Symmetries of cosmological Cauchy horizons

  title={Symmetries of cosmological Cauchy horizons},
  author={Vincent Moncrief and James Allen Isenberg},
  journal={Communications in Mathematical Physics},
We consider analytic vacuum and electrovacuum spacetimes which contain a compact null hypersurface ruled byclosed null generators. We prove that each such spacetime has a non-trivial Killing symmetry. We distinguish two classes of null surfaces, degenerate and non-degenerate ones, characterized by the zero or non-zero value of a constant analogous to the “surface gravity” of stationary black holes. We show that the non-degenerate null surfaces are always Cauchy horizons across which the Killing… 
Symmetries of Cosmological Cauchy Horizons with Non-Closed Orbits
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 closed curves,
Non-degenerate Killing horizons in analytic vacuum spacetimes
We prove a geometric characterization of all possible 4-dimensional real analytic vacuum spacetimes near non-degenerate Killing horizons. It is known that any such horizon admits a canonically
Symmetries of vacuum spacetimes with a compact Cauchy horizon of constant non-zero surface gravity
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
Extension of Killing vector fields beyond compact Cauchy horizons
Extended symmetries at the black hole horizon
A bstractWe prove that non-extremal black holes in four-dimensional general relativity exhibit an infinite-dimensional symmetry in their near horizon region. By prescribing a physically sensible set
Symmetries of cosmological Cauchy horizons with exceptional orbits
We show here that if an analytic space‐time satisfying the vacuum (or electrovacuum) Einstein equations contains a compact null hypersurface with closed generators, then the space‐time must have a
Symmetries of higher dimensional black holes
We prove that if a stationary, real analytic, asymptotically flat vacuum black hole spacetime of dimension n ⩾ 4 contains a non-degenerate horizon with compact cross-sections that are transverse to
On the Rigidity Theorem for Spacetimes with a Stationary Event Horizon or a Compact Cauchy Horizon
Abstract: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
On the existence of Killing fields in smooth spacetimes with a compact Cauchy horizon
We prove that the surface gravity of a compact non-degenerate Cauchy horizon in a smooth vacuum spacetime, can be normalized to a non-zero constant. This result, combined with a recent result by


The Large Scale Structure of Space-Time
The theory of the causal structure of a general space-time is developed, and is used to study black holes and to prove a number of theorems establishing the inevitability of singualarities under certain conditions.
Infinite Dimensional Family of Vacuum Cosmological Models With Taub - {NUT} (Newman-Unti-Tamburino) Type Extensions
We show that the Gowdy metrics on T/sup 3/ x R contain an infinite-dimensional subfamily of solutions which each admit a Taub-NUT (Newman-Unti-Tamburino)-type extension. However we also show that the
The structure of the space of solutions of Einstein's equations. I. One Killing field.
This paper deals with globally hyperbolic solutions of the vacuum Einstein equations in a neighborhood of spacetimes that have a compact Cauchy surface of constant mean curvature. The first part of
General Relativity; an Einstein Centenary Survey
List of contributors Preface 1. An introductory survey S. W. Hawking and W. Israel 2. The confrontation between gravitation theory and experiment C. M. Will 3. Gravitational-radiation experiments D.