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.
Existence and uniqueness of gravitating vortices on Riemann surfaces with specific properties.
This paper is the sequel of our previous article "From ALE to ALF gravitational instantons", where we constructed ALF hyperkahler metrics on minimal resolutions of dihedral Kleinian singularities. In the present article we generalize the construction to smooth deformations of these Kleinian singularities, with help of …
The paper proves cylindrical nature of singular minimal ruled surfaces.
Penrose's conjecture links black holes and gravitational singularities.
The paper examines gravitational singularities in spacetimes and proves inextendibility.
We construct a family of instanton metric obtained from new exact singular solutions for minimal surfaces by noticing the correspondence between minimal surfaces in the three dimesional Euclidean space and gravitational instantons possessing two killing vectors. By Calabi's correspondence, we derive a family of explici…
New estimates quantify blow-up rates of spacelike singularities in gravitational collapse.
We present an elementary argument that one can shield linearised gravitational fields using linearised gravitational fields. This is done by using third-order potentials for the metric, which avoids the need to solve singular equations in shielding or gluing constructions for the linearised metric.
Study proves interaction of three impulsive gravitational waves, showing local solution and Lipschitz continuity.
In this paper we explicitly calculate the analogue of the 't Hooft SU(2) Yang--Mills instantons on Gibbons--Hawking multi-centered gravitational instantons which come in two parallel families: the multi-Eguchi--Hanson, or A_k ALE gravitational instantons and the multi-Taub--NUT, or A_k ALF gravitational instantons. We …
We provide a geometric explanation for the existence of magnification relations for the A, D, E family of caustic singularities, which were established in recent work. In particular, it was shown that for families of general mappings between planes exhibiting any of these caustic singularities, and for any non-caustic …
The study finds polynomial upper bounds for singularities in Einstein-scalar field system.
In this paper, we initiate the study of the instability of naked singularities without symmetries. In a series of papers, Christodoulou proved that naked singularities are not stable in the context of the spherically symmetric Einstein equations coupled with a massless scalar field. We study in this paper the next simp…
Study of harmonic maps and instantons in 4D.
Published in 1999, Christodoulou proved that the naked singularities of a self-gravitating scalar field are not stable in spherical symmetry and therefore the cosmic censorship conjecture is true in this context. The original proof is by contradiction and sharp estimates are obtained strictly depending on spherical sym…
Study describes ALF instantons with conical singularities.
First we review the definition of a negative point mass singularity. Then we examine the gravitational lensing effects of these singularities in isolation and with shear and convergence from continuous matter. We review the Inverse Mean Curvature Flow and use this flow to prove some new results about the mass of a sing…
Second paper in series solves Einstein vacuum equations for three impulsive waves.
Study on curvature blow-up rates in black hole interiors from gravitational collapse.
Classifies 4D toric Hermitian ALF metrics with conical singularities.
Sharp mass bounds for ALE and ALF toric 4-manifolds.
Study shows instability of naked singularities in perfect fluid models.
Kaehler-Einstein metrics on orbifolds derived from Einstein sequences.
Continuous process closes cusps in complex algebraic surfaces.
We construct ALE Calabi-Yau metrics with cone singularities along the exceptional set of resolutions of with non-positive discrepancies. In particular, this includes the case of the minimal resolution of two dimensional quotient singularities for any finite subgroup acting freely on t…
Proves uniqueness and existence of toric gravitational instantons.
The paper proves extremal black holes form at a critical point of gravitational collapse.
We consider the mean curvature evolution of rotationally symmetric surfaces. Using numerical methods, we detect critical behavior at the threshold of singularity formation resembling the one of gravitational collapse. In particular, the mean curvature simulation of a one-parameter family of initial data reveals the exi…
The Bakry-Emery generalized Ricci tensor arises in scalar-tensor gravitation theories in the conformal gauge known as the Jordan frame. Recent results from the mathematics literature show that standard singularity and splitting theorems that hold when an energy condition is applied in general relativity also hold when …
Study collapsing geometry of hyperkähler 4-manifolds and prove conjectures.
Paper proves existence of anisotropic dynamical horizons in gravitational collapse.
New black hole models with both null and spacelike singularities.
We study Einstein metrics on smooth compact 4-manifolds with an edge-cone singularity of specified cone angle along an embedded 2-manifold. To do so, we first derive modified versions of the Gauss-Bonnet and signature theorems for arbitrary Riemannian 4-manifolds with edge-cone singularities, and then show that these y…
Nearly all field theories suffer from singularities when particles are introduced. This is true in both classical and quantum physics. Classical field singularities result in the notorious self-force problem, where it is unknown how the dynamics of a particle change when the particle interacts with its own (self) field…
Classifies gravitational instantons with quadratic volume growth.
Survey of recent progress in gravitational instantons
This paper provides a classification result for gravitational instantons with cubic volume growth and cyclic fundamental group at infinity. It proves that a complete hyperkähler manifold asymptotic to a circle fibration over the Euclidean three-space is either the standard $\rl^3 \times \sph^1$ or a multi-Taub-NUT mani…
New theorem shows black holes are real, with clearer event horizon.
The paper proves unique characterization of gravitational instantons with specific volume growth.
Study gluing event horizons of Minkowski and Schwarzschild spacetimes.
Period maps surjective for certain gravitational instantons.
We study the fractional gravity for spacetimes with non-integer dimensions. Our constructions are based on a geometric formalism with the fractional Caputo derivative and integral calculus adapted to nonolonomic distributions. This allows us to define a fractional spacetime geometry with fundamental geometric/physical …
This work presents a classification of all smooth 't Hooft-Jackiw-Nohl-Rebbi instantons over Gibbons-Hawking spaces. That is, we find all smooth SU(2) Yang-Mills instantons over these spaces which arise by conformal rescalings of the metric with suitable functions. Since the Gibbons-Hawking spaces are hyper-Kahler grav…
Authors prove Torelli theorem for a specific type of gravitational instantons.
This is our third paper in a series on the gravitational instantons. In this paper, we classify ALG and ALH gravitational instantons. In ALG case, we extend Hein's construction slightly and show that it's the only ALG gravitational instanton. In ALH case, we prove a Torelli-type theorem.
Study of spacelike singularities in spherical spacetimes with scalar matter.
Gravitational instantons are non-Kähler, providing a counterexample to Euclidean Black Hole Uniqueness.
We prove that the essential smoothness of the gravitational metric at shock waves in GR, a PDE regularity issue for weak solutions of the Einstein equations, is determined by a geometrical condition which we introduce and name the {\it Riemann-flat condition}. The Riemann-flat condition determines whether or not the es…