arXiv research

Wide neural networks can learn complex functions like gravitational force law.

The paper proves cylindrical nature of singular minimal ruled surfaces.

The Standard Model of elementary particles is a theory unifying three of the four basic forces of the Nature: electromagnetic, weak, and strong interactions. In this paper we consider the Standard Model in the presence of a classical (non-quantized) gravitation field and apply a bundle approach for describing it.

Solves time-optimal navigation on slippery slopes with cross gravitational wind.

Hyperelastic bodies in Riemannian manifolds can levitate due to curvature-induced forces.

In this paper, we give a brute-force proof of the Kastler-Kalau-Walze type theorem for $7$-dimensional manifolds with boundary about Witten deformation, and give a theoritic explaination of the gravitational action for $7$ dimensional manifolds with boundary.

In this paper, we consider the motion of a particle on a surface of revolution under the influence of a central force field. We prove that there are at most two analytic central potentials for which all the bounded, nonsingular orbits are closed and that there are exactly two on some surfaces with constant Gaussian cur…

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…

Starting from a relativistic phenomenology of anyons in crystals, we discuss the concept of relativistic interaction and the need to unify electromagnetism and gravitation within the Spencer cohomology of Lie equations. Then, from the sophisticated non-linear Spencer complex of the Poincaré and conformal Lie pseudogrou…

We introduce an approach for imposing physically motivated inductive biases on graph networks to learn interpretable representations and improved zero-shot generalization. Our experiments show that our graph network models, which implement this inductive bias, can learn message representations equivalent to the true fo…

Formally constructs metrics near timelike geodesics in vacuum spacetimes.

Given a real vector space V of finite dimension, together with a particular homogeneous field of bivectors that we call a "field of projective forces", we define a law of dynamics such that the position of the particle is a "ray" i.e. a half-line drawn from the origin of V. The impulsion is a bivector whose support is …

We develop a gluing construction which adds scaled and truncated asymptotically Euclidean solutions of the Einstein constraint equations to compact solutions with potentially non-trivial cosmological constants. The result is a one-parameter family of initial data which has ordinary and scaled "point-particle" limits an…

The liquid shape between two vertical parallel plates in a gravity field due to capillary forces is studied. When the physical system achieves its mechanical equilibrium, the capillary surface has mean curvature proportional to its height above a horizontal reference plane and it meets the vertical walls in a prescribe…

Proposes a Coulomb-like model for international trade flows, fitting real-world data.

Solves time-minimizing navigation on a mountain slope using Riemann-Finsler geometry.

New theorem shows black holes are real, with clearer event horizon.

Classifies gravitational instantons with quadratic volume growth.

Survey of recent progress in gravitational instantons

We develop a non-relativistic twistor theory, in which Newton--Cartan structures of Newtonian gravity correspond to complex three-manifolds with a four-parameter family of rational curves with normal bundle ${\mathcal O}\oplus{\mathcal O}(2)$. We show that the Newton--Cartan space-times are unstable under the general K…

The paper proves unique characterization of gravitational instantons with specific volume growth.

Period maps surjective for certain gravitational instantons.

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.

This work discovers latent field effects governing interacting dynamical systems.

Gravitational instantons are non-Kähler, providing a counterexample to Euclidean Black Hole Uniqueness.

Existence proved for specific types of gravitational instantons.

This is our second paper in a series to study gravitational instantons, i.e. complete hyperkäler 4-manifolds with faster than quadratic curvature decay. We prove two main theorems: 1.The asymptotic rate of gravitational instantons to the standard models can be improved automatically. 2.Any ALF-D_k gravitational instant…

Proves infinitesimal rigidity of Hermitian gravitational instantons.

The holographic description in the presence of gravitational Chern-Simons term is studied. The modified gravitational equations are integrated by using the Fefferman-Graham expansion and the holographic stress-energy tensor is identified. The stress-energy tensor has both conformal anomaly and gravitational or, if re-f…

Study proves interaction of three impulsive gravitational waves, showing local solution and Lipschitz continuity.

New approach proves existence of gravitating vortices on Riemann surfaces.

Review of gravitational instantons in physics.

Gravitational instantons collapse to a punctured plane with a special Kahler metric.

The holographic duality can be extended to include quantum theories with broken coordinate invariance leading to the appearance of the gravitational anomalies. On the gravity side one adds the gravitational Chern-Simons term to the bulk action which gauge invariance is only up to the boundary terms. We analyze in detai…

Gravitational waves are predicted by the general theory of relativity. In [6] D. Christodoulou showed that gravitational waves have a nonlinear memory. We proved in [3] that the electromagnetic field contributes at highest order to the nonlinear memory effect of gravitational waves. In the present paper, we study this …

Charge measurements for instantons and gravitational perturbations.

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 …

The paper studies how test particles' mass and charge vary in Kaluza-Klein models.

In general relativity, the local gravitational energy is best characterised by the quasilocal mass. The small sphere limit of quasilocal mass provides us the most local notion of gravitational energy. In four dimensions, the limits were shown be the stress tensor in non-vacuum and the Bel-Robinson tensor in vacuum. We …

Study of twistor spaces and minitwistor spaces for ALE gravitational instantons.

Study on mode stability of gravitational instantons of type D.

Vacuum gravity shows black holes can form without collapse.

The paper studies gravitational instantons with flat limits and finds elliptic regularity estimates.

Study limits of quasi-local angular momentum at infinity of gravitating systems.

Researchers construct explicit bundles for ALF metrics, revealing rational patching matrices for gravitational instantons.

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 constructs gravitational instantons with unique collapse patterns.