相关论文: Reconsidering Schwarzschild's original solution

We consider ruled surfaces with finite multiplicity. We study behaviors of the striction curves and the singularities of the ruled surfaces. We also give geometric meanings of invariants related to the ruled surfaces.

The singular real second order 1D Schrodinger operators are considered here with such potentials that all local solutions near singularities to the eigenvalue problem are meromorphic for all values of the spectral parameter. All…

In our previous works we have classified real non-singular cubic hypersurfaces in the 5-dimensional projective space up to equivalence that includes both real projective transformations and continuous variations of coefficients preserving…

The Schwarzschild singularity's resolution has key values in cracking the key mysteries related with black holes, the origin of their horizon entropy and the information missing puzzle involved in their evaporations. We provide in this work…

Following up on earlier work on the regularization of the singular Schwarzschild solution, we now apply the same procedure to the singular Friedmann solution. Specifically, we are able to remove the divergences of the big bang singularity,…

We study self-dual multi-vortex solutions of Chern-Simons Higgs theory in a background curved spacetime. The existence and decaying property of a solution are demonstrated.

We consider solutions to the linear wave equation on a (maximally extended) Schwarzschild spacetime, assuming only that the solution decays suitably at spatial infinity on a complete Cauchy hypersurface. (In particular, we allow the support…

In this Brief Report we give the proof that the solution of any static test charge distribution in Schwarzschild space is unique. In order to give the proof we derive the first Green's identity written with p-forms on (pseudo) Riemannian…

A general geometrical scheme is presented for the construction of novel classical gravity theories whose solutions obey two-sided bounds on the sectional curvatures along certain subvarieties of the Grassmannian of two-planes. The…

We give a direct interpretation of Neumann's combinatorial formula for the Chern-Simons invariant of a 3-manifold with a representation in PSL(2,C) whose restriction to the boundary takes values in upper triangular matrices. Our…

There are two well known tasks, related to Newton polyhedra: to study invariants of singularities in terms of their Newton polyhedra, and to describe Newton polyhedra of resultants and discriminants. We introduce so called resultantal…

We define a Rasmussen $s$-invariant over the coefficient ring of the integers, and show how it is related to the $s$-invariants defined over a field. A lower bound for the slice genus of a knot arising from it is obtained, and we give…

Here we construct new solution for the Einstein equations -- some analog of the Schwarzschild metric in anti--de Sitter--Beltrami space in the $c\to \infty$ limit ($R$-space). In this case we derive an adiabatic invariant for finite…

The charged and spinning lightlike solutions are obtained in the Kerr-Schild formalism. In particular, one of them may be considered as an ultrarelativistic boost of the Kerr-Newman solution along the direction of angular momentum. The Kerr…

We obtain a global embedding of the surface of a rapidly rotating Kerr-Newman black hole in an Euclidean 4-dimensional space.

We show that the Schwarzschild solution can be embedded in a class of nonstandard solutions of the vacuum Einstein's equations with arbitrary rotation curves. These nonstandard solutions have to be taken as physical if dark matter as needed…

Schr\"odinger operators often display singularities at the origin, the Coulomb problem in atomic physics or the various matter coupling terms in the Friedmann-Robertson-Walker problem being prominent examples. For various applications it…

We estimate $\delta$-invariants of some singular del Pezzo surfaces with quotient singularities, which we studied ten years ago. As a result, we show that each of these surfaces admits an orbifold K\"ahler--Einstein metric.

We study static spherically symmetric solutions of Einstein gravity plus an action polynomial in the Ricci scalar, $R$, of arbitrary degree, $n$, in arbitrary dimension, $D$. The global properties of all such solutions are derived by…

Rastall's theory belongs to the class of non-conservative theories of gravity. In vacuum, the only non-trivial static, spherically symmetric solution is the Schwarzschild one, except in a very special case. When a canonical scalar field is…