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.
New research proves uniqueness of maximal spacetime boundaries under certain conditions.
Study on unique spacetime extensions in 1+1 dimensions with applications to weak null singularities.
The paper explores uniqueness and non-uniqueness of spacetime extensions in general relativity.
A spacetime can be embedded in an enveloping space with all its extensions.
Article strengthens initial data rigidity theorem to show unique spacetime extension.
Jebsen-Birkhoff theorem extended to Berwald spacetimes.
We revisit the problem of extension of a Killing vector field in a spacetime which is solution to the Einstein-Maxwell equation. This extension has been proved to be unique in the case of a Killing vector field which is normal to a bifurcate horizon by Yu. Here we generalize the extension of the vector field to a stron…
Study finds unique and non-existent constant mean curvature hypersurfaces in specific spacetimes.
In the first part of this work we show a uniqueness result for globally hyperbolic spacetimes with a spacelike conformal boundary satisfying the vacuum Einstein equations with positive cosmological constant. Then we present applications of this result in the contexts of cosmic censorship and the initial value problem i…
Paper proves uniqueness of specific spacetime surfaces in a lightcone.
Adapting Israel's proof of static black hole uniqueness, we show that the Schwarzschild spacetime is the only static vacuum asymptotically flat spacetime that possesses a suitably defined photon sphere.
In this paper, under natural geometric and physical assumptions we provide new uniqueness and non-existence results for complete maximal hypersurfaces in spatially open Robertson-Walker spacetimes whose fiber is flat. Moreover, our results are applied to relevant spacetimes as the steady state spacetime, Einstein-de Si…
Characterizes photon surfaces in static spacetimes, proving uniqueness.
Alternative proof for static black hole uniqueness with nonpositive mass.
We prove that every -dimensional flat GHMC Minkowski spacetime which is not a translation spacetime or a Misner spacetime carries a unique foliation by spacelike hypersurfaces of constant scalar curvature. In otherwords, we prove that every such spacetime carries a unique time function with isochrones of constan…
Solves initial boundary value problem for vacuum Einstein equations and proves geometric uniqueness.
Study maximal hypersurfaces in open spacetimes using a maximum principle.
We study global aspects of complete, non-singular asymptotically locally AdS spacetimes solving the vacuum Einstein equations whose conformal infinity is an arbitrary globally stationary spacetime. It is proved that any such solution which is asymptotically stationary to the past and future is itself globally stationar…
In a recent paper, the authors established the uniqueness of photon spheres in static vacuum asymptotically flat spacetimes by adapting Bunting and Masood-ul-Alam's proof of static vacuum black hole uniqueness. Here, we establish uniqueness of suitably defined sub-extremal photon spheres in static electro-vacuum asympt…
We establish a moduli space of stationary vacuum metrics in a spacetime, and set up a well-defined boundary map in , assigning a metric class with its Bartnik boundary data. Furthermore, we prove the boundary map is Fredholm by showing that the stationary vacuum equations (combined with p…
Study on black holes and photon surfaces in 4D spacetimes, proving uniqueness theorems.
We solve Bartnik's stationary extension problem near Schwarzschild spheres.
Paper reviews and proves the uniqueness of multipole moments for stationary spacetimes.
The paper classifies coverings and non-Hausdorff extensions of Misner spacetime.
Research proves unique continuation for Einstein-vacuum equations on aAdS spacetimes.
Unique AdS spacetime found with prescribed metric on a convex surface.
Causal spacetimes with Ricci tensor have unique transformations.
Proves uniqueness of certain spacetime solutions with extremal horizons.
Researchers prove unique embedding of curved surfaces into Minkowski spacetime.
Milne-like spacetimes are a class of FLRW models which admit spacetime extensions through the big bang. The boundary of a Milne-like spacetime can be identified with a null cone in the extension. We find that the comoving observers all emanate from a single point in the extension. This suggests that something phy…
The paper proves that certain FLRW spacetimes cannot be extended past the big bang.
In this paper, we extend a technique due to Romero, Rubio and Salamanca establishing sufficient conditions to guarantee the parabolicity of complete spacelike hypersurfaces immersed in a weighted generalized Robertson-Walker spacetime whose fiber has phi-parabolic universal Riemannian covering. As some applications of …
Proves properties of maximal hypersurfaces in specific spacetimes.
A spacelike surface S immersed in a 4-dimensional Lorentzian manifold will be said to be umbilical along a direction N normal to S if the second fundamental form along N is proportional to the first fundamental form of S. In particular, S is pseudo-umbilical if it is umbilical along the mean curvature vector field H, a…
We establish a black hole uniqueness theorem for Schwarzschild-de Sitter spacetime, also called Kottler spacetime, which satisfies Einstein's field equations of general relativity with positive cosmological constant. Our result concerns the class of static vacuum spacetimes with compact spacelike slices and regular max…
Anti-de Sitter spacetimes embed cone-metrics as bent Cauchy surfaces.
New proofs of unique photon surfaces in 4D spacetimes, extending previous work.
Paper proves uniqueness of black holes and photon surfaces in higher dimensions.
New rigidity results for specific hypersurfaces in spacetimes.
We prove two theorems, announced in hep-th/0108170, for static spacetimes that solve Einstein's equation with negative cosmological constant. The first is a general structure theorem for spacetimes obeying a certain convexity condition near infinity, analogous to the structure theorems of Cheeger and Gromoll for manifo…
The paper studies hyperbolic equations in a spacetime foliation, proving existence and uniqueness.
Several uniqueness results on compact maximal hypersurfaces in a wide class of sta- bly causal spacetimes are given. They are obtained from the study of a distinguished function on the maximal hypersurface, under suitable natural first order conditions of the spacetime. As a consequence several applications to Geometri…
The uniqueness of the AdS spactime in proved for dimension n\leq 7 or any dimension under the spin assumption.
New approach confirms Kruskal-Szekeres extension for Schwarzschild spacetime.
This paper continues the investigation of constant mean curvature (CMC) time functions in maximal globally hyperbolic spatially compact spacetimes of constant sectional curvature, which was started in math.DG/0604486. In that paper, the case of flat spacetimes was considered, and in the present paper, the remaining cas…
In this paper we study the problem of uniqueness for spacelike hypersurfaces with constant higher order mean curvature in generalized Robertson-Walker (GRW) spacetimes. In particular, we consider the following question: Under what conditions must a compact spacelike hypersurface with constant higher order mean curvatur…
We study the following problem: Given initial data on a compact Cauchy horizon, does there exist a unique solution to wave equations on the globally hyperbolic region? Our main results apply to any spacetime satisfying the null energy condition and containing a compact Cauchy horizon with surface gravity that can be no…
Anti-de Sitter spacetimes with convex boundaries are uniquely determined by their boundary metrics.