arXiv subjects

Victor Luis Espinoza

Publications and source records attributed to Victor Luis Espinoza.

3 recordsLinked to original sources

arXiv2026

Transverse stable causality in Lorentzian foliations

We introduce and investigate a notion analogous to stable causality for Lorentzian foliations, considerably extending the framework of transverse causality initiated in a recent work. It is well-known that in spacetime geometry stable causality is characterized by several equivalent conditions, such as the stability of non-existence of causal loops under metric perturbations, the existence of smooth temporal functions, and relation-theoretic formulations via the so-called Seifert and $K^+$ relations. We define natural transversal analogues of these distinct formulations and establish partial logical implications between them in the foliation setting. Whether and to what extent the full equivalences can be established remains an open question for general foliations, partly due to the eventual non-Hausdorff nature and other topological complexities of arbitrary leaf spaces. Furthermore, we demonstrate that for the important class of \textit{simple} foliations, which are defined by certain submersions, the equivalences of almost all the transverse analogues of stable causality are indeed recovered.

math.DG↗

arXiv2025

Genericity of singularities in spacetimes with weakly trapped submanifolds

Using the standard Whitney topologies on spaces of Lorentzian metrics, we show that the existence of causal incomplete geodesics is a $C^\infty$-generic feature within the class of spacetimes of a given dimension $n\geq 3$ that are stably causal, satisfy the timelike convergence condition (``strong energy condition'') and contain a codimension-two spacelike weakly trapped closed submanifold such as, e.g., a marginally outer trapped surface (MOTS). By using a singularity theorem of Galloway and Senovilla for spacetimes containing trapped closed submanifolds of codimension higher than two we also prove an analogous $C^\infty$-genericity result for stably causal spacetimes with a suitably modified curvature condition and weakly trapped closed spacelike submanifold of any codimension $k> 2$.

math.DG↗

arXiv2025

On the genericity of singularities in spacetimes with weakly trapped submanifolds

We investigate suitable, physically motivated conditions on spacetimes containing certain submanifolds - the so-called {weakly trapped submanifolds} - that ensure, in a set of neighboring metrics with respect to a convenient topology, that the phenomenon of nonspacelike geodesic incompleteness (i.e., the existence of singularities) is generic in a precise technical sense. We obtain two sets of results. First, we use strong Whitney topologies on spaces of Lorentzian metrics on a manifold $M$, in the spirit of Lerner and obtain that while the set of singular Lorentzian metrics around a fiducial one possessing a weakly trapped submanifold $Σ$ is not really generic, it is nevertheless prevalent in a sense we define, and thus still quite ``large'' in this sense. We prove versions of that result both for the case when $Σ$ has codimension 2, and for the case of higher codimension. The second set of results explore a similar question, but now for initial data sets containing MOTS. For this case, we use certain well-known infinite dimensional, Hilbert manifold structures on the space of initial data and use abstract functional-analytic methods based on the work of Biliotti, Javaloyes, and Piccione to obtain a true genericity of null geodesic incompleteness around suitable initial data sets containing MOTS.

math.DG↗