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.
Linearized Einstein equations simplified via Calabi operator.
Study generalizes Hermitian-Einstein equation for cyclic Higgs bundles, proving existence and inequality.
Introduces new equations linking Kähler-Einstein and Hermitian-Yang-Mills theories.
The paper studies Einstein-type manifolds with structural conditions.
The paper proves quasi-Einstein structures on manifolds admit Killing vector fields and provides new examples.
We considered an extension of the standard functional for the Einstein-Dirac equation where the Dirac operator is replaced by the square of the Dirac operator and a real parameter controlling the length of spinors is introduced. For one distinguished value of the parameter, the resulting Euler-Lagrange equations provid…
We classify up to automorphisms all left-invariant non-Einstein solutions to the Einstein--Maxwell equations on 4-dimensional Lie algebras.
Study Einstein warped-product manifolds with specific curvature conditions.
Solves Einstein constraint equations on compact manifolds with specified boundaries.
In this work we initiate the mathematical study of naked singularities for the Einstein vacuum equations in dimensions by constructing solutions which correspond to the exterior region of a naked singularity. A key element is our introduction of a new type of self-similarity for the Einstein vacuum equations. Con…
We study the affine quasi-Einstein Equation for homogeneous surfaces. This gives rise through the modified Riemannian extension to new half conformally flat generalized quasi-Einstein neutral signature manifolds, to conformally Einstein manifolds and also to new Einstein manifolds through a warped product const…
Researchers create solutions for naked singularities in Einstein vacuum equations.
Proves global existence and uniqueness of solutions for Einstein-scalar-field equations.
Study on 4D Einstein manifolds with Kähler conformal geometry.
We prove several theorems concerning the connection between the local CR embeddability of 3-dimensional CR manifolds, and the existence of algebraically special Maxwell and gravitational fields. We reduce the Einstein equations for spacetimes associated with such fields to a system of CR invariant equations on a 3-dime…
Smooth solutions and classification of Dirac-Einstein equations on 3-manifolds.
We study the Einstein-Dirac equation as well as the weak Killing equation on Riemannian spin manifolds with codimension one foliation. We prove that, for any manifold admitting real Killing spinors (resp. parallel spinors), there exist warped product metrics on such that $(M^n \ti…
Unique global solutions found for specific initial data.
Maps dBKP solutions to MS system solutions, defining Einstein-Weyl structures.
We establish a regularity theorem for the Harmonic - Einstein Equation. As a byproduct of the local regularity, we also have a compactness theorem on Harmonic - Einstein equation. The method is mainly the Moser iteration technique which has been used and developed by \cite{BKN89}, \cite{Tian90}, \cite{TV05a} and others…
Study Dirac-Einstein equations on manifolds with boundary, focusing on constant volume and chiral conditions.
As seen in the works of Calabi, Cheng-Yau and Loftin, affine sphere equations have a close relationship with Kaehler-Einstein metrics. The main purpose of this note is to show that an equation analogous to those of hyperbolic affine spheres arises naturally from Kaehler-Einstein metrics on Einstein toric surfaces. The …
We construct exact solutions of the Einstein-Dirac equation, which couples the gravitational field with an eigenspinor of the Dirac operator via the energy-momentum tensor. For this purpose we introduce a new field equation generalizing the notion of Killing spinors. The solutions of this spinorial field equation are c…
Proves conditions for weighted Hermite-Einstein metrics on vector bundles.
We establish new existence and non-existence results for positive solutions of the Einstein-scalar field Lichnerowicz equation on compact manifolds. This equation arises from the Hamiltonian constraint equation for the Einstein-scalar field system in general relativity. Our analysis introduces variational techniques, i…
I show that solutions of the SU(infinity) Toda field equation generating a fixed Einstein-Weyl space are governed by a linear equation on the Einstein-Weyl space. From this, obstructions to the existence of Toda solutions generating a given Einstein-Weyl space are found. I also give a classification of Einstein-Weyl sp…
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…
An almost Einstein manifold satisfies equations which are a slight weakening of the Einstein equations; Einstein metrics, Poincare-Einstein metrics, and compactifications of certain Ricci-flat asymptotically locally Euclidean structures are special cases. The governing equation is a conformally invariant overdetermined…
Paper solves Hermitian-Einstein equations on noncompact manifolds.
Geometric equation defines canonical metrics on vector bundle families.
We study transformations of coordinates on a Lorentzian Einstein manifold with a parallel distribution of null lines and show that the general Walker coordinates can be simplified. In these coordinates, the full Lorentzian Einstein equation is reduced to equations on a family of Einstein Riemannian metrics.
In this paper we consider an Einstein-type equation which generalizes important geometric equations, like static and critical point equations. We prove that a complete Einstein-type manifold with fourth-order divergence-free Weyl tensor and zero radial Weyl curvature is locally a warped product with -dimensional…
Short-time existence for the Einstein-Euler and the vacuum Einstein equations is proven using a Friedrich inspired formulation due to Choquet-Bruhat and York, where the system is cast into a symmetric hyperbolic form and the Riemann tensor is treated as one of the fundamental unknowns of the problem. The reduced system…
The Einstein-scalar field theory can be used to model gravitational physics with scalar field matter sources. We discuss the initial value formulation of this field theory, and show that the ideas of Leray can be used to show that the Einstein-scalar field system of partial differential equations is well-posed as an ev…
New method constructs flat initial data for Einstein's equations.
We consider hypersurfaces in Einstein-Sasaki 5-manifolds which are tangent to the characteristic vector field. We introduce evolution equations that can be used to reconstruct the 5-dimensional metric from such a hypersurface, analogous to the (nearly) hypo and half-flat evolution equations in higher dimensions. We use…
We provide classification results for and examples of half conformally flat generalized quasi Einstein manifolds of signature . This analysis leads to a natural equation in affine geometry called the affine quasi-Einstein equation that we explore in further detail.
Original abstract: "We construct periodic solutions of nonlinear wave equations using analytic continuation. The construction applies in particular to Einstein equations, leading to infinite-dimensional families of time-periodic solutions of the vacuum, or of the Einstein-Maxwell-dilaton-scalar fields-Yang-Mills-Higgs-…
We consider 3+1 rotationally symmetric Lorentzian Einstein spacetime manifolds with and reduce the equations to 2+1 Einstein equations coupled to `shifted' wave maps. Subsequently, we prove various (explicit) positive mass-energy theorems. No smallness is assumed.
This article, written to appear as a chapter in "The Springer Handbook of Spacetime", is a review of the initial value problem for Einstein's gravitational field theory in general relativity. Designed to be accessible to graduate students who have taken a first course in general relativity, the article first discusses …
The quadric ansatz solves dKP equations in arbitrary dimensions, leading to Einstein-Weyl structures.
The study examines properties of perfect fluid spacetimes in Einstein's theory.
We define a functional for Hermitian metrics using the curvature of the Chern connection. The Euler-Lagrange equation for this functional is an elliptic equation for Hermitian metrics. Solutions to this equation are related to Kähler-Einstein metrics, and are automatically Kähler-Einstein under certain conditions. Give…
The paper studies Einstein-Hilbert action on complex manifolds.
Any constant-scalar-curvature Kaehler (cscK) metric on a complex surface may be viewed as a solution of the Einstein-Maxwell equations, and this allows one to produce solutions of these equations on any 4-manifold that arises as a compact complex surface with b_1 even. It is shown, however, that not all solutions of th…
We construct low regularity solutions of the vacuum Einstein constraint equations. In particular, on 3-manifolds we obtain solutions with metrics in $H^s\loc$ with . The theory of maximal asymptotically Euclidean solutions of the constraint equations descends completely the low regularity setting. Moreove…
New self-similarity for Einstein vacuum equations identified.
On a conformal manifold, it is well known that parallel sections of the standard tractor bundle with non-vanishing scale are in 1-1 correspondence with solutions of the conformal Einstein equation. In 2 dimensions conformal geometry carries no local information but one can remedy this by equipping the surface with a Mö…