Related papers: Kerr metric from two commuting complex structures
This is a master thesis concerning the search for a Kerr-type metric in the pseudocomplex General Relativity. Two different ways of deriving the standard Kerr-metric are presented and a solution for a Kerr-type metric in the pseudocomplex…
We derive the Kerr solution in a pedagogically transparent way, using physical symmetry and gauge arguments to reduce the candidate metric to just two unknowns. The resulting field equations are then easy to obtain, and solve. Separately,…
The Euclidean Kerr metric is conformal, in two distinct ways, to a Kahler metric, with conformal factors determined by the repeated eigenvalue of the two chiral halves of the Weyl curvature. A Lorentzian analogue holds, where the…
General Relativity's Kerr metric is famous for its many symmetries which are responsible for the separability of the Hamilton-Jacobi equation governing the geodesic motion and of the Teukolsky equation for wave dynamics. We show that there…
Generalized Kahler geometry is the natural analogue of Kahler geometry, in the context of generalized complex geometry. Just as we may require a complex structure to be compatible with a Riemannian metric in a way which gives rise to a…
A combined model of the Kerr spinning particle and superparticle is considered. The structure of the Kerr geometry is presented in a complex form as being created by a complex source. A natural supergeneralization of this construction is…
In this paper we show that it is possible to derive the Kerr solution in an alternative, intuitive way, based on physical reasoning and starting from an orthogonal metric ansatz having manifest ellipsoidal space-time symmetry (ellipsoidal…
The geodesics of Kerr's metric are described by the four-dimensional Hamiltonian dynamics integrable in the Arnold--Liouville sense. It can be reduced to two-dimensional one by the use of Fermat's principle. The resulting Hamiltonian is,…
A characterization of the Kerr-NUT-(A)de Sitter metric among four dimensional \Lambda-vacuum spacetimes admitting a Killing vector is obtained in terms of the proportionality of the self-dual Weyl tensor and a natural self-dual double…
We present the whole class of Gaussian coordinate systems for the Kerr metric. This is achieved through the uses of the relationship between Gaussian observers and the relativistic Hamilton-Jacobi equation. We analyze the completeness of…
In this paper we analyze the Kerr geometry in the context of Conformal Gravity, an alternative theory of gravitation, which is a direct extension of General Relativity. Following previous studies in the literature, we introduce an explicit…
Every graph G can be embedded in a Euclidean space as a two-distance set. The Euclidean representation number of G is the smallest dimension in which G is representable by such an embedding. We consider spherical and J-spherical…
The remarkable and unexpected separability of the Hamilton-Jacobi and Klein-Gordon equations in the background of a rotating four-dimensional black hole played an important role in the construction of generalisations of the Kerr metric, and…
A generalisation of the four-dimensional Kerr-de Sitter metrics to include a NUT charge is well known, and is included within a class of metrics obtained by Plebanski. In this paper, we study a related class of Kerr-Taub-NUT-de Sitter…
We examine three-dimensional metric deformations based on a tetrad transformation through the action the matrices of scalar fields. We describe by this approach to deformation the results obtained by Coll et al. in [1], where it is stated…
We develop a real-analytic framework, called perplex analysis, in which the complex, split-complex, and dual numbers arise as members of a single four-parameter family of two-dimensional commutative real algebras. Within this unified…
In this work we study in detail new kinds of motions of the metric tensor. The work is divided into two main parts. In the first part we study the general existence of Kerr-Schild motions --a recently introduced metric motion. We show that…
We give a self-contained survey of some approaches aimed at a global description of the geometry underlying double field theory. After reviewing the geometry of Courant algebroids and their incarnations in the AKSZ construction, we develop…
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…
The inclusion of a flat metric tensor in gravitation permits the formulation of a gravitational stress-energy tensor and the formal derivation of general relativity from a linear theory in flat spacetime. Building on the works of Kraichnan…