相关论文: On the existence of Killing fields in smooth space…

We prove that any smooth vacuum spacetime containing a compact Cauchy horizon with surface gravity that can be normalised to a non-zero constant admits a Killing vector field. This proves a conjecture by Moncrief and Isenberg from 1983…

We prove that any compact Cauchy horizon with constant non-zero surface gravity in a smooth vacuum spacetime is a smooth Killing horizon. The novelty here is that the Killing vector field is shown to exist on both sides of the horizon. This…

Smooth spacetimes with a compact Cauchy horizon ruled by closed null geodesics are considered. The compact Cauchy horizon is assumed to be non-degenerate. Then, supporting the validity of Penrose's strong cosmic censor hypothesis, the…

We consider analytic, vacuum spacetimes that admit compact, non-degenerate Cauchy horizons. Many years ago we proved that, if the null geodesic generators of such a horizon were all \textit{closed} curves, then the enveloping spacetime…

We consider smooth electrovac spacetimes which represent either (A) an asymptotically flat, stationary black hole or (B) a cosmological spacetime with a compact Cauchy horizon ruled by closed null geodesics. The black hole event horizon or,…

We prove that under the dominant energy condition any non-degenerate smooth compact totally geodesic horizon admits a smooth tangent vector field of constant non-zero surface gravity. This result generalizes previous work by Isenberg and…

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…

We prove that in any spacetime dimension and under the null energy condition, every totally geodesic connected smooth compact null hypersurface (hence every compact Cauchy horizon) admits a smooth lightlike tangent vector field of constant…

A rigidity theorem that applies to smooth electrovac spacetimes which represent either (A) an asymptotically flat stationary black hole or (B) a cosmological spacetime with a compact Cauchy horizon ruled by closed null geodesics was given…

We prove that if a stationary, real analytic, asymptotically flat vacuum black hole spacetime of dimension $n\geq 4$ contains a non-degenerate horizon with compact cross sections that are transverse to the stationarity generating Killing…

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…

The weak cosmic censorship hypothesis can be understood as a statement that there exists a global Cauchy evolution of a selfgravitating system outside an event horizon. The resulting Cauchy problem has a free null-like inner boundary. We…

We discuss various properties of rotating Killing horizons in generic $F(R)$ theories of gravity in dimension four for spacetimes endowed with two commuting Killing vector fields. Assuming there is no curvature singularity anywhere on or…

We prove that compact Cauchy horizons in a smooth spacetime satisfying the null energy condition are smooth. As an application, we consider the problem of determining when a cobordism admits Lorentzian metrics with certain properties. In…

A Theorem is proved which reduces the problem of completeness of orbits of Killing vector fields in maximal globally hyperbolic, say vacuum, space--times to some properties of the orbits near the Cauchy surface. In particular it is shown…

We survey some known facts and open questions concerning the global properties of 3+1 dimensional spacetimes containing a compact Cauchy surface. We consider spacetimes with an $\ell$-dimensional Lie algebra of space-like Killing fields.…

Hawking's local rigidity theorem, proven in the smooth setting by Alexakis-Ionescu-Klainerman, says that the event horizon of any stationary non-extremal black hole is a non-degenerate Killing horizon. In this paper, we prove that the full…

The extendibility of spacetime and the existence of weak solutions to the Einstein field equations beyond Cauchy horizons, is a crucial ingredient to examine the limits of General Relativity. Strong Cosmic Censorship serves as a firewall…

We prove that smooth asymptotically flat solutions to the Einstein vacuum equations which are assumed to be periodic in time, are in fact stationary in a neighborhood of infinity. Our result applies under physically relevant regularity…

Transforming Penrose's intuitive picture of a strong cosmic censorship principle, that generically forbids the appearance of locally naked space-time singularities, into a formal mathematical proof, remains at present, one of the most…