Related papers: An Elementary Derivation of the Five Dimensional M…
We study separability of scalar, vector and tensor fields in 5-dimensional Myers-Perry spacetimes with equal angular momenta. In these spacetimes, there exists enlarged symmetry, $U(2) \simeq SU(2) \times U(1)$. Using the group theoretical…
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…
Using the inverse scattering method we construct a six-parameter family of exact, stationary, asymptotically flat solutions of the 4+1 dimensional vacuum Einstein equations, with U(1)^2 rotational symmetry. It describes the superposition of…
We review the vacuum solutions of Einstein's equations in higher dimensions known as Myers-Perry metrics. In many respects, these solutions describing spinning black holes admit the same remarkable properties as the standard Kerr black hole…
We determine the most general solution of the five-dimensional vacuum Einstein equation, allowing for a cosmological constant, with (i) a Weyl tensor that is type II or more special in the classification of Coley et al., (ii) a…
It is well-known that the Kerr-metric (rotating black hole in four dimensions) has Petrov type D. We prove a similar property in five dimensions. The Myers-Perry metric (rotating black hole in five dimensions) with one non-zero angular…
We present an exact solution to the Einstein field equations which is Ricci and Riemann flat in five dimensions, but in four dimensions is a good model for the early vacuum-dominated universe.
The exponential decay of the relative entropy associated to a fully discrete porous-medium equation in one space dimension is shown by means of a discrete Bakry-Emery approach. The first ingredient of the proof is an abstract discrete…
In this note we demonstrate the existence of a one-parameter family of initial data for the vacuum Einstein equations in five dimensions representing small deformations of the extreme Myers-Perry black hole. This initial data set has…
This article provides an attempt to extend concepts from the theory of Riemannian manifolds to piecewise linear spaces. In particular we propose an analogue of the Ricci tensor, which we give the name of an Einstein vector field. On a given…
We solve the five dimensional vacuum Einstein equations for several kinds of anisotropic geometries. We consider metrics in which the spatial slices are characterized as Bianchi types-II and V, and the scale factors are dependent both on…
Starting from a model of an elastic medium, partial differential equations with the form of the coupled Einstein-Dirac-Maxwell equations are derived. The form of these equations describes particles with mass and spin coupled to…
The usual derivation of Einstein's field equations from the Einstein--Hilbert action is performed by silently assuming the metric tensor's symmetric character. If this symmetry is not assumed, the result is a new theory, such as Einstein's…
We are interested in finding a solution to the tensor complementarity problem with a strong M-tensor, which we call the M-tensor complementarity problem. We propose a lower dimensional linear equation approach to solve that problem. At each…
A framework based on an extension of Kaluza's original idea of using a five dimensional space to unify gravity with electromagnetism is used to analyze Maxwell\'{}s field equations. The extension consists in the use of a six dimensional…
We consider a radiating shear-free spherically symmetric metric in higher dimensions. Several new solutions to the Einstein's equations are found systematically using the method of Lie analysis of differential equations. Using the five Lie…
We employ a theorem due to Campbell to build some simple 4-dimensional cosmological models which originate from solutions describing waves propagating along the extra-dimension of a 5-dimensional Ricci-flat space. The dimensional reduction…
The Dirac equation for the electron around a five-dimensional rotating black hole with two different angular momenta is separated into purely radial and purely angular equations. The general solution is expressed as a superposition of…
In this article, we achieved several non-naturally reductive Einstein metrics on exceptional simple Lie groups, which are formed by the decomposition arising from general Wallach spaces. By using the decomposition corresponding to the two…
In the standard Einstein's theory the exterior gravitational field of any static and axially symmetric stellar object can be described by means of a single function from which we obtain a metric into a four-dimensional space-time. In this…