric properties of the rescaled Weyl tensor. In particular, we identify the most general boundary conditions that, in an initial-boundary value problem, ensure absence of gravitational radiation traversing $\mathscr{J}$, namely (functional) proportionality between the Cotton-York tensor field and the holographic stress tensor field at $\mathscr{J}$. We also present novel conditions ensuring the absence of just incoming (outgoing) radiation at $\mathscr{J}$. These are given in a covariant way and also in terms of standard rescaled Weyl tensor scalars. The results are compatible with any matter content of the physical spacetime.

gr-qc↗

arXiv2025

Characterization of gravitational radiation at infinity with a cosmological constant

The existence or absence of gravitational radiation escaping from the spacetime at $\mathscr{J}$ is characterized in the presence of a cosmological constant $Λ$ of any sign. To that end, the properties of the asymptotic super-momentum are used. When $Λ=0$, the characterization is equivalent to that based on the News tensor. For $Λ\neq 0$, it provides the first reliable definition of existence of radiation at $\mathscr{J}$, and it gives fully satisfactory results in known exact solutions.

gr-qc↗

arXiv2025

Analysis of gravitational radiation generated by type D black holes with positive cosmological constant

The criterion for existence of gravitational radiation at conformal infinity in the presence of a positive cosmological constant is applied to a general family of exact solutions representing generic (pairs of) black holes of algebraic type D. Our analysis shows that only accelerating black holes generate gravitational radiation measurable at infinity. This very satisfactory result confirms the goodness of the criterion. To that end, a new metric form of the family of exact type D black holes is constructed -- including any cosmological constant and a (double-aligned) non-null electromagnetic field -- whose expression is suitable for investigation of the asymptotic structure of this large family of spacetimes. The family depends on seven physical parameters, namely $m$, $a$, $l$, $α$, $e$, $g$, and $Λ$ that characterize mass, specific angular momentum parameter, NUT parameter, acceleration, electric and magnetic charges, and the cosmological constant, respectively.

gr-qc↗

arXiv2024

Algebraic classification of the gravitational field in general metric-affine geometries

We present the algebraic classification of the gravitational field in four-dimensional general metric-affine geometries, thus extending the current results of the literature in the particular framework of Weyl-Cartan geometry by the presence of the traceless nonmetricity tensor. This quantity switches on four of the eleven fundamental parts of the irreducible representation of the curvature tensor under the pseudo-orthogonal group, in such a way that three of them present similar algebraic types as the ones obtained in Weyl-Cartan geometry, whereas the remaining one includes thirty independent components and gives rise to a new algebraic classification. The latter is derived by means of its principal null directions and their levels of alignment, obtaining a total number of sixteen main algebraic types, which can be split into many subtypes. As an immediate application, we determine the algebraic types of the broadest family of static and spherically symmetric black hole solutions with spin, dilation and shear charges in Metric-Affine Gravity.

gr-qc↗

arXiv2024

Semi-Riemannian manifolds with linear differential conditions on the curvature

Semi-Riemannian manifolds that satisfy (homogeneous) linear differential conditions of arbitrary order on the curvature are analyzed. They include, in particular, the spaces with (higher-order) recurrent curvature, (higher-order) symmetric spaces, as well as entire new families of semi-Riemannian manifolds rarely, or never, considered before in the literature --such as the spaces whose derivative of the Riemann tensor field is recurrent, among many others. Definite proof that all types of such spaces do exist is provided by exhibiting explicit examples of all possibilities in all signatures, except in the Riemannian case with a positive definite metric. Several techniques of independent interest are collected and presented. Of special relevance is the case of Lorentzian manifolds, due to its connection to the physics of the gravitational field. This connection is discussed with particular emphasis on Gauss-Bonnet gravity and in relation with Penrose limits. Many new lines of research open up and a handful of conjectures, based on the results found hitherto, is put forward.

math.DG↗

arXiv2022

Ultra-massive spacetimes

A positive cosmological constant $Λ>0$ sets an upper limit for the area of marginally future-trapped surfaces enclosing a black hole (BH). Does this mean that the mass of the BH cannot increase beyond the corresponding limit? I analyze some simple spherically symmetric models where regions within a dynamical horizon keep gaining mass-energy so that eventually the $Λ$ limit is surpassed. This shows that the black hole proper transmutes into a collapsing universe, and no observers will ever reach infinity, which dematerializes together with the event horizon and the `cosmological horizon'. The region containing the dynamical horizon cannot be causally influenced by the vast majority of the spacetime, its past being just a finite portion of the total, spatially infinite, spacetime. Thereby, a new type of horizon arises, but now relative to past null infinity: the boundary of the past of all marginally trapped spheres, which contains in particular one with the maximum area $4π/Λ$. The singularity is universal and extends mostly outside the collapsing matter. The resulting spacetimes models turn out to be inextendible and globally hyperbolic. It is remarkable that they cannot exist if $Λ$ vanishes. Given the accepted value of $Λ$ deduced from cosmological observations, such ultra-massive objects will need to contain a substantial portion of the total {\it present} mass of the {\it observable} Universe.

gr-qc↗

arXiv2022

Gravitational radiation at infinity with non-negative cosmological constant

The existence of gravitational radiation arriving at null infinity -- i.e. escaping from the physical system -- is addressed in the presence of a non-negative cosmological constant $Λ\geq 0$. The case with vanishing $Λ$ is well understood and relies on the properties of the News tensor field (or the News function) defined at infinity. The situation is drastically different when $Λ>0$ where there is no known notion of `News' with similar good properties. In this paper both situations are considered jointly from a {\em tidal} point of view, that is, taking into account the strength (or energy) of the curvature tensors. The fundamental object used for that purposes in the {\em asymptotic (radiant) super-momentum}, a causal vector defined at infinity with remarkable properties. This leads to a novel characterization of gravitational radiation valid for the general case with $Λ\geq 0$ that has been proven to be equivalent, when $Λ=0$, to the standard one based on News. The implications of this result are analyzed in some detail when $Λ>0$. A general procedure to construct `news tensors' when $Λ>0$ is depicted, a proposal for asymptotic symmetries provided, and an example of a conserved charge that may detect gravitational radiation at infinity exhibited. A series of illustrative examples is listed.

gr-qc↗

arXiv2021

Asymptotic Structure with vanishing cosmological constant

This is the first of two papers devoted to the asymptotic structure of space-time in the presence of a non-negative cosmological constant $Λ$. This first paper is concerned with the case of $Λ=0$. Our approach is fully based on the tidal nature of the gravitational field and therefore on the `tidal energies' built with the Weyl curvature. In particular, we use the (radiant) asymptotic supermomenta computed from the rescaled Weyl tensor at infinity to provide a novel characterisation of radiation escaping from, or entering into, the space-time. Our new criterion is easy to implement and shown to be fully equivalent to the classical one based on the news tensor. One of its virtues is that its formulation can be easily adapted to the case with $Λ>0$ covered in the second paper. We derive the general energy-momentum-loss formulae including the matter terms and all factors associated to the choices of arbitrary foliation and of super-translation. We also revisit and present a full reformulation of the traditional peeling behaviour with a neat geometrical construction that leads, in particular, to an asymptotic alignment of the supermomenta in accordance with the radiation criterion.

gr-qc↗

arXiv2021

Asymptotic Structure with a positive cosmological constant

This is the second of two papers that study the asymptotic structure of space-times with a non-negative cosmological constant $Λ$. This paper deals with the case $Λ>0$. Our approach is founded on the `tidal energies' built with the Weyl curvature and, specifically, we use the asymptotic super-Poynting vector computed from the rescaled Bel-Robinson tensor at infinity to provide a covariant, gauge-invariant, criterion for the existence, or absence, of gravitational radiation at infinity. The fundamental idea we put forward is that the physical asymptotic properties are encoded in $(\scri,h_{ab},D_{ab})$, where the first element of the triplet is a 3-dimensional manifold, the second is a representative of a conformal class of Riemannian metrics on $\scri$, and the third element is a traceless symmetric tensor field on $\scri$. We similarly propose a no-incoming radiation criterion based also on the triplet $(\scri,h_{ab},D_{ab})$ and on radiant supermomenta deduced from the rescaled Bel-Robinson tensor too. We search for news tensors and argue that any news-like object must be associated to, and depends on, 2-dimensional cross-sections of $\scri$. We identify one component of news for every such cross-section and present a general strategy to find the second component. We also introduce the concept of equipped $\scri$, consider the limit $Λ\rightarrow 0$ and apply all our results to selected exact solutions of Einstein Field Equations. The full-length abstract is available in the paper.

gr-qc↗

arXiv2021

A critical appraisal of the singularity theorems

The 2020 Nobel prize in Physics has revived the interest in the singularity theorems and, in particular, in the Penrose theorem published in 1965. In this short paper I briefly review the main ideas behind the theorems and then proceed to an evaluation of their hypotheses and implications. I will try to dispel some common misconceptions about the theorems and their conclusions, as well as to convey some of their rarely mentioned consequences. In particular, a discussion of spacetime extensions in relation to the theorems is provided. The nature of the singularity inside black holes is also analyzed.

gr-qc↗

arXiv2021

The peeling theorem with arbitrary cosmological constant

A method for deriving the asymptotic behaviour of any physical field is presented. This leads to a geometrically meaningful derivation of the peeling properties for arbitrary values of the cosmological constant. Application to the outstanding case of the physical Weyl tensor provides the explicit form of all terms that determine its asymptotic behaviour along arbitrary lightlike geodesics. The results follow under the assumption of a conformal completion à la Penrose. The only freedom available is the choice of a null vector at the conformal boundary of the space-time (which determines the lightlike geodesic arriving there).

gr-qc↗

arXiv2021

Area deficits and the Bel-Robinson tensor

The first law of causal diamonds relates the area deficit of a small ball relative to flat space to the matter energy density it contains. At second order in the Riemann normal coordinate expansion, this energy density should receive contributions from the gravitational field itself. In this work, we study the second-order area deficit of the ball in the absence of matter and analyze its relation to possible notions of gravitational energy. In the small ball limit, any proposed gravitational energy functional should evaluate to the Bel-Robinson energy density $W$ in vacuum spacetimes. A direct calculation of the area deficit reveals a result that is not simply proportional to $W$. We discuss how the deviation from $W$ is related to ambiguities in defining the shape of the ball in curved space, and provide several proposals for fixing these shape ambiguities.

gr-qc↗