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It is shown that in a class of maximal globally hyperbolic spacetimes admitting two local Killing vectors, the past (defined with respect to an appropriate time orientation) of any compact constant mean curvature hypersurface can be covered…

General Relativity and Quantum Cosmology · Physics 2009-10-28 Alan D. Rendall

We prove an intrinsic analogue of Hawking's rigidity theorem for extremal horizons in arbitrary dimensions: any compact cross-section of a rotating extremal horizon in a spacetime satisfying the null energy condition must admit a Killing…

General Relativity and Quantum Cosmology · Physics 2025-12-12 Alex Colling

Some basic theorems on Killing vector fields are reviewed. In particular, the topic of a constant-curvature space is examined. A detailed proof is given for a theorem describing the most general form of the metric of a homogeneous isotropic…

General Relativity and Quantum Cosmology · Physics 2016-10-19 M. O. Katanaev

Recently, a no inner (Cauchy) horizon theorem for static black holes with non-trivial scalar hairs has been proved in Einstein-Maxwell-scalar theories. In this paper, we extend the theorem to the static black holes in…

High Energy Physics - Theory · Physics 2022-04-20 Deniz O. Devecioglu , Mu-In Park

We prove that a smooth Riemannian manifold admitting an imaginary generalized Killing spinor whose Dirac current satisfies an additional algebraic constraint condition can be embedded as spacelike Cauchy hypersurface in a smooth Lorentzian…

Differential Geometry · Mathematics 2015-03-18 Andree Lischewski

We introduce the concept of a geometric horizon, which is a surface distinguished by the vanishing of certain curvature invariants which characterize its special algebraic character. We motivate its use for the detection of the event…

General Relativity and Quantum Cosmology · Physics 2018-01-10 Alan Coley , David McNutt

In general relativity, nonsingular black holes contain (at least) a Cauchy horizon, a null hypersurface beyond which determinism breaks down. Even though the strong cosmic censorship conjecture establishes the impossibility of extending…

General Relativity and Quantum Cosmology · Physics 2023-05-05 Jorge Ovalle

We discuss the structure of horizons in spacetimes with two metrics, with applications to the Vainshtein mechanism and other examples. We show, without using the field equations, that if the two metrics are static, spherically symmetric,…

General Relativity and Quantum Cosmology · Physics 2015-05-28 Cédric Deffayet , Ted Jacobson

Although previous results have ruled out the possibility of a static horizon in cosmology, we present black hole and white hole metrics that retain static horizons while reproducing cosmological behavior at large distances. Using an…

General Relativity and Quantum Cosmology · Physics 2025-08-05 Ida M. Rasulian , Amjad Ashoorioon

It is known that a Killing field on a compact pseudo-K\"ahler manifold is necessarily (real) holomorphic, as long as the manifold satisfies some relatively mild additional conditions. We provide two further proofs of this fact and discuss…

Differential Geometry · Mathematics 2025-08-25 Andrzej Derdzinski

Smooth four-dimensional electrovac spacetimes in Einstein's theory are considered each possessing a pair of null hypersurfaces, $H_1$ and $H_2$, generated by expansion and shear free geodesically complete null congruences such that they…

General Relativity and Quantum Cosmology · Physics 2015-01-16 István Rácz

We consider solutions to the linear wave equation $\Box_g\phi=0$ on a non-extremal maximally extended Schwarzschild-de Sitter spacetime arising from arbitrary smooth initial data prescribed on an arbitrary Cauchy hypersurface. (In…

General Relativity and Quantum Cosmology · Physics 2007-09-19 Mihalis Dafermos , Igor Rodnianski

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…

General Relativity and Quantum Cosmology · Physics 2017-01-25 Eric Larsson

We prove the existence of general relativistic perfect fluid black hole solutions, and demonstrate the phenomenon for the $P=w\rho$ class of equations of state. While admitting a local time-like Killing vector on the event horizon itself,…

General Relativity and Quantum Cosmology · Physics 2012-11-28 Aharon Davidson , Shimon Rubin , Yosef Verbin

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…

General Relativity and Quantum Cosmology · Physics 2021-08-16 Spyros Alexakis , Volker Schlue

Using the general solution to the Einstein equations on intersecting null surfaces developed by Hayward, we investigate the non-linear instability of the Cauchy horizon inside a realistic black hole. Making a minimal assumption about the…

General Relativity and Quantum Cosmology · Physics 2016-08-31 Patrick R Brady , Chris M Chambers

We study the scalar wave equation on the open exterior region of an extreme Reissner-Nordstr\"om black hole and prove that, given compactly supported data on a Cauchy surface orthogonal to the timelike Killing vector field, the solution,…

General Relativity and Quantum Cosmology · Physics 2013-02-04 Sergio Dain , Gustavo Dotti

We show that given a compact, connected $m$-quasi Einstein manifold $(M,g,X)$ without boundary, the potential vector field $X$ is Killing if and only if $(M, g)$ has constant scalar curvature. This extends a result of…

Differential Geometry · Mathematics 2024-10-04 Eric Cochran

In relativistic gravity, requiring a spacetime hypersurface be a Killing horizon breaks the general covariance of general relativity. The residual algebra of horizon preserving diffeomorphisms can be extended to a Virasoro algebra near the…

General Relativity and Quantum Cosmology · Physics 2018-10-26 David Mattingly , Matthew Roberson , Sayandeb Basu

Lorentz-violating gravity theories with a preferred foliation can have instantaneous propagation. Nonetheless, it has been shown that black holes can still exist in such theories and the relevant notion of an event horizon has been dubbed…

General Relativity and Quantum Cosmology · Physics 2017-12-06 Nicola Franchini , Mehdi Saravani , Thomas P. Sotiriou