Recommended by Christian Corda We obtain a height estimate concerning to a compact spacelike hypersurface Σ n immersed with constant mean curvature H in the anti-de Sitter space H n1 1 , when its boundary ∂Σ is contained into an umbilical spacelike hypersurface of this spacetime which is isometric to the hyperbolic space H n. Our estimate depends only on the value of H and on the geometry of ∂Σ...

In this paper we consider a variational problem for spacelike hypersurfaces in the (n + 1)-dimensional Lorentz-Minkowski space L, whose critical points are hypersurfaces supported in a spacelike hyperplane determined by two facts: the mean curvature is a linear function of the distance to and the hypersurface makes a constant angle with along its boundary. We prove that the hypersurface is rota...

We show that the entropy created by Ohmic dissipation inside an accreting charged black hole may exceed the Bekenstein-Hawking entropy by a large factor. The second law of thermodynamics does not hold on spacelike slices inside these model black holes, even when the slices avoid Planck scale densities and curvatures. This result is distinct from, but consistent with, the fact that there is no e...

We study the Lorentzian analogues of the squashed 3-sphere, namely 2+1 dimensional anti-de Sitter space squashed or stretched along fibres that are either spacelike or timelike. The causal structure, and the property of being an Einstein–Weyl space, depend critically on whether we squash or stretch. We argue that squashing, and stretching, completely destroys the conformal boundary of the unsqu...

In this work we extend the Weierstrass representation for maximal spacelike surfaces in the 3-dimensional Lorentz–Minkowski space to spacelike surfaces whose mean curvature is proportional to its Gaussian curvature (linear Weingarten surfaces of maximal type). We use this representation in order to study the Gaussian curvature and the Gauss map of such surfaces when the immersion is complete, p...

We introduce the notion of relative volume entropy for two spacetimes with preferred compact spacelike foliations. This is accomplished by applying the notion of Kullback-Leibler divergence to the volume elements induced on spacelike slices. The resulting quantity gives a lower bound on the number of bits which are necessary to describe one metric given the other. For illustration, we study som...