Related papers: Multiple Killing Horizons: the initial value formu…
Violating Lorentz-invariance, and so implicitly permitting some form of superluminal communication, necessarily alters the notion of a black hole. Nevertheless, in both Einstein-{\AE}ther gravity, and Ho\v{r}ava-Lifshitz gravity, there is…
This paper is concerned with several not-quantum aspects of black holes, with emphasis on theoretical and mathematical issues related to numerical modeling of black hole space-times. Part of the material has a review character, but some new…
We provide a complete characterization of the metric Killing bundles (or metric bundles) of the Kerr geometry. Metric bundles, first introduced in [21] can be generally defined for axially symmetric spacetimes with Killing horizons and, for…
A three-dimensional Riemannian manifold has locally 6, 4, 3, 2, 1 or none independent Killing vectors. We present an explicit algorithm for computing dimension of the infinitesimal isometry algebra. It branches according to the values of…
In covariant metric theories of coupled gravity-matter systems the necessary and sufficient conditions ensuring the existence of a Killing vector field are investigated. It is shown that the symmetries of initial data sets are preserved by…
A de Sitter black hole or a black hole spacetime endowed with a positive cosmological constant has two Killing horizons -- a black hole and a cosmological event horizon surrounding it. It is natural to expect that the total…
It is shown that Kundt's metric for vacuum cannot be constructed when two-dimensional space-like sections of null hypersurfaces are compact, connected manifolds with no boundary unless they are tori or spheres, i.e. higher genus $\mathbf{g}…
In this paper, we study generalized $m$-quasi-Einstein $(M^n,g,X,\lambda)$ under natural conditions on the potential vector field. We show that, under suitable integral assumptions, the potential vector field is Killing, extending earlier…
We present a new class of near-horizon geometries which solve Einstein's vacuum equations, including a negative cosmological constant, in all even dimensions greater than four. Spatial sections of the horizon are inhomogeneous S^2-bundles…
We explore spacetime torsion in a two-dimensional setting, wherein it corresponds to a vector field. Without invoking field equations of a particular gravitational theory, we develop visualization techniques for such torsion fields,…
In the Carlip-Majhi-Padmanabhan approach, we calculate microscopic entropy of trapping (apparent) horizon of the FRW metric. We solve Killing equations for $t,r$ part of the metric without fixing {\it a piori} the form of the scaling factor…
On the largest scales, the universe appears to be almost homogeneous and isotropic, adhering to the cosmological principle. In contrast, on smaller scales inhomogeneities and anisotropy become increasingly prominent, reflecting the origin,…
We formulate several criteria under which the symmetries associated with the Killing and Killing-Yano tensors on the base space can be lifted to the symmetries of the full warped geometry. The procedure is explicitly illustrated on several…
We study vector fields generating a local flow by automorphisms of a parabolic geometry with higher order fixed points. We develop general tools extending the techniques of [1], [2], and [3]. We apply these tools to almost Grassmannian,…
$\Lambda^{\mu}_{\nu}$-geometry is a geometry with a variable cosmological term described by a second-rank symmetric tensor $\Lambda^{\mu}_{\nu}$ whose asymptotics are Einstein cosmological term $\Lambda \delta ^{\mu}_{\nu}$ at the origin…
We present a new method for computing the best approximation to a Killing vector on closed 2-surfaces that are topologically S^2. When solutions of Killing's equation do not exist, this method is shown to yield results superior to those…
This note describes the behavior of null-geodesics near nondegenerate Killing horizons in language amenable to the application of a general framework, due to Vasy and Hintz, for the analysis of both linear and nonlinear wave equations.…
We study hidden symmetries, the symmetries associated with the Killing tensors, of the near horizon geometry of odd-dimensional Kerr-AdS-NUT black hole in two limits: generic extremal and extremal vanishing horizon (EVH) limits. Starting…
Conformal Killing equations and their integrability conditions for expanding hyperheavenly spaces with Lambda in spinorial formalism are studied. It is shown that any conformal Killing vector reduces to homothetic or isometric Killing…
We discuss black hole spacetimes with a geometrically defined quasi-local horizon on which the curvature tensor is algebraically special relative to the alignment classification. Based on many examples and analytical results, we conjecture…