arXiv research

Study null curves and their motion in 3D flat space-time, leading to integrable hierarchies.

The notion of maximal extension of a globally hyperbolic space-time arises from the notion of maximal solutions of the Cauchy problem associated to the Einstein's equations of general relativity. In 1969 Choquet-Bruhat and Geroch proved that if the Cauchy problem has a local solution, this solution has a unique maximal…

This paper aims to study the $W$-curvature tensor on relativistic space-times. The energy-momentum tensor T of a space-time is semi-symmetric given that the $W$-curvature tensor is semi-symmetric whereas energy-momentum tensor T of a space-time having a divergence free $W$-curvature tensor is of Codazzi type. A space-t…

In this paper, we study Ricci-flat and Einstein Lorentzian multiply warped products. We also consider the case of having constant scalar curvatures for this class of warped products. Finally, after we introduce a new class of spacetimes called as generalized Kasner space-times, we apply our results to this kind of spac…

Small deformations of a specific type of Lorentzian space-time preserve its structure.

We prove a perturbative result concerning the uniqueness of Kerr-Newman family of black holes: given an asymptotically flat space-time with bifurcate horizons, if it agrees with a non-extremal Kerr-Newman space-time asymptotically flat at infinity and it is sufficiently close to the Kerr-Newman family, then the space-t…

New distances defined between space-times, proving some definite.

Proves a Minkowski inequality for static Einstein-Maxwell space-time.

In this paper, based on an intrinsic definition of asymptotically AdS space-times, we show that the standard anti-de Sitter space-time is the unique strictly stationary asymptotically AdS solution to the vacuum Einstein equations with negative cosmological constant in dimension less than 7. Instead of using the positiv…

Theory of space-time currents for geometric evolutions.

New flat surfaces found in 3D sphere space.

Margulis space-times with parabolic holonomy elements are stable under sufficiently small deformations.

Let $\mathbf{E}$ be a flat Lorentzian space of signature $(2, 1)$. A Margulis space-time is a noncompact complete flat Lorentzian $3$-manifold $\mathbf{E}/Γ$ with a free holonomy group $Γ$ of rank $\mathbf{g}, \mathbf{g} \geq 2$. We consider the case when $Γ$ contains a parabolic element. We obtain a characterization o…

Study on stochastic covariant derivatives in curved space-time.

Detect spacetime curvature without rulers and clocks in 3D.

Study constructs solutions for evolving hypersurfaces using inverse spacetime mean curvature.

The study characterizes constant curvature manifolds using ruled surfaces.

We offer an example of the second order Kawaguchi metric function the extremal flow of which generalizes the flat space-time model of the semi-classical spinning particle to the framework of the pseudo-Riemannian space-time. The general shape of the variational Euler-Poisson equation of the fourth order in the (pseudo-…

We study in details the long-time asymptotic behavior of a relativistic diffusion taking values in the unitary tangent bundle of a curved Lorentzian manifold, namely a spatially flat and fast expanding Robertson-Walker space-time. We prove in particular that the Poisson boundary of the diffusion can be identified with …

Study on flat metrics on 3D and 4D manifolds, focusing on topology and algebra.

Study Codazzi tensors in space-times, linking to Cotton gravity.

Let $V$ be a maximal globally hyperbolic flat $n+1$--dimensional space--time with compact Cauchy surface of hyperbolic type. We prove that $V$ is globally foliated by constant mean curvature hypersurfaces $M_τ$, with mean curvature $τ$ taking all values in $(-\infty, 0)$. For $n \geq 3$, define the rescaled volume of $…

In fivebrane compactifications on 3-manifolds, we point out the importance of all flat connections in the proper definition of the effective 3d N=2 theory. The Lagrangians of some theories with the desired properties can be constructed with the help of homological knot invariants that categorify colored Jones polynomia…

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…

Locally symplectic structure found on Kerr space-time.

Some aspects of Dirac spinors are resumed and studied in order to interpret mathematically the P and T operations in a gravitational field.

This paper proves a positive energy-momentum theorem for oriented Riemannian 3-manifolds that are asymptotic to a standard hyperbolic slice in anti de Sitter space-time. Analogously to the original Witten's proof in the asymptotically flat case, this result relies on spinorial methods. We also give a rigidity theorem: …

New approach connects 3D Chern-Simons theory to spectral networks.

Paper proves stable minimal surfaces in 3D are flat.

This study aims mainly at investigating the effects of concircular flatness and concircular symmetry of a warped product manifold on its fibre and base manifolds. Concircularly flat and concircularly symmetric warped product manifolds are investigated. The divergence free concircular curvature tensor on warped product …

Sharp 3D Alexandrov inequality applied to volume-preserving flows.

We provide the classification of locally conformally flat gradient Yamabe solitons with positive sectional curvature. We first show that locally conformally flat gradient Yamabe solitons with positive sectional curvature have to be rotationally symmetric and then give the classification and asymptotic behavior of all r…

We propose in this paper a new approach to the Kaluza-Klein idea of a five dimensional space-time unifying gravitation and electromagnetism, and extension to higher-dimensional space-time. By considering a natural geometric definition of a matter fluid and abandoning the usual requirement of a Ricci-flat five dimension…

We prove a positive mass theorem for spaces which asymptotically approach a flat Euclidean space times a Calabi-Yau manifold (or any special honolomy manifold except the quaternionic Kähler). This is motivated by the very recent work of Hertog-Horowitz-Maeda.

The study connects knot complements to 3d theories via half-index calculations.

Minkowski space is a physically important space-time for which the finding an adequate holographic description is an urgent problem. In this paper we develop further the proposal made in hep-th/0303006 for the description as a duality between Minkowski space-time and a Conformal Field Theory defined on the boundary of …

Corrected proof for 3D harmonic manifolds with minimal horospheres.

The paper classifies 3D complete gradient Yamabe solitons.

We show how the theory of $\mathbb{Z}_2^n$ -manifolds - which are a non-trivial generalisation of supermanifolds - may be useful in a geometrical approach to mixed symmetry tensors such as the dual graviton. The geometric aspects of such tensor fields on both flat and curved space-times are discussed.

Proof that stable minimal surfaces in 3D are flat.

Compact 3D Cotton-parallel manifolds are always conformally flat.

In this work we simulate null geodesics for the Bonnor massive dipole metric by implementing a symbolic-numerical algorithm in Sage and Python. This program is also capable of visualizing in 3D, in principle, the geodesics for any given metric. Geodesics are launched from a common point, collectively forming a cone of …

Study biharmonic conformal immersions into a 3D flat space, finding new examples and classifications.

Study shows smooth convergence of round surfaces in flat space-time models.

The paper classifies path structures on 3D Lie groups and reduces non-flat ones to Z/2Z-structures.

Tensor neural network improves human pose classification from 3D skeleton data.

Proves Lorentzian manifold properties for analytic 3D spaces.

No Hantzsche-Wendt manifolds over 3D admit spin^c structures.