Related papers: Approximate Killing Vectors on S^2

All Killing symmetries in complex $\mathcal{H}$-spaces with $\Lambda$ in terms of the Pleba\'nski - Robinson - Finley coordinate system are found. All $\mathcal{H}$-metrics with $\Lambda$ admitting a null Killing vector are explicitly…

In this paper, we investigate static spherically symmetric solutions in the context of Conformal Killing Gravity, a recently proposed modified theory of gravity that offers a new approach to the cosmological constant problem. Coupling this…

This work consists of two distinct parts. In the first part we present a new method for solving the initial value problem of general relativity. Given any spatial metric with a surface orthogonal Killing field and two freely specified…

We introduce the notion of metric Lie algebras of Killing type, which are characterized by the fact that all conformal Killing symmetric tensors are sums of Killing tensors and multiples of the metric tensor. We show that if a Lie algebra…

A new derivation of the five-dimensional Myers-Perry black-hole metric as a 2-soliton solution on a non-flat background is presented. It is intended to be an illustration of how the well-known Belinski-Zakharov method can be applied to find…

We give the first $2$-approximation algorithm for the cluster vertex deletion problem. This is tight, since approximating the problem within any constant factor smaller than $2$ is UGC-hard. Our algorithm combines the previous approaches,…

In this paper, we use the Killing vector method to formulate the de Sitter/Anti-de Sitter invariant special relativity (dS/AdS-SR). Through solving the Einstein equation with $\Lambda\neq 0$, the basic inertial metric for dS/AdS-SR is…

We study the head-on collision of two equal-mass momentarily stationary black holes, using black hole perturbation theory up to second order. Compared to first-order results, this significantly improves agreement with numerically computed…

We put into light the Killing vector fields on $\mathbb R^2$ endowed with a family of diagonal Riemannian metrics. According to certain restrictions on the Lam\'{e} coefficients, we concretely describe the symmetries of the metric.

We present a purely geometric method for constructing a rank two Killing tensor in a spacetime with a codimension one foliation that lifts the trivial Killing tensors from slices to the entire manifold. The resulting Killing tensor can be…

A symmetric tensor field on a Riemannian manifold is called Killing field if the symmetric part of its covariant derivative is equal to zero. There is a one to one correspondence between Killing tensor fields and first integrals of the…

We consider four-dimensional $N=2$ supergravity coupled to vector- and hypermultiplets, where abelian isometries of the quaternionic K\"ahler hypermultiplet scalar manifold are gauged. Using the recipe given by Meessen and Ort\'{\i}n in…

We show that the so-called flat-space rotational Killing vector method for measuring the Cartesian components of a black hole spin can be derived from the surface integral of Weinberg's pseudotensor over the apparent horizon surface when…

We study new separable orthogonally transitive abelian G_2 on S_2 models with two mutually orthogonal integrable Killing vector fields. For this purpose we consider separability of the metric functions in a coordinate system in which the…

A vector field $V$ on any (semi-)Riemannian manifold is said to be mixed Killing if for some nonzero smooth function $f$, it satisfies $L_VL_Vg=fL_Vg$, where $L_V$ is the Lie derivative along $V$. This class of vector fields, as a…

Using a Morse function and a Witten deformation argument, we obtain an upper bound for the dimension of the space of divergence-free symmetric Killing $p$-tensors on a closed Riemannian manifold, and calculate it explicitly for $p=2$.

Asymptotically locally AdS black hole geometries of dimension d > 2 are studied for nontrivial topologies of the transverse section. These geometries are static solutions of a set of theories labeled by an integer 0 < k < [(d-1)/2] which…

An exact spherically symmetric black hole solution of a recently proposed noncommutative gravity theory based on star products and twists is constructed. This is the first nontrivial exact solution of that theory. The resulting…

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…

An approximate solution to Einstein's equations representing two widely-separated non-rotating black holes in a circular orbit is constructed by matching a post-Newtonian metric to two perturbed Schwarzschild metrics. The spacetime metric…