Related papers: Reconsidering Schwarzschild's original solution
We investigate geometric invariants of cuspidal edges on focal surfaces of regular surface. In particular, we shall clarify the sign of the singular curvature at a cuspidal edge on a focal surface using singularities of parallel surface of…
We combine numerical analysis with the inverse scattering method to study the periodic analog of Kerr solution. The periodic analog of the Schwarzschild solution is known to be regular and exhibit Kasner asymptotic behaviour for an…
We define a completely new space-time starting from the well known Schwarzschild Space time by defining a new polar angle $\phi '= \phi - \omega t$ and then redefining the periodicity: instead of demanding that the original angle be…
We give an explicit formula for singular surfaces of revolution with prescribed unbounded mean curvature. Using it, we give conditions for singularities of that surfaces. Periodicity of that surface is also discussed.
We introduce a geometric realization of noncommutative singularity resolutions. To do this, we first present a new conjectural method of obtaining conventional resolutions using coordinate rings of matrix-valued functions. We verify this…
In this note we discuss the geometry of Riemannian surfaces having a discrete set of singular points. We assume the conformal structure extends through the singularities and the curvature is integrable. Such points are called \emph{simple…
We present a time-dependent uniform-density interior Schwarzschild solution, an exact solution to the Einstein field equations. Our solution describes the collapse (or the time-reversed expansion) of an object from an infinite radius to an…
The purpose of this work is to show a possible reconciliation between Mach's principle and the Schwarzschild solution, using a description of this solution in terms of a new radial cooordinate related to the behaviour of Unruh detectors.
We give a description of the equisingularity of a family of normal surface singularities by numerical invariants belonging to them. By equisingularity we mean Whitney regularity or a more restrictive condition using the Nash modification.
We present a new solution in Einstein's General Relativity representing a Schwarzschild black hole immersed in a rotating universe. Such a solution is constructed analytically by means of the last unexplored Lie point symmetry of the Ernst…
In this paper we extend the concept of Milnor fiber and Milnor number of a curve singularity allowing the ambient space to be a quotient surface singularity. A generalization of the local {\delta}-invariant is defined and described in terms…
The equilibrium configurations between a Schwarzschild black hole and a hyperextreme Kerr object are shown to be described by a three-parameter subfamily of the extended double-Kerr solution. For this subfamily, its Ernst potential and…
The algebraic and geometric properties of a novel generalization of Clifford's classical C4 point-circle configuration are analysed. A connection with the integrable quaternionic discrete Schwarzian Kadomtsev-Petviashvili equation is…
It is shown how the use of the Kerr-Schild coordinate system can greatly simplify the formulation of the geodesic equation of the Schwarzschild solution. An application of this formulation to the numerical computation of the aspect of a…
A new spherically-symmetric solution is determined in a noncompactified Kaluza-Klein theory in which a time character is ascribed to the fifth coordinate. This solution contains two independent parameters which are related with mass and…
We study the singularity created in the supercritical collapse of a spherical massless scalar field. We first model the geometry and the scalar field to be homogeneous, and find a generic solution (in terms of a formal series expansion)…
A systematic approach to the coordinate transformations in the Schwarzschild singularity problem is considered. It is shown that both singularities at r=0 and r=2m can be eliminated by suitable coordinate transformations.
We define refined invariants which "count" nodal curves in sufficiently ample linear systems on surfaces, conjecture that their generating function is multiplicative, and conjecture explicit formulas in the case of K3 and abelian surfaces.…
Certain exact solutions of the Einstein field equations over nonsimply-connected manifolds are reviewed. These solutions are spherically symmetric and have no curvature singularity. They provide a regularization of the standard…
This paper deals with a complete invariant $R_X$ for cyclic quotient surface singularities. This invariant appears in the Riemann Roch and Numerical Adjunction Formulas for normal surface singularities. Our goal is to give an explicit…