Tootfinder

Newman-Penrose-like exact and approximate conservation laws: a covariant and conformal formulation
Berend Schneider
https://arxiv.org/abs/2507.02237 https:…

Newman-Penrose-like exact and approximate conservation laws: a covariant and conformal formulation
Using a conformal extension of the Geroch-Held-Penrose (GHP) formalism I derive a manifestly covariant and conformal expression of Newman-Penrose (NP) constants, which are a set of conserved quantities associated to solutions to the wave equation on light cones in Minkowski space. The resulting expression generalizes to massless fields of arbitrary spin -- including the electromagnetic field, Weyl fermions, and the linearized Weyl tensor -- on conformally flat space-times. In some non-conformal…

Obstructions to Reality: Torsors & Visual Paradox
Robert Ghrist, Zoe Cooperband
https://arxiv.org/abs/2507.01226 https://arxiv.or…

Obstructions to Reality: Torsors & Visual Paradox
Visual paradoxes like the Penrose staircase present a fundamental tension: locally coherent geometric relationships that cannot be realized globally. Inspired by Penrose's observations connecting such paradoxes to cohomology, we develop a mathematical framework that precisely characterizes this phenomenon through network torsors and sheaf cohomology. Network torsors capture the essential nature of visual paradoxes by formalizing relative geometric attributes (height changes, orientation flips) …

Nonlinearities in Kerr Black Hole Ringdown from the Penrose Limit
D. Perrone, A. Kehagias, A. Riotto
https://arxiv.org/abs/2507.01919 https://

Nonlinearities in Kerr Black Hole Ringdown from the Penrose Limit
We provide a fully analytical approach to calculate the nonlinearities of the gravitational waves in the ringdown of a Kerr black hole in the eikonal limit. The corresponding quasi-normal modes are associated to the orbits of a closed circular null geodesic and the problem can be analyzed by taking the Penrose limit around it. We calculate analytically the amplitude and the phase of the quadratic quasi-normal modes as well as its dependence on the black hole spin.

Axial quasi-normal modes of slowly rotating black holes in dynamical Chern-Simons gravity to second-order in spin and coupling
Tharaka Alapati (IIT Bombay), S. Shankaranarayanan (IIT Bombay)
https://arxiv.org/abs/2506.03600

Axial quasi-normal modes of slowly rotating black holes in dynamical Chern-Simons gravity to second-order in spin and coupling
We compute the quasi-normal mode (QNM) frequencies of slowly rotating black holes in dynamical Chern-Simons (dCS) gravity, including corrections up to second order in the black hole's dimensionless spin parameter ($χ$) and second order in the dCS coupling parameter ($α$). Due to the complexities of constructing a Newman-Penrose tetrad at this order, we employ a metric perturbation approach. We derive a system of coupled ordinary differential equations for the primary axial $l$-mode and the po…

Ordine privo di periodicit\`a: il fascino matematico delle tassellazioni
Francesco D'Andrea
https://arxiv.org/abs/2505.21379 https://

Ordine privo di periodicità: il fascino matematico delle tassellazioni
This is a review (in Italian) on aperiodic tilings of the plane intended for a general audience. First, we recall some basic results about lattices and periodic tilings. Then, we move on to one-dimensional (domino) tilings and Wang tilings. We present a beautiful proof of the existence of an aperiodic set of Wang prototiles due to J. Kari. Next, we discuss Penrose tilings and their properties. Finally, we briefly present the recent discovery by D. Smith and his collaborators of an aperiodic mon…

Eigenvalue spectrum support of paired random matrices with pseudo-inverse
Uri Cohen
https://arxiv.org/abs/2506.21244 https://arxiv.or…

Eigenvalue spectrum support of paired random matrices with pseudo-inverse
The Moore-Penrose pseudo-inverse $X^\dagger$, defined for rectangular matrices, naturally emerges in many areas of mathematics and science. For a pair of rectangular matrices $X, Y$ where the corresponding entries are jointly Gaussian and i.i.d., we analyse the support of the eigenvalue spectrum of $XY^\dagger$.

from my link log —
That fractal that's been up on my wall for 12 years.
https://chriskw.xyz/2025/05/21/Fractal/
saved 2025-05-23 htt…

Rigidity of pseudofunction algebras of ample groupoids
Eusebio Gardella, Mathias Palmstr{\o}m, Hannes Thiel
https://arxiv.org/abs/2506.09563 https://

Rigidity of pseudofunction algebras of ample groupoids
We show that a Hausdorff, ample groupoid $\mathcal{G}$ can be completely recovered from the $I$-norm completion of $C_c(\mathcal{G})$. More generally, we show that this is also the case for the algebra of symmetrized $p$-pseudofunctions, as well as for the reduced groupoid $L^p$-operator algebra, for $p\neq 2$. Our proofs are based on a new construction of an inverse semigroup built from Moore-Penrose invertible partial isometries in an $L^p$-operator algebra. Along the way, we verify a conje…

Resolving space-time singularities in spherically symmetric black holes: geodesic completeness, curvature scalars, and tidal forces
Haroldo C. D. Lima Junior, Renan B. Magalh\~aes, Gonzalo J. Olmo, Diego Rubiera-Garcia
https://arxiv.org/abs/2506.17918

Resolving space-time singularities in spherically symmetric black holes: geodesic completeness, curvature scalars, and tidal forces
The existence of black holes in the Universe is nowadays established on the grounds of a blench of astrophysical observations, most notably those of gravitational waves from binary mergers and the imaging of supermassive objects at the heart of M87 and Milky Way galaxies. However, this success of Einstein's General Relativity~(GR) to connect theory of black holes with observations is also the source of its doom, since Penrose's theorem proves that, under physically sensible conditions, the deve…

Regular Power-Maxwell Black Holes
Yi-bo Liang, Hong-Rong Li
https://arxiv.org/abs/2506.13676 https://arxiv.org/pdf/2506.13676

Regular Power-Maxwell Black Holes
We present a new class of regular, spherically symmetric spacetimes in nonlinear electrodynamics that are asymptotically dynamical but not de Sitter, exhibiting power-law Maxwell behavior at infinity. Starting from magnetic solutions, we demonstrate that the weak energy condition is satisfied, while the dominant energy condition is also fulfilled. These configurations are extended to include regular black holes, with their existence conditions and global structures analyzed via novel Penrose di…

Analytical solutions of CPT-odd Maxwell equations in Schwarzschild spacetime
Hao Wang, Zhi Xiao, Bing Sun
https://arxiv.org/abs/2506.10409 https://

Analytical solutions of CPT-odd Maxwell equations in Schwarzschild spacetime
In this work, we present the CPT-violating (CPTV) Maxwell equations in curved spacetime using the Newman-Penrose (NP) formalism. We obtain a semi-analytical solution to the Maxwell equations in Schwarzschild spacetime under the assumption that the CPT-odd $\left(k_{AF}\right)^μ$ term exhibits spherical symmetry in the Schwarzschild background. Retaining only terms up to linear order in the $\left(k_{AF}\right)^μ$ coefficient, we obtain perturbative solutions by treating the solutions of the L…