Related papers: Yet another proof of Hawking and Ellis's Lemma 8.5…
It is proved that every compactly generated future Cauchy horizon has past complete generators, and dually. No condition on the differentiability of the horizon is imposed.
It is standard assertion in relativity that, subject to an energy condition and the cosmic censorship hypothesis, closed trapped surfaces are not visible from future null infinity. A proof given by Hawking & Ellis in ''The Large Scale…
We obtain an improved version of the area theorem for not necessarily differentiable horizons which, in conjunction with a recent result on the completeness of generators, allows us to prove that under the null energy condition every…
Hawking has shown that if black holes were to exist in a universe that expands forever, black holes would completely evaporate, violating unitarity. I argue this means unitarity requires that the universe exist for only a finite future…
Cauchy horizons are shown to be differentiable at endpoints where only a single null generator leaves the horizon. A Cauchy horizon fails to have any null generator endpoints on a given open subset iff it is differentiable on the open…
We prove that the area of sections of future event horizons in space-times satisfying the null energy condition is non-decreasing towards the future under any one of the following circumstances: 1) the horizon is future geodesically…
Recently, Almheiri et. al. argued, via a delicate thought experiment, that it is not consistent to simultaneosuly require that (a) Hawking radiation is pure, (b) effective field theory is valid outside a stretched horizon and (c) infalling…
We give an alternative proof of the global existence result originally due to Hidano and Yokoyama for the Cauchy problem for a system of quasi-linear wave equations in three space dimensions satisfying the weak null condition. The feature…
Under a weakened version of Hardy-Littlewood Conjecture on the number of representations in Goldbach problem, J. H. Fei proved bounds for the Siegel zeros. Recently G. Bhowmik and K. Halupczok generalized Fei's result under a weaker…
In a recent paper Kr\'olak and Beem have shown differentiability of Cauchy horizons at all points of multiplicity one. In this note we give a simpler proof of this result.
Black hole complementarity, as originally formulated in the 1990's by Preskill, 't Hooft, and myself is now being challenged by the Almheiri-Marolf-Polchinski-Sully firewall argument. The AMPS argument relies on an implicit assumption---the…
Let $H$ be a (past directed) horizon in a time-oriented Lorentz manifold and $\gamma:[\left( \alpha,\beta\right) \rightarrow H$ a past directed generator of the horizon, where $[\left( \alpha,\beta\right) $ is $[\alpha,\beta)$ or $\left(…
A key result in four dimensional black hole physics, since the early 1970s, is Hawking's topology theorem asserting that the cross-sections of an "apparent horizon", separating the black hole region from the rest of the spacetime, are…
It is folklore knowledge amongst general relativists that horizons are well behaved, continuously differentiable hypersurfaces except perhaps on a negligible subset one needs not to bother with. We show that this is not the case, by…
We establish a complete classification theorem for the topology and for the null generators of compact non-degenerate Cauchy horizons of time orientable smooth vacuum $3+1$-spacetimes. We show that, either: (i) all generators are closed, or…
We investigate the possibility of firewalls in the Einstein-dilaton gravity model of CGHS. We use the results of the numerical simulation carried out by Ashtekar et al. to demonstrate that firewalls are absent and the horizon is drama free.…
We prove that if in a spacetime endowed with a merely continuous metric, a complete partial Cauchy hypersurface has nonempty Cauchy horizon, then the horizon is caused by the presence of almost closed causal curves behind it or by the…
We study general S2xS1 Gowdy models with a regular past Cauchy horizon and prove that a second (future) Cauchy horizon exists, provided that a particular conserved quantity $J$ is not zero. We derive an explicit expression for the metric…
In this paper we present a proof of a mathematical version of the strong cosmic censor conjecture attributed to Geroch-Horowitz and Penrose but formulated explicitly by Wald. The proof is based on the existence of future-inextendible causal…
We extend both the Hawking-Penrose Theorem and its generalisation due to Galloway and Senovilla to Lorentzian metrics of regularity $C^1$. For metrics of such low regularity, two main obstacles have to be addressed. On the one hand, the…