13 citations · 42 across the 9 of their papers we have counts for
9 papers
On the affine parametrization of null geodesics in low regularity
Saúl Burgos, Leonardo García-Heveling, Melanie Graf
In low-regularity spacetimes and Lorentzian length spaces, achronal causal curves play the role of null (pre-)geodesics. Because of the lack of a geodesic equation, they do not com…
Isometries of spacetimes without observer horizons
Leonardo García-Heveling, Abdelghani Zeghib
We study the isometry groups of (non-compact) Lorentzian manifolds with well-behaved causal structure, aka causal spacetimes satisfying the ``no observer horizons'' condition. Our…
Mean Curvature, Singularities and Time Functions in Cosmology
Gregory J. Galloway, Leonardo García-Heveling
In this contribution, we study spacetimes of cosmological interest, without making any symmetry assumptions. We prove a rigid Hawking singularity theorem for positive cosmological…
Minimal Elements of the Causal Boundary with Applications to Spacetime Splitting
Leonardo García-Heveling
In 1972, Geroch, Kronheimer, and Penrose introduced what is now called the causal boundary of a spacetime. This boundary is constructed out of Terminal Indecomposable Past sets (TI…
Radial Gravitational Collapse Causes Timelike Incompleteness
Leonardo García-Heveling
We show that a globally hyperbolic spacetime containing a trapped surface and satisfying the strong energy condition and a condition on certain radial tidal forces must be timelike…
Volume Singularities in General Relativity
Leonardo García-Heveling
We propose a new notion of singularity in General Relativity which complements the usual notions of geodesic incompleteness and curvature singularities. Concretely, we say that a s…
Global Hyperbolicity through the Eyes of the Null Distance
Annegret Burtscher, Leonardo García-Heveling
No Hopf-Rinow Theorem is possible in Lorentzian Geometry. Nonetheless, we prove that a spacetime is globally hyperbolic if and only if it is metrically complete with respect to the…
Topology change with Morse functions: progress on the Borde-Sorkin conjecture
Leonardo García-Heveling
Topology change is considered to be a necessary feature of quantum gravity by some authors, and impossible by others. One of the main arguments against it is that spacetimes with c…
Time functions on Lorentzian length spaces
Annegret Burtscher, Leonardo García-Heveling
In general relativity, time functions are crucial objects whose existence and properties are intimately tied to the causal structure of a spacetime and also to the initial value fo…