Related papers: Binary black hole spacetimes with a helical Killin…
We continue to study the response of black-hole space-times on the presence of additional strong sources of gravity. Restricting ourselves to static and axially symmetric (electro-)vacuum exact solutions of Einstein's equations, we first…
The presence of a horizon is the principal marker for black holes as they appear in the classical theory of gravity. In General Relativity (GR), horizons have several defining properties. First, there exists a static spherically symmetric…
Einstein complex spacetimes admitting null Killing or null homothetic Killing vectors are studied. These vectors define totally null and geodesic 2-surfaces called the null strings or twistor surfaces. Geometric properties of these null…
Killing vectors play a crucial role in characterizing the symmetries of a given spacetime. However, realistic astrophysical systems are in most cases only approximately symmetric. Even in the case of an astrophysical black hole, one might…
In numerically constructing a spacetime that has an approximate timelike Killing vector, it is useful to choose spacetime coordinates adapted to the symmetry, so that the metric and matter variables vary only slowly with time in these…
In this chapter, we study special photon orbits defined by means of Killing vectors and present a framework based on the properties of such null orbits. For concreteness, we restrict ourselves to the case of axially symmetric spacetimes…
The geometry of two infinitely long lines of mass moving in a fixed circular orbit is considered as a toy model for the inspiral of a binary system of compact objects due to gravitational radiation. The two Killing fields in the toy model…
We discuss a solution of the Einstein equations, obtained by gluing the external Kerr metric and the internal Weyl metric, describing an axisymmetric static vacuum distorted black hole. These metrics are glued at the null surfaces…
We prove that if a stationary, real analytic, asymptotically flat vacuum black hole spacetime of dimension $n\geq 4$ contains a non-degenerate horizon with compact cross sections that are transverse to the stationarity generating Killing…
The Einstein equations for spacetimes with two commuting spacelike Killing field symmetries are studied from a Hamiltonian point of view. The complexified Ashtekar canonical variables are used, and the symmetry reduction is performed…
In our recent work [Van de Moortel, The coexistence of null and spacelike singularities inside spherically symmetric black holes], we analyzed the transition between null and spacelike singularities in spherically symmetric dynamical black…
We consider numerical black hole solutions in the Weyl conformal geometry, and its associated conformally invariant Weyl quadratic gravity. In this model Einstein gravity (with a positive cosmological constant) is recovered in the…
A new solution of four-dimensional vacuum General Relativity is presented. It describes the near horizon region of the extreme (maximally spinning) binary black hole system with two identical extreme Kerr black holes held in equilibrium by…
We write explicitly the complete Lorentzian metric of a singularity-free spacetime where a black hole transitions into a white hole located in its same asymptotic region. In particular, the metric interpolates between the black and white…
We investigate static and spherically symmetric solutions in a gravity theory that extends the standard Hilbert-Einstein action with a Lagrangian constructed from a three-form field $A_{\alpha \beta \gamma}$, which is related to the field…
Working in a semi-classical setting, we consider solutions of the Einstein equations that exhibit light trapping in finite time according to distant observers. In spherical symmetry, we construct near-horizon quantities from the assumption…
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,…
An exhaustive list of four-dimensional $\Lambda$-vacuum spacetimes admitting a Killing vector whose self-dual Killing two-form ${\cal F}$ is null is obtained assuming that the self-dual Weyl tensor is proportional to the tensor product of…
We study a special two-dimensional dilaton gravity with Lagrangian $\mathcal{L}=\frac{1}{2}\sqrt{-g}(\phi R+{\lambda^2}{\rm sech}^2\phi)$ where $\lambda$ is a parameter of dimension mass. This theory describes two-dimensional spacetimes…
We consider the spacetime geometry of a static but otherwise generic black hole (that is, the horizon geometry and topology are not necessarily spherically symmetric). It is demonstrated, by purely geometrical techniques, that the curvature…