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.
This paper is motivated by the non-linear stability problem for the expanding region of Kerr de Sitter cosmologies in the context of Einstein's equations with positive cosmological constant. We show that under dynamically realistic assumptions the conformal Weyl curvature of the spacetime decays towards future null inf…
We consider globally hyperbolic spacetimes with compact Cauchy surfaces in a setting compatible with the presence of a positive cosmological constant. More specifically, for 3+1 dimensional spacetimes which satisfy the null energy condition and contain a future expanding compact Cauchy surface, we establish a precise c…
This paper gives a new proof that maximal, globally hyperbolic, flat spacetimes of dimension n≥3 with compact Cauchy hypersurfaces are globally foliated by Cauchy hypersurfaces of constant mean curvature, and that such spacetimes admit a globally defined constant mean curvature time function precisely when they a…
We establish the conjectured area-angular momentum-charge inequality for stable apparent horizons in the presence of a positive cosmological constant, and show that it is saturated precisely for extreme Kerr-Newman-de Sitter horizons. As with previous inequalities of this type, the proof is reduced to minimizing an `ar…
Classification of toric self-dual Einstein gravitational instantons with negative cosmological constant
problem Classification of toric self-dual Einstein gravitational instantons
method Proving that if the conformal Kähler structure associated to one of the torus Killing fields is global and extends to an ALE manifold with no additional fixed points, then the corresponding self-dual Einstein instanton is precisely given by the infinite class of multipole solutions
result The classification of toric self-dual Einstein gravitational instantons is precisely given by the infinite class of multipole solutions
Understanding the nature of dark energy, the mysterious force driving the accelerated expansion of the Universe, is a major challenge of modern cosmology. The next generation of cosmological surveys, specifically designed to address this issue, rely on accurate measurements of the apparent shapes of distant galaxies. H…
For a stable marginally outer trapped surface (MOTS) in an axially symmetric spacetime with cosmological constant Λ>0 and with matter satisfying the dominant energy condition, we prove that the area A and the angular momentum J satisfy the inequality 8π∣J∣≤A(1−ΛA/4π)(1−ΛA/12π) which is saturated pre…
A grand challenge of the 21st century cosmology is to accurately estimate the cosmological parameters of our Universe. A major approach to estimating the cosmological parameters is to use the large-scale matter distribution of the Universe. Galaxy surveys provide the means to map out cosmic large-scale structure in thr…
Prominent approaches to quantum gravity struggle when it comes to incorporating a positive cosmological constant in their models. Using quantization of a complex SL(2,C) Chern-Simons theory we include a cosmological constant, of either sign, into a model of quantum gravity.
Improved formulation of spinfoam quantum gravity with cosmological constant, ensuring all amplitudes are finite and providing semiclassical asymptotics.
problem Ensuring the finiteness of spinfoam amplitudes and providing semiclassical asymptotics for quantum gravity.
method Using state-integral model of PSL(2, C) Chern-Simons theory and implementing simplicity constraint.
result All spinfoam amplitudes are finite and provide semiclassical asymptotics with oscillatory terms related to the Regge action.
We study Einstein's equation in (m+n)D and (1+n)D warped spaces (Mˉ,gˉ) and classify all such spaces satisfying Einstein equations Gˉ=−Λˉgˉ. We show that the warping function not only can determine the cosmological constant Λˉ but also it can determine the cosmological constant Λ a…
We discuss a class of (local and non-local) theories of gravity that share same properties: i) they admit the Einstein spacetime with arbitrary cosmological constant as a solution; ii) the on-shell action of such a theory vanishes and iii) any (cosmological or black hole) horizon in the Einstein spacetime with a positi…
We show that the horizon geometry for supersymmetric black hole solutions of minimal five-dimensional gauged supergravity is that of a particular Einstein-Cartan-Weyl (ECW) structure in three dimensions, involving the trace and traceless part of both torsion and nonmetricity, and obeying some precise constraints. In th…
In this paper we propose and discuss a notion of mass for compact static metrics with positive cosmological constant. As a consequence, we characterise the de Sitter solution as the only static vacuum metric with zero mass. Finally, we show how to adapt our analysis to the case of negative cosmological constant, leadin…
The study examines conditions that prevent null geodesic lines in spacetimes, impacting cosmological geometry.
problem Preventing the existence of null geodesic lines in spacetimes.
method Identifying geometric conditions on foliations of spacetimes that prevent null geodesic lines, especially for spacetimes with compact Cauchy hypersurfaces.
result Conditions on foliations can prevent null geodesic lines, leading to restrictions on cosmological spacetime geometry.
This is the second of two works, in which we discuss the definition of an appropriate notion of mass for static metrics, in the case where the cosmological constant is positive and the model solutions are compact. In the first part, we have established a positive mass statement, characterising the de Sitter solution as…
SU(2) flat connection on 2D Riemann surface is shown to relate to the generalized twisted geometry in 3D space with cosmological constant. Various flat connection quantities on Riemann surface are mapped to the geometrical quantities in discrete 3D space. We propose that the moduli space of SU(2) flat connections on Ri…
New findings on static near horizon geometries and quasi-Einstein manifolds, including rigidity results for negative cosmological constant.
problem Rigidity of quasi-Einstein manifolds under different cosmological constant conditions.
method Analysis of quasi-Einstein equations on closed manifolds, focusing on static vacuum solutions and their properties.
result For negative cosmological constant, rigidity holds under specific conditions on the 1-form \(X\), including incompressibility, constant norm, and nontrivial cohomology.
We show that there are isometrically nonequivalent Robertson-Walker metrics which have the same set of geodesics. While one of these metrics satisfies the Einstein equations of pure dust without a cosmological constant, all the other describe pure dust with additional energy momentum tensor of cosmological constant typ…
In this letter a generic counterexample to the strong cosmic censor conjecture is exhibited. More precisely---taking into account that the conjecture lacks any precise formulation yet---first we make sense of what one would mean by a "generic counterexample" by introducing the mathematically unambigous and logically st…
A proof is given that the maximal Fermi coordinate chart for any comoving observer in a broad class of Robertson-Walker spacetimes consists of all events within the cosmological event horizon, if there is one, or is otherwise global. Exact formulas for the metric coefficients in Fermi coordinates are derived. Sharp uni…
In this global study of solutions to the linear wave equation on Schwarzschild de Sitter spacetimes we attend to the cosmological region of spacetime which is bounded in the past by cosmological horizons and to the future by a spacelike hypersurface at infinity. We prove an energy estimate capturing the expansion of th…