arXiv subjects

José M. M. Senovilla

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

At least 37 records · Page 2Linked to original sources

arXiv2020

Gravitational radiation condition at infinity with a positive cosmological constant

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 long-standing gravitational puzzle and present a geometric, gauge-invariant radiation condition at infinity.

gr-qc↗

arXiv2020

A novel characterisation of gravitational radiation in asymptotically flat space-times

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 with the classical characterisation using the News tensor is analysed in detail. A new balance law at infinity is presented, which may be useful to define `radiation states'.

gr-qc↗

arXiv2019

Multiple Killing Horizons: the initial value formulation for $Λ$-vacuum

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 study the emergence of Multiple Killing Horizons in terms of characteristic initial value problems for two transversally intersecting null hypersurfaces. As a relevant outcome, a more general definition of Near Horizon Geometry is put forward. This new definition avoids the use of Gaussian null coordinates associated to the corresponding degenerate Killing vector and thereby allows for inclusion of its fixed points.

gr-qc↗

arXiv2019

Singularity theorems for warped products and the stability of spatial extra dimensions

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, hence we consider "extra-dimensional evolution". Explicit conditions on the warping function that lead to geodesic incompleteness are given. These conditions can be appropriately rewritten, given a warping function, as restrictions on the intrinsic geometry of the fibers ---i.e. the extra dimensional space. To find the results, the conditions for parallel transportation in warped products in terms of their projections onto the base and the fibers have been solved, a result of independent mathematical interest that have been placed on an Appendix.

gr-qc↗

arXiv2019

La cosmolog\'ıa y los matemáticos (Cosmology and mathematicians)

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 geometrization of the former performed by Einstein after his General theory of Relativity, is described in detail with a thorough analysis of the contributions and collaborations by distinguished XX-th century mathematicians.

math.HO↗

arXiv2018

Equations for general shells

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 degrees of freedom encoded exclusively in the distributional part of the Weyl tensor. For non-null shells the standard Israel equations are recovered but not only, the additional relations containing also relevant information. The results are applicable to a widespread literature on domain walls, branes and braneworlds, gravitational layers, impulsive gravitational waves, and the like. Moreover, they are of a geometric nature, and thus they can be used in any theory based on a Lorentzian manifold.

gr-qc↗

arXiv2018

Multiple Killing Horizons and Near Horizon Geometries

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 $\mathcal{H}$. For each of these Killing vectors on a given cut, there are three different possibilities for the Near Horizon metric which are presented explicitly. The structure of the metric for Near Horizon Geometries with multiple Killing horizons of order $m\geq 3$ is thereby completely determined, and in particular we prove that the cuts on $\mathcal{H}$ must be warped products with maximally symmetric fibers (ergo of constant curvature). The question whether multiple degenerate Killing horizons may lead to inequivalent Near Horizon Geometries by using different degenerate Killings is addressed, and answered on the negative: all Near Horizon geometries built from a given multiple degenerate Killing horizon (using different degenerate Killings) are isometric.

gr-qc↗

arXiv2018

Multiple Killing Horizons

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 surface gravities to such multiple Killing horizons, as they have an essentially unique non-zero surface gravity (or none). $\mathcal{A}_{\mathcal{H}}$ always contains an Abelian (sub)-algebra ---whose elements all have vanishing surface gravity--- of dimension equal to or one less than dim $\mathcal{A}_{\mathcal{H}}$. There arise only two inequivalent possibilities, depending on whether or not there exists the non-zero surface gravity. We show the connection with Near Horizon geometries, and also present a linear system of PDEs, the master equation, for the proportionality function on the horizon between two Killing vectors of a multiple Killing horizon, with its integrability conditions. We provide explicit examples of all possible types of multiple Killing horizons, as well as a full classification of them in maximally symmetric spacetimes.

gr-qc↗

arXiv2018

Singularity Theorems and Their Consequences

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 file here contains the right information. ORIGINAL ABSTRACT: A detailed study of the singularity theorems is presented. I discuss the plausibility and reasonability of their hypotheses, the applicability and implications of the theorems, as well as the theorems themselves. The consequences usually extracted from them, some of them without the necessary rigour, are widely and carefully analysed with many clarifying examples and alternative views.

gr-qc↗

arXiv2017

The limit of Kerr-de Sitter spacetime with infinite angular-momentum parameter $a$

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 $Λ$, vanishing Mars-Simon tensor and conformally flat scri. It possesses an Abelian 2-dimensional group of symmetries whose orbits are spacelike or timelike in different regions, and it includes, as a particular case, de Sitter spacetime. The global structure of the solution is analyzed in detail, with particular attention to its Killing horizons: they are foliated by non-compact marginally trapped surfaces of finite area, and one of them `touches' the curvature singularity, which resembles a null 2-dimensional surface. Outside the region between these horizons there exist trapped surfaces that again are non-compact. The solution contains, apart from $Λ$, a unique free parameter which can be related to the angular momentum of the non-singular horizon in a precise way. A maximal extension of the (axis of the) spacetime is explicitly built. We also analyze the structure of scri, whose topology is $\mathbb{R}^3$.

gr-qc↗

arXiv2017

Umbilical spacelike submanifolds of arbitrary co-dimension

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 space} as the spaces generated by the total shear tensor and by the umbilical vector fields, respectively. We show that the sum of their dimensions must equal the co-dimension.

math.DG↗

arXiv2016

A spacetime characterization of the Kerr-NUT-(A)de Sitter and related metrics

A characterization of the Kerr-NUT-(A)de Sitter metric among four dimensional Λ-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 Kerr and Kerr-NUT metrics. The method of proof is based on (i) the presence of a second Killing vector field which is built in terms of geometric information arising from the previous Killing vector exclusively, and (ii) the existence of an interesting underlying geometric structure involving a Riemannian submersion of a conformally related metric, both of which may be of independent interest.

gr-qc↗

arXiv2016

Characterization of (asymptotically) Kerr-de Sitter-like spacetimes at null infinity

We investigate solutions $(\mathcal{M}, g)$ to Einstein's vacuum field equations with positive cosmological constant $Λ$ which admit a smooth past null infinity $\mathcal{J}^-$ à 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 spacetimes in terms of their Cauchy data on $\mathcal{J}^-$. Along the way, we also study spacetimes for which the MST does not vanish. In that case there is an ambiguity in its definition which is captured by a scalar function $Q$. We analyze properties of the MST for different choices of $Q$. In doing so, we are led to a definition of "asymptotically Kerr-de Sitter-like spacetimes", which we also characterize in terms of their asymptotic data on $\mathcal{J}^-$.

gr-qc↗

arXiv2016

Classification of Kerr-de Sitter-like spacetimes with conformally flat Scri

We provide a classification of $Λ>0$-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 $\mathbb{S}^3$ up to Möbius transformations shedding light on the two fundamental constants that characterize the family of Kerr-de Sitter-like spacetimes, which turn out to be well-defined geometrical invariants. The topology of $\mathcal{J}$ is determined in every case, and a characterization result at $\mathcal{J}$ of the Kerr-de Sitter family presented.

gr-qc↗

arXiv2016

Spacetime characterizations of $Λ$-vacuum metrics with a null Killing 2-form

An exhaustive list of four-dimensional $Λ$-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 ${\cal F}$. We analyze both cases with $Λ$ vanishing or not. In the latter case we prove that $Λ< 0$ must hold necessarily, and we find a characterization of the Einstein spacetimes conformal to pp-waves. In the former case we obtain spacetime characterizations of vacuum plane waves and of the stationary vacuum Brinkmann spacetimes. At the light of the full set of results, old and new, we reformulate the case with non-null ${\cal F}$ and $Λ= 0$. We finally present a table collecting the results for both null, and non-null, ${\cal F}$.

gr-qc↗

arXiv2016

Umbilical properties of spacelike co-dimension two submanifolds

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 notions of umbilical submanifolds are then considered along with the classical concepts of totally umbilical and pseudo-umbilical submanifolds. Then we focus on the case of co-dimension $2$, and we present necessary and sufficient conditions for the submanifold to be umbilical with respect to a normal direction. Moreover, we prove that the umbilical direction, if it exists, is unique ---unless the submanifold is totally umbilical--- and we give a formula to compute it explicitly. When the ambient manifold is Lorentzian we also provide a way of determining its causal character. We end the paper by illustrating our results on the Lorentzian geometry of the Kerr black hole.

math.DG↗

arXiv2015

Junction conditions in quadratic gravity: thin shells and double layers

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 only finite jumps of the energy-momentum tensor are allowed. In the latter case we prove that the matching conditions are more demanding than in General Relativity. In the former case, we show that generically the shells/domain walls are of a new kind because they possess, in addition to the standard energy-momentum tensor, a double layer energy-momentum contribution which actually induces an external energy flux vector and an external scalar pressure/tension on the shell. We prove that all these contributions are necessary to make the entire energy-momentum tensor divergence-free, and we present the field equations satisfied by these energy-momentum quantities. The consequences of all these results are briefly analyzed.

gr-qc↗

arXiv2015

Particle production from marginally trapped surfaces of general spacetimes

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 cases. Our approach naturally leads to an expression for the effective surface gravity of marginally trapped surfaces. The procedure is applicable to general astrophysical and cosmological dynamical situations. Some practical examples for known and new cases are provided.

gr-qc↗