José M. M. Senovilla

• Professor
• Professor (Full) at University of the Basque Country

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...

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 infin...

Semi-Riemannian manifolds that satisfy (homogeneous) linear differential conditions of arbitrary order r on the curvature are analyzed. They include, in particular, the spaces with (rth-order) recurrent curvature, (rth-order) symmetric spaces, as well as entire new families of semi-Riemannian manifolds rarely, or never, considered before in the lit...

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...

It has been long known that in spacetimes with a positive cosmological constant Λ > 0 the area of spatially stable marginally trapped surfaces (MTSs) has a finite upper bound given by 4π/Λ. In this paper I show that any such spacetime containing spatially stable MTSs with area approaching indefinitely that bound acquire universal properties generical...

It has been long known that in spacetimes with a positive cosmological constant $\Lambda >0$ the area of spatially stable marginally trapped surfaces (MTSs) has a finite upper bound given by $4\pi/\Lambda$. In this paper I show that any such spacetime containing spatially stable MTSs with area approaching indefinitely that bound acquire universal p...

A positive cosmological constant \Lambda >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...

Penrose’s crucial contributions to General Relativity, symbolized by his 1965 singularity theorem, received (half of) the 2020 Nobel prize in Physics. A renewed interest in the ideas and implications behind that theorem, its later developments, and other Penrose’s ideas improving our understanding of the gravitational field thereby emerged. In this...

A positive cosmological constant $\Lambda >0$ 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...

The existence of gravitational radiation arriving at null infinity J+, i.e., escaping from the physical system, is addressed in the presence of a non-negative cosmological constant Λ≥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 J+. The situation is drasticall...

This is the first of two papers [1] 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 part...

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 tens...

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 $\Lambda\geq 0$. The case with vanishing $\Lambda$ is well understood and relies on the properties of the News tensor field (or the News function) defined at infinity. T...

Penrose's crucial contributions to General Relativity, symbolized by his 1965 singularity theorem, received (half of) the 2020 Nobel prize in Physics. A renewed interest in the ideas and implications behind that theorem, its later developments, and other Penrose's ideas improving our understanding of the gravitational field thereby emerged. In this...

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 beha...

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...

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 t...

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 beha...

This is the first of two papers devoted to the asymptotic structure of space-time in the presence of a non-negative cosmological constant $\Lambda$. This first paper is concerned with the case of $\Lambda =0$. Our approach is fully based on the tidal nature of the gravitational field and therefore on the `tidal energies' built with the Weyl curvatu...

This is the second of two papers that study the asymptotic structure of space-times with a non-negative cosmological constant $\Lambda$. This paper deals with the case $\Lambda >0$. 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...

Singularity theorems constitute a major milestone of relativity. They generated a panoply of fertile lines of research with dazzling physical consequences. (Los teoremas de singularidades constituyen uno de los mayores hitos de la relatividad. Generaron una panoplia de f\'ertiles l\'ineas de investigaci\'on con consecuencias f\'isicas deslumbrantes...

An elusive idea that emerged on a pedestrian crossing revealed some of the mysteries inside black holes. Announced in barely a couple of pages, it has been worth the 2020 Nobel Prize in Physics.

Gravitational waves have been directly detected and astronomical observations indicate that our Universe has a positive cosmological constant Λ. Nevertheless, a theoretical gauge-invariant notion of gravitational waves arriving at infinity (escaping from the space-time) in the presence of a positive Λ has been elusive. We find the answer to this lo...

Gravitational waves have been directly detected and astronomical observations indicate that our Universe has a positive cosmological constant $\Lambda$. Nevertheless, a theoretical gauge-invariant notion of gravitational waves arriving at infinity (escaping from the space-time) in the presence of a positive $\Lambda$ has been elusive. We find the a...

Las dificultades que las mujeres encuentran para acceder, permanecer y ascender en la academia, especialmente en las disciplinas científicas y tecnológicas, no pueden ser explicadas mediante un solo marco conceptual, antes bien al contrario, hace falta utilizar tres marcos conceptuales distintos: el individual, que permite centrar el análisis en có...

A novel criterion to determine the presence of gravitational radiation arriving to, or departing from, null infinity of any weakly asymptotically simple spacetime with vanishing cosmological constant is given. The quantities involved are geometric, of tidal nature, with good gauge behavior and univocally defined at null infinity. The relationship w...

In Mars et al (2018 Class. Quantum Grav . 35 155015) we have introduced the notion of ‘multiple Killing horizon’ and analyzed some of its general properties. Multiple Killing horizons are Killing horizons for two or more linearly independent Killing vectors simultaneously. In this paper we focus on the vacuum case, possibly with cosmological consta...

A novel criterion to determine the presence of gravitational radiation arriving to, or departing from, null infinity of any weakly asymptotically-simple space-time with vanishing cosmological constant is given. The quantities involved are geometric, of tidal nature, with good gauge behaviour and univocally defined at null infinity. The relationship...

Este trabajo plantea y aspira a contestar las siguientes preguntas múltiples: ¿cuáles son los mecanismos que contribuyen a perpetuar, y los que podrían ayudar a modificar, la discriminación de las mujeres en el mundo de la investigación científica?, ¿cuáles son las medidas adecuadas para poder aumentar, equilibrando, el número de mujeres en el camp...

In Class. Quantum Grav. 35 (2018) 155015 we have introduced the notion of "Multiple Killing Horizon" and analyzed some of its general properties. Multiple Killing Horizons are Killing horizons for two or more linearly independent Killing vectors simultaneously. In this paper we focus on the vacuum case, possibly with cosmological constant, and stud...

A bstract New singularity theorems are derived for generic warped-product spacetimes of any dimension. The main purpose is to analyze the stability of (compact or large) extra dimensions against dynamical perturbations. To that end, the base of the warped product is assumed to be our visible 4-dimensional world, while the extra dimensions define th...

Free translation of the original abstract in Spanish: Some of the most relevant milestones due to, or instigated by, mathematicians concerning the creation, development and advances of Cosmology as a scientific discipline are presented and discussed. In particular, the close relationship between Cosmology and Mathematics, derived from the geometriz...

New singularity theorems are derived for generic warped-product spacetimes of any dimension. The main purpose is to analyze the stability of (compact or large) extra dimensions against dynamical perturbations. To that end, the base of the warped product is assumed to be our visible 4-dimensional world, while the extra dimensions define the fibers,...

Near horizon geometries with multiply degenerate Killing horizons H are considered, and their degenerate Killing vector fields identified. We prove that they all arise from hypersurface-orthogonal Killing vectors of any cut of H with the inherited metric-cuts are spacelike co-dimension two submanifolds contained in H. For each of these Killing vect...

A bstract The complete set of (field) equations for shells of arbitrary, even changing, causal character are derived in arbitrary dimension. New equations that seem to have never been considered in the literature emerge, even in the traditional cases of everywhere non-null, or everywhere null, shells. In the latter case there arise field equations...

Killing horizons which can be such for two or more linearly independent Killing vectors are studied. We provide a rigorous definition and then show that the set of Killing vectors sharing a Killing horizon is a Lie algebra $\mathcal{A}_{\mathcal{H}}$ of dimension at most the dimension of the spacetime. We prove that one cannot attach different surf...

Near Horizon Geometries with multiply degenerate Killing horizons $\mathcal{H}$ are considered, and their degenerate Killing vector fields identified. We prove that they all arise from hypersurface-orthogonal Killing vectors of any cut of $\mathcal{H}$ with the inherited metric -- cuts are spacelike co-dimension two submanifolds contained in $\math...

The complete set of (field) equations for shells of arbitrary, even changing, causal character are derived in arbitrary dimension. New equations that seem to have never been considered in the literature emerge, even in the traditional cases of everywhere non-null, or everywhere null, shells. In the latter case there arise field equations for some d...

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...

Killing horizons which can be such for two or more linearly independent Killing vectors are studied. We provide a rigorous definition and then show that the set of Killing vectors sharing a Killing horizon is a Lie algebra $\mathcal{A}_{\mathcal{H}}$ of dimension at most the dimension of the spacetime. We prove that one cannot attach different surf...

This is a 20-year old review on singularities and singularity theorems. The main reason to submit it now is -apart from increasing its availability- to correct a very strange error that appears in the journal's online version: it contains wrong headers and footers in its 1st page. This has led to many wrong citations, and to some confusion. The pdf...

We consider the limit $a\rightarrow \infty$ of the Kerr-de Sitter spacetime. The spacetime is a Petrov type-D solution of the vacuum Einstein field equations with a positive cosmological constant $\Lambda$, vanishing Mars-Simon tensor and conformally flat scri. It possesses an Abelian 2-dimensional group of symmetries whose orbits are spacelike or...

We consider the limit $a\rightarrow \infty$ of the Kerr-de Sitter spacetime. The spacetime is a Petrov type-D solution of the vacuum Einstein field equations with a positive cosmological constant $\Lambda$, vanishing Mars-Simon tensor and conformally flat scri. It possesses an Abelian 2-dimensional group of symmetries whose orbits are spacelike or...

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...

For Riemannian submanifolds of a semi-Riemannian manifold, we introduce the concepts of \emph{total shear tensor} and \emph{shear operators} as the trace-free part of the corresponding second fundamental form and shape operators. The relationship between these quantities and the umbilical properties of the submanifold is shown. Several novel notion...

We provide a classification of $\Lambda>0$-vacuum spacetimes which admit a Killing vector field with respect to which the associated "Mars-Simon tensor" (MST) vanishes and having a conformally flat $\mathcal{J}^-$ (or $\mathcal{J}^+$). To that end, we also give a complete classification of conformal Killing vector fields on the $3$-sphere $\mathbb{...

We present a class of spherically symmetric spacetimes corresponding to bubbles separating two regions with constant values of the scalar curvature, or equivalently with two different cosmological constants, in quadratic F(R) theory. The bubbles are obtained by means of the junction formalism and the matching hypersurface supports in general a thin...

We present a class of spherically symmetric spacetimes corresponding to bubbles separating two regions with constant values of the scalar curvature, or equivalently with two different cosmological constants, in quadratic F(R) theory. The bubbles are obtained by means of the junction formalism, and the matching hypersurface supports in general a thi...

Given a semi-Riemannian manifold, we give necessary and sufficient conditions for a Riemannian submanifold of arbitrary co-dimension to be umbilical along normal directions. We do that by using the so-called \emph{total shear tensor}, i.e., the trace-free part of the second fundamental form. We define the \emph{shear space} and the \emph{umbilical...

We provide a classification of $\Lambda>0$-vacuum spacetimes which admit a Killing vector field with respect to which the associated "Mars-Simon tensor" (MST) vanishes and having a conformally flat $\mathcal{J}^-$ (or $\mathcal{J}^+$). To that end, we also give a complete classification of conformal Killing vector fields on the $3$-sphere $\mathbb{...

An exhaustive list of four-dimensional $\Lambda$-vacuum spacetimes admitting a Killing vector whose self-dual Killing two-form ${\cal F}$ is null is obtained assuming that the self-dual Weyl tensor is proportional to the tensor product of ${\cal F}$ by itself. Our analysis complements previous results concerning the case with non-null ${\cal F}$. W...

We investigate solutions $(\mathcal{M}, g)$ to Einstein's vacuum field equations with positive cosmological constant $\Lambda$ which admit a smooth past null infinity $\mathcal{J}^-$ \`a la Penrose and a Killing vector field whose associated Mars-Simon tensor (MST) vanishes. The main purpose of this work is to provide a characterization of these sp...

The junction conditions for the most general gravitational theory with a Lagrangian containing terms quadratic in the curvature are derived. We include the cases with a possible concentration of matter on the joining hypersurface -termed as thin shells, domain walls or braneworlds in the literature- as well as the proper matching conditions where o...

An exhaustive list of four-dimensional $\Lambda$-vacuum spacetimes admitting a Killing vector whose self-dual Killing two-form ${\cal F}$ is null is obtained assuming that the self-dual Weyl tensor is proportional to the tensor product of ${\cal F}$ by itself. Our analysis complements previous results concerning the case with non-null ${\cal F}$. W...

For Riemannian submanifolds of a semi-Riemannian manifold, we introduce the concepts of \emph{total shear tensor} and \emph{shear operators} as the trace-free part of the corresponding second fundamental form and shape operators. The relationship between these quantities and the umbilical properties of the submanifold is shown. Several novel notion...

We investigate solutions $(\mathcal{M}, g)$ to Einstein's vacuum field equations with positive cosmological constant $\Lambda$ which admit a smooth past null infinity $\mathcal{J}^-$ \`a la Penrose and a Killing vector field whose associated Mars-Simon tensor (MST) vanishes. The main purpose of this work is to provide a characterization of these sp...

The junction conditions for the most general gravitational theory with a Lagrangian containing terms quadratic in the curvature are derived. We include the cases with a possible concentration of matter on the joining hypersurface -termed as thin shells, domain walls or braneworlds in the literature- as well as the proper matching conditions where o...

This is an author created, un copyedited version of an article accepted for publication in Classical and quantum gravity. The publisher is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at http://dx.doi.org/10.1088/0264-9381/32/18/189501.

We review the first modern singularity theorem, published by Penrose in 1965. This is the first genuine post-Einstenian result in General Relativity, where the fundamental and fruitful concept of closed trapped surface was introduced. We include historical remarks, an appraisal of the theorem's impact, and relevant current and future work that belo...

We provide a general formalism that allows to analyze the phenomenon of tunneling in arbitrary spacetimes. We show that a flux of particles produced by tunneling through general marginally trapped surfaces may be perceived by some privileged observers. We discuss how this particle perception can be related to Hawking/Unruh radiation in specific cas...

I revisit a known solution of the Einstein field equations to show that it describes the formation of non-spherical black holes by the collapse of pure electromagnetic monochromatic radiation. Both positive and negative masses are feasible without ever violating the dominant energy condition. The solution can also be used to model the destruction o...

Gravitational double layers, unlike their classical electromagnetic counterparts, are thought to be forbidden in gravity theories. It has been recently shown, however, that they are feasible in, for instance, gravity theories with a Lagrangian quadratic in the curvature. This is surprising with many potential consequences and the possibility of new...

We provide a general formalism based on previous tunneling methods to treat the Hawking radiation phenomenon in arbitrary spacetimes. We show that Hawking radiation should be associated with general marginally trapped surfaces. Our approach naturally leads to an expression for the effective surface gravity of marginally trapped surfaces. The proced...

I analyze the properties of thin shells through which the scalar curvature R is discontinuous in gravity theories with R + R^2 Lagrangian on the bulk. These shells/domain walls are of a new kind because they possess, in addition to the standard energy-momentum tensor, an external energy flux vector, an external scalar pressure/tension and, most exo...

A characterization of the Kerr-NUT-(A)de Sitter metric among four dimensional \Lambda-vacuum spacetimes admitting a Killing vector is obtained in terms of the proportionality of the self-dual Weyl tensor and a natural self-dual double two-form constructed from the Killing vector. This result recovers and extends a previous characterization of the K...

The Oppenheimer-Snyder solution models a homogeneous round dust cloud collapsing to a black hole. Inside its event horizon there is a region through which trapped surfaces pass. We try to determine exactly where the boundary of this region meets the centre of the cloud. We present explicit examples of the relevant trapped (topological) spheres; the...

I review the definition and types of (closed) trapped surfaces. Surprising global properties are pointed out, such as their “clairvoyance” and the possibility that they enter into flat portions of the spacetime. Several results on the interplay of trapped surfaces with vector fields and with spatial hypersurfaces are presented. Applications to the...

I present the junction conditions for F(R) theories of gravity and their implications: the generalized Israel conditions and equations. These junction conditions are necessary to construct global models of stars, galaxies, etc., where a vacuum region surrounds a finite body in equilibrium, as well as to describe shells of matter and braneworlds, an...

A space-like surface S immersed in a 4-dimensional Lorentzian manifold will be said to be umbilical along a direction N normal to S if the second fundamental form along N is proportional to the first fundamental form of S. In particular, S is pseudo-umbilical if it is umbilical along the mean curvature vector field H and (totally) umbilical if it i...

A number of scalar invariant characterizations of the Kerr solution are presented. These characterizations come in the form of {\em quality factors} defined in stationary space-times. A quality factor is a scalar quantity varying in the interval $[0,1]$ with the value 1 being attained if and only if the space-time is locally isometric to the Kerr s...

Small deformations of marginally outer trapped surfaces (MOTS) are studied by using the stability operator introduced by Andersson-Mars-Simon. Novel formulae for the principal eigenvalue are presented. A characterization of the many marginally outer trapped tubes (MOTT) passing through a given MOTS is given, and the possibility of selecting a privi...

Small deformations of marginally (outer) trapped surfaces are considered by using their stability operator. In the case of spherical symmetry, one can use these deformations on any marginally trapped round sphere to prove several interesting results. The concept of 'core' of a black hole is introduced: it is a minimal region that one should remove...

I review the definition and types of (closed) trapped surfaces. Surprising global properties are shown, such as their "clairvoyance" and the possibility that they enter into flat portions of the spacetime. Several results on the interplay of trapped surfaces with vector fields and with spatial hypersurfaces are presented. Applications to the quasi-...

I review the definition and types of (closed) trapped surfaces. Surprising global properties are shown, such as their "clairvoyance" and the possibility that they enter into flat portions of the spacetime. Several results on the interplay of trapped surfaces with vector fields and with spatial hypersurfaces are presented. Applications to the quasi-...

A spacelike surface S immersed in a 4-dimensional Lorentzian manifold will be said to be umbilical along a direction N normal to S if the second fundamental form along N is proportional to the first fundamental form of S. In particular, S is pseudo-umbilical if it is umbilical along the mean curvature vector field H, and (totally) umbilical if it i...

Inspired by classical work of Bel and Robinson, a natural purely algebraic construction of super-energy (s-e) tensors for arbitrary fields is presented, having good mathematical and physical properties. Remarkably, there appear quantities with mathematical characteristics of energy densities satisfying the dominant property, which provides s-e esti...

The problem of constructing global models describing isolated axially symmetric rotating bodies in equilibrium is analyzed. It is claimed that, whenever the global space–time is constructed by giving boundary data on the limiting surface of the body and integrating Einstein's equations on both inside and outside the body, the problem becomes overde...

Semisymmetric spaces are a natural generalisation of symmetric spaces. For semisymmetric spaces in four dimensions with Lorentz signature, the Weyl tensor is easily seen (via spinors) to have a particularly simple quadratic property, which we call a special semisymmetric Weyl tensor. Using dimensionally dependent tensor identities, all (conformally...

New singularity theorems are proven in Lorentzian manifolds of arbitrary dimension n if they contain closed trapped submanifolds of arbitrary co-dimension. The timelike or null convergence conditions must be generalized to a condition on sectional curvatures, or tidal forces, which reduces to the former in the cases of co-dimension 1, 2 or n. Appli...

Second-order symmetric Lorentzian spaces, that is to say, Lorentzian manifolds with vanishing second derivative of the curvature tensor R, are characterized by several geometric properties, and explicitly presented. Locally, they are a product M=M_1 x M_2 where each factor is uniquely determined as follows: M_2 is a Riemannian symmetric space and M...

We give a summary of recent results on the explicit local form of the second-order symmetric Lorentzian manifolds in arbitrary dimension, and its global version. These spacetimes turn out to be essentially a specific subclass of plane waves.

"La Relatividad General es uno de los campos de mayor intersección entre las geometrías, y las matemáticas en general, y los conceptos físicos. Uno de los momentos culminantes de esta interacción fue el desarrollo y las aplicaciones de los llamados «teoremas de singularidades» (...)"

The relation between the presence of closed trapped surfaces and the existence of black holes is reviewed paying special attention to the possibility of defining the surface of the latter. Closed future‐trapped surfaces are believed to signal the formation of black holes and its event horizon. Trapped surfaces are, however, easier to handle, as the...

The algebraic classification of the Weyl tensor in the arbitrary dimension n is recovered by means of the principal directions of its 'superenergy' tensor. This point of view can be helpful in order to compute the Weyl aligned null directions explicitly, and permits one to obtain the algebraic type of the Weyl tensor by computing the principal eige...

We consider the region $\mathscr{T}$ in spacetime containing future-trapped closed surfaces and its boundary $\B$, and derive some of their general properties. We then concentrate on the case of spherical symmetry, but the methods we use are general and applicable to other situations. We argue that closed trapped surfaces have a non-local property,...

The algebraic classification of the Weyl tensor in arbitrary dimension n is recovered by means of the principal directions of its "superenergy" tensor. This point of view can be helpful in order to compute the Weyl aligned null directions explicitly, and permits to obtain the algebraic type of the Weyl tensor by computing the principal eigenvalue o...

Standard singularity theorems are proven in Lorentzian manifolds of arbitrary dimension n if they contain closed trapped submanifolds of arbitrary co-dimension. By using the mean curvature vector to characterize trapped submanifolds, a unification of the several possibilities for the boundary conditions in the traditional theorems and their general...

We provide a simple proof that conformally semi-symmetric spacetimes are actually semi-symmetric. We also present a complete refined classification of the semi-symmetric spacetimes.

As a difference with the positive-definite Riemannian case, in the Lorentzian case there exists proper second-order symmetric spacetimes, i.e., those with vanishing second covariant derivative of the Riemannian tensor ($R_{\lambda\mu\nu\rho;\alpha;\beta}=0$) which are not locally symmetric ($R_{\lambda\mu\nu\rho;\alpha}\neq 0$). In fact, they lie i...

We discuss the boundary of the spacetime region through each point of which a trapped surface passes, first in some simple soluble examples, and then in the self-similar Vaidya solution. For the latter the boundary must lie strictly inside the event horizon. We present a class of closed trapped surfaces extending strictly outside the apparent horiz...

We provide a simple proof that conformally semi-symmetric spacetimes are actually semi-symmetric. We also present a complete refined classification of the semi-symmetric spacetimes.

In this lecture we will show some properties of a singularity-free solution to Einstein's equations and its accordance with some theorems dealing with singularities. We will also discuss the implications of the results. Comment: 5 pp. Published in Proceedings of ERE'91

The boundary of the region in spacetime containing future-trapped closed surfaces is considered. In asymptotically flat spacetimes, this boundary does not need to be the event horizon nor a dynamical/trapping horizon. Some properties of this boundary and its localization are analyzed, and illustrated with examples. In particular, fully explicit fut...