A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Stability of Schwarzschild singularity in near-Schwarzschild black holes under perturbations.
It is shown that the Schwarzschild spacetime can be extended so that the metric becomes analytic at the singularity. The singularity continues to exist, but it is made degenerate and smooth, and the infinities are removed by an appropriate choice of coordinates. A family of analytic extensions is found, and one of thes…
The Schwarzschild spacetime metric of negative mass is well-known to contain a naked singularity. In a spacelike slice, this singularity of the metric is characterized by the property that nearby surfaces have arbitrarily small area. We develop a theory of such "zero area singularities" in Riemannian manifolds, general…
The study finds regular null hypersurfaces in a perturbed Schwarzschild black hole exterior.
We solve spacelike spherically symmetric constant mean curvature (SS-CMC) hypersurfaces in Schwarzschild spacetimes and analyze their asymptotic behavior near the coordinate singularity r = 2M. Furthermore, we join SS-CMC hypersurfaces in the Kruskal extension to obtain complete ones and discuss the smooth properties.
We present a gluing construction which adds, via a localized deformation, exactly Delaunay ends to generic metrics with constant positive scalar curvature. This provides time-symmetric initial data sets for the vacuum Einstein equations with positive cosmological constant with exactly Kottler-Schwarzschild-de Sitter en…
Einstein's equation is rewritten in an equivalent form, which remains valid at the singularities in some major cases. These cases include the Schwarzschild singularity, the Friedmann-Lemaître-Robertson-Walker Big Bang singularity, isotropic singularities, and a class of warped product singularities. This equation is co…
We find necessary and sufficient conditions for existence of a locally isometric embedding of a vacuum space-time into a conformally-flat 5-space. We explicitly construct such embeddings for any spherically symmetric Lorentzian metric in dimensions as a hypersurface in . For the Schwarzschild metric the…
Proves positive mass theorem for AF spin manifolds with conical singularities.
We consider branes $N=I\times\so$, where $\so$ is an \ndash dimensional space form, not necessarily compact, in a Schwarzschild-AdS_{(n+2)} bulk $\mc N$. The branes have a big crunch singularity. If a brane is an ARW space, then, under certain conditions, there exists a smooth natural transition flow through the sin…
Study on curvature blow-up rates in black hole interiors from gravitational collapse.
We study Jang's equation on a one-parameter family of asymptotically flat, spherically symmetric Cauchy hypersurfaces in the maximally extended Schwarzschild spacetime. The hypersurfaces contain apparent horizons and are parametrized by their proximity to the singularity at . We show that on those hypersurfaces …
The maximal analytic Schwarzschild spacetime is manifestly inextendible as a Lorentzian manifold with a twice continuously differentiable metric. In this paper, we prove the stronger statement that it is even inextendible as a Lorentzian manifold with a continuous metric. To capture the obstruction to continuous extens…
Smooth metrics satisfying Penrose inequality are necessarily smooth.
Causal fermion systems and Riemannian fermion systems are proposed as a framework for describing non-smooth geometries. In particular, this framework provides a setting for spinors on singular spaces. The underlying topological structures are introduced and analyzed. The connection to the spin condition in differential…
We construct large families of initial data sets for the vacuum Einstein equations with positive cosmological constant which contain exactly Delaunay ends; these are non-trivial initial data sets which coincide with those for the Kottler-Schwarzschild-de Sitter metrics in regions of infinite extent. From the purely Rie…
Proves Penrose inequality in all dimensions for specific manifolds.
We derive new inequalities between the boundary capacity of an asymptotically flat 3-manifold with nonnegative scalar curvature and boundary quantities that relate to quasi-local mass; one relates to Brown--York mass and the other is new. We argue by recasting the setup to the study of mean-convex fill-ins with nonnega…
The Weyl curvature hypothesis of Penrose attempts to explain the high homogeneity and isotropy, and the very low entropy of the early universe, by conjecturing the vanishing of the Weyl tensor at the Big-Bang singularity. In previous papers it has been proposed an equivalent form of Einstein's equation, which extends i…
The study finds polynomial upper bounds for singularities in Einstein-scalar field system.
Paper extends foliation results in higher dimensions for Schwarzschild spaces.
Existence proved for static vacuum extensions near Schwarzschild spheres.
Study gluing event horizons of Minkowski and Schwarzschild spacetimes.
Warped-product black hole spacetimes are -inextendible.
Study finds new minimal surfaces in Schwarzschild space.
Study on minimal hypersurfaces in Schwarzschild manifolds intersecting the horizon orthogonally.
Revises Schwarzschild manifold rigidity proof for spin manifolds.
The paper studies the stability of volume and area preserving mean curvature flows in Schwarzschild and asymptotic Schwarzschild spaces.
Two rigidity results for surfaces in Schwarzschild spacetime.
Higher-dimensional Schwarzschild spacetimes violate the Penrose property.
Seminar held at JINR, Dubna, May 15, 2012. In General Relativity, spacetime singularities raise a number of problems, both mathematical and physical. One can identify a class of singularities - with smooth but degenerate metric - which, under a set of conditions, allow us to define proper geometric invariants, and to w…
Schwarzschild 3-manifold stability proven for 3D Penrose inequality.
Complete minimal surfaces with any genus found in a specific 3-manifold.
Proves stability of Schwarzschild black holes without symmetry assumptions.
Global existence and geometry of constant mass aspect function foliation in perturbed Schwarzschild spacetime studied.
Study on spacelike submanifolds in generalized Schwarzschild spacetimes with lightlike foliations.
We formulate the concept of time machine structure for spacetimes exhibiting a compactely constructed region with closed timelike curves. After reviewing essential properties of the pseudo Schwarzschild spacetime introduced by A. Ori, we present an analysis of its geodesics analogous to the one conducted in the case of…
Paper defines semi-quasi-Einstein manifolds and applies to Schwarzschild and Kottler spacetimes.
In this article, we prove a rigidity theorem for isometric embeddings into the Schwarzschild manifold, by using the variational formula of quasi-local mass.
We study the problem of existence of isoperimetric regions for large volumes, in -locally asymptotically Euclidean Riemannian manifolds with a finite number of -asymptotically Schwarzschild ends. Then we give a geometric characterization of these isoperimetric regions, extending previous results contained in …
We consider branes in a Schwarzschild- bulk, where the stress energy tensor is dominated by the energy density of a scalar fields map $\f:N\ra \mc S$ with potential , where $\mc S$ is a semi-Riemannian moduli space. By transforming the field equation appropriately, we get an equivalent field …
Using the weak solution of Inverse mean curvature flow, we prove the sharp Minkowski-type inequality for outward minimizing hypersurfaces in Schwarzschild space.
Study of marginally trapped surfaces in a perturbed Schwarzschild spacetime.
The paper proves the stability of a flow in Schwarzschild space.
Scattering theory developed for linearised gravity near Schwarzschild black hole.
In this note we address the problem of finding Abelian instantons of finite energy on the Euclidean Schwarzschild manifold. This amounts to construct self-dual L^2 harmonic 2-forms on the space. Gibbons found a non-topological L^2 harmonic form in the Taub-NUT metric, leading to Abelian instantons with continuous energ…
In this paper, we prove the existence of an ancient solution to the Ricci flow whose limit at is the Euclidean Schwarzschild metric.
In this paper, we will show that the limit of the Brown-York mass of a family of convex revolution surfaces in an asymptotically Schwarzschild manifold is the ADM mass.