Related papers: De/re-constructing the Kerr Metric

We revisit the Kerr metric in Boyer-Lindquist coordinates and construct the corresponding class of nonstandard solutions of Einstein's equations. These solutions can be used to describe the outer part of spiral galaxies without assuming…

We briefly discuss explicit compact object solutions in higher-order scalar-tensor theories. We start by so-called stealth solutions, whose metric are General Relativity (GR) solutions, but accompanied by a non-trivial scalar field, in both…

The original Kerr theorem provides the foundation for Kerr-Schild transformations by classifying all shear-free and geodesic null congruences in flat spacetime; the key ingredient of the Kerr-Schild ansatz. However, due to the high level of…

We derive a family of exact solutions for bi-metric gravity with an exchange symmetry between the two metrics. In this two-parameter family of solutions the gravitational field is sourced by a time-independent massless scalar field. We find…

In this paper, we study the theory of linearized gravity and prove the linear stability of Schwarzschild black holes as solutions of the vacuum Einstein equations. In particular, we prove that solutions to the linearized vacuum Einstein…

A method to the explict solutions of general systems of algebraic equations is presented via the metric form of affiliated K\"ahler manifolds. The solutions to these systems arise from sets of geodesic second order non-linear differential…

We provide a prescription to solve the metric completion problem in gravitational self-force calculations on a Kerr spacetime by fixing the remaining gauge freedom. We discuss the explicit example of eccentric equatorial orbits, recovering…

We develop the General Theory of Relativity in a formalism with extended causality that describes physical interaction through discrete, transversal and localized pointlike fields. The homogeneous field equations are then solved for a…

The eigenproblem for a class of Hamiltonians of the parametric down conversion process in the Kerr medium is solved. Some physical characteristics of the system are calculated.

It is thought that the spacetime geometry around black hole candidates is described by the Kerr solution, but an observational confirmation is still missing. Today, the continuum-fitting method and the analysis of the iron K$\alpha$ line…

We develop a new covariant formalism to treat spherically symmetric spacetimes in metric} f(R) theories of gravity. Using this formalism we derive the general equations for a static and spherically symmetric metric in a general…

We show that the exact solution of Einstein's equations describing a system of two aligned identical Kerr black holes separated by a massless strut follows straightforwardly from the extended 2-soliton solution possessing equatorial…

We propose a new geometric framework to address the stability of the Kerr solution to gravitational perturbations in the full sub-extremal range $|a|<M$. Central to our framework is a new formulation of nonlinear gravitational perturbations…

The Kerr-Schild (KS) double copy is celebrated for producing exact gravitational spacetimes from gauge fields, yet the preservation of symmetry content remains largely unexplored. We investigate the fate of residual symmetries in the KS…

As a consequence of Birkhoff's theorem, the exterior gravitational field of a spherically symmetric star or black hole is always given by the Schwarzschild metric. In contrast, the exterior gravitational field of a rotating (axisymmetric)…

The Einstein field equations have no known and acceptable interior solution that can be matched to an exterior Kerr field. In particular, there are no interior solutions that could represent objects like the Earth or other rigidly rotating…

The Kerr-Schild form provides a natural way of realizing the classical double copy that relates exact solutions in general relativity to exact solutions in gauge theory. In this paper, we examine the asymptotic structure of Kerr-Schild…

Complete sequences of new analytic solutions of Einstein's equations which describe thin super massive disks are constructed. These solutions are derived geometrically. The identification of points across two symmetrical cuts through a…

We revise the work of Scholtz, Flandera and G\"urlebeck [Kerr-Newman black hole in the formalism of isolated horizons, Phys. Rev. D 96, 064024 (2017)]. We cast the Kerr metric explicitly in the form suitable for the framework of isolated…

In this second paper, we develop an analytical theory of quasi-equatorial lensing by Kerr black holes. In this setting we solve perturbatively our general lens equation with displacement given in Paper I, going beyond weak-deflection Kerr…