Related papers: New embedding of Schwarzschild geometry. II. Inter…
Coupling the Maxwell tensor to the Riemann-Christoffel curvature tensor is shown to lead to a geometricized theory of electrodynamics. While this geometricized theory leads directly to the classical Maxwell equations, it also extends their…
We present a simple spherically symmetric and regular solution of Einstein's equations with two parameters $k$ and $M$, which matches to Schwarzschild's solution, satisfies the weak energy conditions in the interior region and for small $r$…
We consider cosmological and black hole solutions in the Einstein and higher-derivative gravity in two dimensions where the theory is formulated first in $D$ dimensions. In the limit that $D$ tends to $2$ with simultaneous singular…
New exact asymptotically flat solutions of five-dimensional Einstein equations with horizon are found to describe multidimensional black stars generated by matter on the brane, conceivably on high energy colliders. The five-dimensional…
It has recently been suggested that our universe is a three-brane embedded in a higher dimensional spacetime. In this paper I examine static, spherically symmetric solutions that satisfy the effective Einstein field equations on a brane…
The dynamics of the leading self-force (0SF) order, corresponding to the geodesic motion of a light body in the exact background of a heavy body, are explicitly derived for the first time using a flat space scattering amplitude-based…
It is elaborated the complete classification of the possible types of the spherically symmetric global geometries for two types of electrically charged shells: (1) The charged shell as a single source of the gravitational field, when…
A spacetime is a connected 4-dimensional semi-Riemannian manifold endowed with a metric $g$ with signature $(- + + +)$. The geometry of a spacetime is described by the metric tensor $g$ and the Ricci tensor $S$ of type $(0, 2)$ whereas the…
The embedding of a curved spacetime in a higher-dimensional flat spacetime has continued to be a topic of interest in the general theory of relativity, as exemplified by the induced-matter theory. This paper deals with spacetimes of…
The exterior and interior Schwarzschild solutions are rewritten replacing the usual radial variable with an angular one. This allows to obtain some results otherwise less apparent or even hidden in other coordinate systems.
Assuming the four-dimensional space-time to be a general warped product of two surfaces we reduce the four-dimensional Einstein equations to a two-dimensional problem which can be solved. All global vacuum solutions are explicitly…
We consider a theory of gravity with a hidden extra-dimension and metric-dependent torsion. A set of physically motivated constraints are imposed on the geometry so that the torsion stays confined to the extra-dimension and the…
It is often easier to study pseudo-Riemannian manifolds by presenting them as surfaces in some ambient space. We propose an algorithm for construction of explicit isometric embeddings of pseudo-Riemannian manifolds with symmetries into an…
A non-geometrical (but with curved space) theory of gravitation characterized by a vector field representing gravitational matter and a metric tensor presenting space is presented. It is derived from a more general theory of matter and…
A quantum Schwarzschild spacetime and a quantum Schwarzschild-de Sitter spacetime with cosmological constant $\Lambda$ are constructed within the framework of a noncommutative Riemannian geometry developed in an earlier publication. The…
We show via an explicit construction how an infinite tower of higher-curvature corrections generically leads to a resolution of the Schwarzschild singularity in any spacetime dimension $D \ge 5$. The theories we consider have two key…
The paper studies the possible interplay between matter and geometry in scalar tensor theories of gravitation where the energy--momentum tensor is directly coupled with the Einstein tensor. After obtaining the scalar tensor representation…
Pandres has shown that an enlargement of the covariance group to the group of conservative transformations leads to a richer geometry than that of general relativity. Using orthonormal tetrads as field variables, the fundamental geometric…
The extreme Schwarzschild-de Sitter space-time is a spherically symmetric solution of Einstein's equations with a cosmological constant Lambda and mass parameter m>0 which is characterized by the condition that 9 Lambda m^2=1. The global…
We consider the modified Einstein equations obtained in the framework of effective spherically symmetric polymer models inspired by Loop Quantum Gravity. When one takes into account the anomaly free point-wise holonomy quantum corrections,…