Tootfinder

This https://arxiv.org/abs/2411.18961 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

The Fefferman metric for twistor CR manifolds and conformal geodesics in dimension three
We give an explicit description of the Fefferman metric for twistor CR manifolds in terms of Riemannian structures on the base conformal $3$-manifolds. As an application, we prove that chains and null chains on twistor CR manifolds project to conformal geodesics, and that any conformal geodesic has lifts both to a chain and a null chain. By using this correspondence, we give a variational characterization of conformal geodesics in dimension three which involves the total torsion functional.

A note on Sobolev-Lorentz Capacity and Hausdorff measure
Daniel Campbell
https://arxiv.org/abs/2506.22042 https://arxiv.org/pdf/2506.…

A note on Sobolev-Lorentz Capacity and Hausdorff measure
In this paper we give an elementary proof that sets of zero $p,1$-Sobolev-Lorentz capacity $\mathcal{H}^{n-p}$-null sets independently of non-linear potential theory. We further show that there exists a set of Sobolev-Lorentz-$(p,1)$ capacity equal zero with Hausdorff dimension equal $n-p$.

Classification of $\Lambda \neq 0$-vacuum algebraically special spacetimes with conformally flat $\mathscr I$ from Weyl tensor expansion
Marc Mars, Carlos Pe\'on-Nieto
https://arxiv.org/abs/2507.21292

Classification of $Λ\neq 0$-vacuum algebraically special spacetimes with conformally flat $\mathscr I$ from Weyl tensor expansion
We introduce a general algebraic decomposition of Riemann-like and Weyl-like tensors with respect to a non-null vector $u$. We derive Gauss, Codazzi and Ricci-type identities for the Weyl tensor, that allow to relate the components of the spacetime Weyl tensor with intrinsic quantities of the hypersurfaces orthogonal to $u$. Restricting to the case of $Λ$-vacuum spacetimes (with $Λ\neq 0$ and any dimension) admiting a conformal compactification, we then study the behaviour of the Weyl tenso…

Compact Cauchy horizons admit constant surface gravity
Raymond A. Hounnonkpe, Ettore Minguzzi
https://arxiv.org/abs/2506.20004 https://

Compact Cauchy horizons admit constant surface gravity
We prove that in any spacetime dimension and under the dominant energy condition, every totally geodesic connected smooth compact null hypersurface (hence every compact Cauchy horizon) admits a smooth lightlike tangent vector field of constant surface gravity. That is, we solve the open degenerate case by showing that, if there is a complete generator, then there exists a smooth future-directed geodesic lightlike tangent field. The result can be stated as an existence result for a particular co…

Simple polynomial equations over (mxm)-matrices
Vitalij A. Chatyrko, Alexandre Karassev
https://arxiv.org/abs/2507.07085 https://arxi…

Simple polynomial equations over (mxm)-matrices
Let $m$ be any integer $\geq 3$. We consider the polynomial equation $$X^n + a_{n-1}\cdot X^{n-1} + \dots + a_1 \cdot X + a_0 \cdot I = O,$$ over $(m \times m)$-matrices $X$ with the real entries, where $I$ is the identity matrix, $O$ is the null matrix, $a_i \in \mathbb R$ for each $i$ and $n \geq 1$. We discuss its solution set $S$ supplied with the natural Euclidean topology. In particular, we describe the solution set $S$ for $m=3$ and calculate its dimension.

A viable wormhole model in a five-dimensional spacetime
Peter K. F. Kuhfittig
https://arxiv.org/abs/2506.09111 https://arxiv.org/pdf/…

A viable wormhole model in a five-dimensional spacetime
This paper generalizes two of the author's earlier wormhole solutions that are characterized by an extra spatial dimension. This paper adds the assumption that the components of the line element are functions not only of the radial coordinate $r$ but of the extra coordinate $l$ as well, resulting in a significant generalization. It is shown that the throat of the wormhole can be threaded with ordinary matter and that the unavoidable violation of the null energy condition can be attributed to th…