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.
A spacetime can be embedded in an enveloping space with all its extensions.
Study baryogenesis in conformally flat spacetimes using causal fermion systems.
Detect spacetime curvature with event causality measurements.
This paper completes globally hyperbolic conformally flat spacetimes, proving they are topological manifolds.
Classification of specific pseudo-Riemannian manifolds.
Detect spacetime curvature without rulers and clocks in 3D.
Maximal spacetimes have unique past/future sets.
We find all Ricci semi-symmetric as well as all conformally semi-symmetric spacetimes. Neither of these properties implies the other. We verify that only conformally flat spacetimes can be Ricci semi-symmetric without being conformally semi-symmetric and show that only vacuum spacetimes and spacetimes with just a -t…
New tractor geometry derived from asymptotically flat spacetimes.
The paper finds conditions for pseudosymmetric spacetimes to be perfect fluids.
Paper reviews and proves the uniqueness of multipole moments for stationary spacetimes.
The Kasner metrics are among the simplest solutions of the vacuum Einstein equations, and we use them here to examine the conformal method of finding solutions of the Einstein constraint equations. After describing the conformal method's construction of constant mean curvature (CMC) slices of Kasner spacetimes, we turn…
The paper analyzes null infinity's geometry without restrictions.
Higher-dimensional spacetimes have well-behaved boundaries.
Anosov representations are linked to specific spacetimes.
Higher-dimensional Schwarzschild spacetimes violate the Penrose property.
One method of studying the asymptotic structure of spacetime is to apply Penrose's conformal rescaling technique. In this setting, the Einstein equations for the metric and the conformal factor in the unphysical spacetime degenerate where the conformal factor vanishes, namely at the boundary representing null infinity.…
Moitvated in part by [3], in this note we obtain a rigidity result for globally hyperbolic vacuum spacetimes in arbitrary dimension that admit a timelike conformal Killing vector field. Specifically, we show that if M is a Ricci flat, timelike geodesically complete spacetime with compact Cauchy surfaces that admits a t…
The paper proves a rigidity theorem for null geodesic travel times in asymptotically AdS spacetimes.
The study characterizes and classifies specific types of manifolds using conformal and quasi-Einstein properties.
The paper aims to initiate a systematic study of conformal mappings between Finsler spacetimes and, more generally, between pseudo-Finsler spaces. This is done by extending several results in pseudo-Riemannian geometry which are necessary for field-theoretical applications and by proposing a technique which reduces a s…
W. Simon proved a conformal positive mass theorem, which was used to prove uniqueness of black holes later. In this note, we will generalize Simon's conformal positive mass theorem in two directions. First we will consider spacetime version of conformal positive mass theorems on asymptotically flat initial data set. Ne…
Vortex solutions on flat surfaces map to harmonic spinors on Nappi-Witten space.
We establish that equally-spaced smectic configurations enjoy an infinite-dimensional conformal symmetry and show that there is a natural map between them and null hypersurfaces in maximally-symmetric spacetimes. By choosing the appropriate conformal factor it is possible to restore additional symmetries of focal struc…
We consider a triality between the Zermelo navigation problem, the geodesic flow on a Finslerian geometry of Randers type, and spacetimes in one dimension higher admitting a timelike conformal Killing vector field. From the latter viewpoint, the data of the Zermelo problem are encoded in a (conformally) Painleve-Gullst…
The paper studies volumes of conformally flat manifolds in light-cone geometry.
The paper introduces and analyzes pseudo generalized Ricci-recurrent spacetimes in modified gravity.
We show that the conformal Penrose limit is an ordinary plane wave limit in a higher dimensional framework which resolves the spacetime singularity. The higher dimensional framework is provided by Ricci-flat manifolds which are of the form M_D = M_d x B, where M_d is an Einstein spacetime that has a negative cosmologic…
Characterizes pseudo B-symmetric spacetimes and their implications in f(R) gravity.
Study curvature properties in special manifolds using specific tensors.
The paper studies conformal Ricci solitons in warped product spaces.
We generalized Xiang, Qi and Wei's results on the M-eigenvalues of Riemann curvature tensor to higher dimensional conformal flat manifolds. The expression of M-eigenvalues and M-eigenvectors are found in our paper. As a special case, M-eigenvalues of conformal flat Einstein manifold have also been discussed, and the co…
New energy measure for isolated systems in general relativity.
In this paper we provide a method capable of producing an infinite number of solutions for Einstein's equation on static spacetimes with perfect fluid as a matter field. All spacetimes of this type which are symmetric with respect to a given group of translations and whose spatial factor is conformally flat, are charac…
The extended constraint equations arise as a special case of the conformal constraint equations that are satisfied by an initial data hypersurface in an asymptotically simple spacetime satisfying the vacuum conformal Einstein equations developed by H. Friedrich. The extended constraint equations consist of a quasi-…
The paper studies a new vacuum field equation and its solutions.
Characterizes Kerr spacetimes using conformal methods.
The paper introduces comprehensive quasi-Einstein spacetimes and explores their properties.
We consider four-dimensional vacuum spacetimes which admit a nonvanishing spacelike Killing field. The quotient with respect to the Killing action is a three-dimensional quotient spacetime . We establish several results regarding maximal hypersurfaces (spacelike hypersurfaces of zero mean curvature) in such quot…
We consider (flat) Cauchy-complete GH spacetimes, i.e., globally hyperbolic flat lorentzian manifolds admitting some Cauchy hypersurface on which the ambient lorentzian metric restricts as a complete riemannian metric. We define a family of such spacetimes - model spacetimes - including four subfamilies: translation sp…
The null distance for Lorentzian manifolds was recently introduced by Sormani and Vega. Under mild assumptions on the time function of the spacetime, the null distance gives rise to an intrinsic, conformally invariant metric that induces the manifold topology. We show when warped products of low regularity and globally…
Study Minkowski formula for conformal Killing-Yano 2-forms in constant curvature spacetimes.
New conformal geometry method solves Einstein-Weyl equations.
Study characterizes conformal boundaries of de Sitter spacetimes.
Proves some flat spacetimes can't be extended smoothly.
It is shown that the space of null geodesics of a causally simple Lorentzian manifold is Hausdorff if it admits an open conformal embedding into a globally hyperbolic spacetime. This provides an obstruction to conformal embeddings of causally simple spacetimes into globally hyperbolic ones irrespective of curvature con…
The paper studies geometric structures in perfect fluid spacetimes with specific metrics.
It has been observed by Maldacena that one can extract asymptotically anti-de Sitter Einstein -metrics from Bach-flat spacetimes by imposing simple principles and data choices. We cast this problem in a conformally compact Riemannian setting. Following an approach pioneered by Fefferman and Graham for the Einstein e…