The theories of gravity which violate local Lorentz invariance do not admit a universal maximum speed of signal-propagation. Different field excitations see a different effective metric and hence a different light cone. In these theories, although one can define the Killing horizon in a conventional way, this definition does not capture the notion of a black hole. This is so because there exist...

Recently there has been growing interest in asymptotically anti–de Sitter ~AdS! black holes, motivated by the discovery of the Bañados-Teitelboim-Zanelli ~BTZ! black hole @1# in general relativity ~for reviews see @2,3#! and by the so-called AdS-CFT ~conformal field theory! speculation in string theory @4#. Very recently, Pretorius and Choptuik presented results of fully nonlinear numerical sim...

We give a Hamiltonian definition of mass for spacelike hypersurfaces in spacetimes with metrics which are asymptotic to the anti-de Sitter one, or to a class of generalizations thereof. We present the results of another paper (Chruściel P T and Nagy G 2001b, in preparation) which show that our definition provides a geometric invariant for a spacelike hypersurface S embedded in a space-time (M, ...

We prove non–existence of static, vacuum, appropriately regular, asymptotically flat black hole space–times with degenerate (not necessarily connected) components of the event horizon. This finishes the classification of static, vacuum, asymptotically flat domains of outer communication in an appropriate class of space–times, showing that the domains of outer communication of the Schwarzschild ...

The Newman-Penrose equations for spacetimes having one spacelike Killing vector are reduced – in a geometrically defined “canonical frame” – to a minimal set, and its differential structure is studied. Expressions for the frame vectors in an arbitrary coordinate basis are given, and coordinate-independent choices of the metric functions are suggested which make the components of the Ricci tenso...

Abstract In this work, we study various geometric properties of embedded spacelike hypersurfaces in $1+1+2$ decomposed spacetimes with a preferred spatial direction, denoted $e^{\mu}$, which are orthogonal to the fluid flow velocity spacetime and admit proper conformal transformation. To ensure non-vanishing positivity scalar curvature induced metric on hypersurface, impose that is non-negative...