arXiv research

Identifies null hypersurfaces with constant surface gravity.

We clarify the relationship between the null geodesic completeness of an Einstein Lorentz manifold and its conformal Kobayashi pseudodistance. We show that an Einstein manifold has at least one incomplete null geodesic if its pseudodistancfe is nontrivial. If its pseudodistance is nondegenerate, all of its null geodesi…

The study finds regular null hypersurfaces in a perturbed Schwarzschild black hole exterior.

Study reveals hidden null components in overparametrized neural networks.

The study examines null curves in specific geometric manifolds and their properties.

Extends Penrose's method to null shells with pressure and energy flux.

In [21], the authors initiated the study of quasi generalized CR (QGCR)-null submanifolds. In this paper, attention is drawn to some distributions on ascreen QGCR-null submanifolds in an indefinite nearly cosymplectic manifold. We characterize totally umbilical and irrotational ascreen QGCR-null submanifolds. We finall…

Study submanifolds in null hypersurfaces of generalized Robertson-Walker spacetimes.

The paper studies canal hypersurfaces in Lorentz-Minkowski 4-space.

The null Penrose inequality, i.e. the Penrose inequality in terms of the Bondi energy, is studied by introducing a funtional on surfaces and studying its properties along a null hypersurface $Ω$ extending to past null infinity. We prove a general Penrose-type inequality which involves the limit at infinity of the Hawki…

Study of optical geometries with intrinsic torsion in general relativity.

In this paper, we investigate the null (light-like) sectional curvatures of Lorentzian warped product manifolds. We derive the formulas for the null sectional curvature of many well-known warped product space-time models such as multiply generalized Robertson-Walker space-times, generalized Kasner spacetimes and standa…

The null energy condition is characterized via convexity of entropy in Lorentzian manifolds.

Study left-invariant pseudo-Riemannian metrics on Lie groups focusing on null cone Lie algebras.

Synthetic framework for null hypersurfaces in non-smooth spacetimes.

Unique solutions found for wave-like decaying null infinity equations.

We define an explicit quasi-local mass functional which is non-decreasing along all foliations (satisfying a convexity assumption) of null cones. We use this new functional to prove the null Penrose conjecture under fairly generic conditions.

The Hopf invariant is linked to null-homotopy properties of maps.

We give new definitions of null infinity and black hole in terms of causal boundaries, applicable to any strongly causal spacetime $(M,g)$. These are meant to extend the standard ones given in terms of conformal boundaries, and use the new definitions to prove a classic result in black hole theory for this more general…

In this study, we define a family of null curves in Minkowski 3-space and called null similar curves. We obtain some properties of these special curves. We show that two null curves are null similar curves if and only if these curves form a null Bertrand pair. Moreover, we obtain that the family of null geodesics and n…

Study extends null distance concept to Lorentzian length spaces for spacetime analysis.

Every knot can be unknotted with two generalized twists; this was first proved by Ohyama. Here we prove that any knot of genus g can be unknotted with 2g null-homologous twists and that there exist genus g knots that cannot be unknotted with fewer than 2g null-homologous twists.

We obtain necessary and sufficient conditions for the existence of "conservation laws" on null hypersurfaces for the wave equation on general four-dimensional Lorentzian manifolds. Examples of null hypersurfaces exhibiting such conservation laws include the standard null cones of Minkowski spacetime and the degenerate …

The null distance for Lorentzian manifolds was recently introduced by Sormani and Vega. Under mild assumptions on the time function of the spacetime, the null distance gives rise to an intrinsic, conformally invariant metric that induces the manifold topology. We show when warped products of low regularity and globally…

Solves characteristic problem in general relativity for null data.

We show that there is a correspondence between totally umbilic null hypersurfaces in generalized Robertson-Walker spaces and twisted decompositions of the fibre. This allows us to prove that nullcones are the unique totally umbilic null hypersurfaces in the closed Friedmann Cosmological model. We also apply this kind o…

New definitions of conserved quantities at null infinity resolve ambiguities in general relativity.

Study optimal transport on null hypersurfaces and null energy condition.

Study transverse metric expansion on null hypersurfaces, proving uniqueness for Killing horizons.

We study the principal configurations around an isolated $η$-umbilical point on a generic spacelike surface $S$ immersed in a null hypersurface $M$ of Minkowski space $\mathbb{R}_1^4$ relative to a well-defined null vector field $η$ orthogonal to the surface $S$. In the particular case of $M$ being a null rotation hype…

In this paper, we define the notion of eikonal helix and eikonal slant helix for null curves in the 4-dimensional Lorentzian manifold M 1 4 and give a characterization for the null curve to be the null eikonal helix. Moreover, we indicate an important relation between the null eikonal helix and null eikonal slant helix…

Study on null helices in semi-Riemannian manifolds with special submanifolds.

Null Kähler metrics are characterized by Painlevé I or II ODEs.

Null Lagrangian-preserving surgeries are a generalization of the Garoufalidis and Rozansky null-moves, that these authors introduced to study the Kricker lift of the Kontsevich integral, in the setting of pairs (M,K) composed of a rational homology sphere M and a null-homologous knot K in M. They are defined as replace…

Study examines null vector fields on Lorentzian manifolds.

A maximum principle for C^0 null hypersurfaces is obtained and used to derive a splitting theorem for spacetimes which contain null lines. As a consequence of this null splitting theorem, it is proved that an asymptotically simple vacuum (Ricci flat) spacetime which contains a null line is isometric to Minkowski space.

Minimal surfaces in Heisenberg group have null curves and lines.

Proves inextendibility of weak null singularities from curvature blow-up.

The purpose of the present work is to study (marginally) trapped submanifolds lying in a null hypersurface. Let $(M,g,N)\to\Bm(c)$ be a null hypersurface of a space-time with constant sectional curvature $c$, endowed with a Screen Integrable and Conformal rigging $N$. The (Marginally) Trapped Submanifolds we are intere…

Study on null-projectability of Levi-Civita connections in neutral metrics.

Study on unique spacetime extensions in 1+1 dimensions with applications to weak null singularities.

Study on null hypersurfaces with constant angle in Lorentzian manifolds.

In this paper, we study inextensible flows of partially null and pseudo null curves in E_1^4. We give neccessary and sufficent conditions for inextensible flows of partially null and pseudo null curves in E_1^4

Bayesian deep learning avoids underfitting by projecting onto null space of generalized Gauss-Newton matrix.

New method to untangle knots using null-homologous twists.

First, we prove that indefinite Sasakian manifolds do not admit any screen conformal $r$-null submanifolds, tangent to the structure vector field. We, therefore, define a special class of null submanifolds, called; {\it contact screen conformal} $r$-null submanifold of indefinite Sasakian manifolds. Several characteriz…

The classical Minkowski formula is extended to spacelike codimension-two submanifolds in spacetimes which admit "hidden symmetry" from conformal Killing-Yano two-forms. As an application, we obtain an Alexandrov type theorem for spacelike codimension-two submanifolds in a static spherically symmetric spacetime: a codim…

Paper defines and proves geometric uniqueness of Einstein field equations.