Tootfinder

Null geodesics, causal structure, and matter accretion in Lorentzian-Euclidean black holes
Salvatore Capozziello, Emmanuele Battista, Silvia De Bianchi
https://arxiv.org/abs/2507.08431

Null geodesics, causal structure, and matter accretion in Lorentzian-Euclidean black holes
Recently, we introduced the Lorentzian-Euclidean black hole, a static and spherically symmetric solution of vacuum Einstein equations that exhibits a change in metric signature across the event horizon. In this framework, the analysis of radial trajectories of freely falling bodies proves that the central singularity can be avoided via a mechanism we interpret as atemporality, which is responsible for the shift of the time variable from real to imaginary values. In this paper, we further expl…

Been experimenting with Shortwave, a frontend to Gmail with serious AI capabilities. So far it impresses me and is able to do the things that Gmail Gemini was failing me at. Main drawback is it's fairly expensive for a consumer product.

Last year I spent some time in the part of Texas where the floods hit on the Guadalupe River last week.
Even to my California-kid eyes, eyes that rarely see a real river, the Guadalupe, as it passed through Comfort, Texas, was more of a creek than a river.
Over the last day I've wondered "what if I had been there when the flood hit?" I am used to having fairly serious topology, so I would have had trouble there in Texas figuring out which way to go to find "hi…

Why Disaster Alerts Keep Failing
Even emergency alerts that reach people can be unclear.

KI-generierte Zusammenfassung von Google führt zu Gerüchten:
Vor knapp einer Woche war unser Leitungswasser wegen einer mikrobiologischen Verschmutzung nicht trinkbar. Die Bevölkerung wurde dazu aufgerufen, das Wasser abzukochen.
Nun gehen in lokalen Chats Screenshots rum, die behaupten, es wären PFAS gewesen. Die Google KI-Zusammenfassung spinnt das wohl aus einem Zeitungsartikel zusammen, in dem nebenbei über vergangene PFAS-Verunreinigungen berichtet wurde

Oh, why aren't you a cat person? I'll tell you: my brother was attacked, bitten and scratched on both hands this week by a feral cat in his kitchen and had to go for surgery to get the infected parts out. And he did all this to protect his own cat. I'll be watching those 'cute' cat videos with a different kind of feeling. I've heard they taste similar to rabbits.

$L^p$ Hardy inequalities with homogeneous weights
Subhajit Roy
https://arxiv.org/abs/2509.05674 https://arxiv.org/pdf/2509.05674

$L^p$ Hardy inequalities with homogeneous weights
For $p\in (1,\infty)$ and $α\in\mathbb{R}$, we consider measurable functions $g$ on $\mathbb{S}^{N-1}$ that satisfy the following weighted Hardy inequality: \begin{equation}\label{abs} \int_{\mathbb{R}^N}\frac{ g (x/|x|)}{|x|^{p+α}}|u(x)|^p dx \leq C\int_{\mathbb{R}^N}\frac{|\nabla u(x)|^p}{|x|^α} dx, \quad\forall\,u\in \mathcal{C}_c^\infty(\mathbb{R}^N), \end{equation} for some constant $C>0$. Depending on $N$, $p$, and $α$, we identify s…

Leeds former head teacher faces no charges following terrorism arrest for holding up a graphic from a satirical magazine.
https://www.bbc.co.uk/news/articles/cz9kdq84j3lo

Leeds former head teacher's terror arrest shock over protest cartoon
Jon Farley is held by police under the Terrorism Act for six hours over a placard he was carrying.

A Gentle Introduction to Algebraic Operads
Felicia Ferraioli
https://arxiv.org/abs/2508.01886 https://arxiv.org/pdf/2508.01886

A Gentle Introduction to Algebraic Operads
This text, based on the author's Bachelor's thesis, introduces the theory of Algebraic Operads, a mathematical formalism that provides a unifying framework for modern algebra. We demonstrate how the fundamental theories of associative, commutative, and Lie algebras can be fully recovered as categories of representations of three archetypal operads: $\mathsf{As}$, $\mathsf{Com}$ and $\mathsf{Lie}$ -- the so-called 'three graces' of algebra. Following a deductive and self-contained approach, th…

The Persistence of Nonlinear Gravitational Wave Memory
Robert R. Caldwell
https://arxiv.org/abs/2506.20751 https://arxiv.org/pdf/2506…

The Persistence of Nonlinear Gravitational Wave Memory
Nonlinear gravitational wave memory is a surprise of theoretical physics. Whereas it is understood that a gravitational wave induces oscillatory squeezing and stretching motion in a collection of freely-falling test masses, it is unexpected that the wave leaves a residual displacement of the test masses. This displacement is the tribute in memoriam to the passing wave. The memory originates in a nonlinear feature of gravitation. Whilst merging black holes are a significant source of gravitation…

Fractional Trudinger-Moser type inequalities with logarithmic convolution potentials
Huxiao Luo, Shiying Wang
https://arxiv.org/abs/2507.20069 https://arxi…

Fractional Trudinger-Moser type inequalities with logarithmic convolution potentials
We establish the following fractional Trudinger-Moser type inequality with logarithmic convolution potential $$ \sup_{u\in W^{\frac{1}{2},2}_0(I),\|u\|_{W_0^{\frac{1}{2},2}}\leq1}\int_{I} \int_{I} \log \frac{1}{|x-y|} G(u(x))G(u(y)) \, dx \, dy<+\infty,$$ where $G(s)\leq C\frac{e^{πs^{2}}}{(1 + |s|)^γ}~ \forall s\in\mathbb{R}$ with some constant $C>0,γ\geq1$, the domain $I\subset\mathbb{R}$ is a bounded interval. This type of inequality in the entire space $\mat…