arXiv research

A new method detects small holes in noisy data.

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 method detects black hole horizons using Lie algebra invariants.

Detects outliers in VAE latent space by identifying vacant holes.

Using black-hole inequalities and the increase of the horizon's areas, we show that there are arbitrarily small electro-vacuum perturbations of the standard initial data of the extreme Reissner-Nordstrom black-hole that, (by contradiction), cannot decay in time into any extreme Kerr-Newman black-hole. This proves the e…

Uniqueness theorem for extremal charged black holes in de Sitter space.

We show that a stationary solution of the Einstein-Maxwell equations which is close to a non-degenerate Reissner-Nordström-de Sitter solution is in fact equal to a slowly rotating Kerr-Newman-de Sitter solution. The proof uses the non-linear stability of the Kerr-Newman-de Sitter family of black holes for small angular…

Simpler autoencoder with regularization outperforms complex alternatives.

New black hole solutions cannot be rotated without breaking their structure.

Gradient flow in a potential energy (or Euclidean action) landscape provides a natural set of paths connecting different saddle points. We apply this method to General Relativity, where gradient flow is Ricci flow, and focus on the example of 4-dimensional Euclidean gravity with boundary S^1 x S^2, representing the can…

Luo and Tan gave a new identity for hyperbolic surfaces with/without geodesic boundary in terms of dilogarithms of the lengths of simple closed geodesics on embedded three-holed spheres or one-holed tori. However, the identity was trivial for a hyperbolic one-holed torus with geodesic boundary. In this paper we adapt t…

Using a smooth triangulation and a Riemannian metric on a compact, connected, closed manifold M of dimension n we have got that every such M can be represented as a union of a n-dimensional cell and a connected union K of some subsimplexes of the triangulation. A sufficiently small closed neighborhood of K is called a …

We bound the locations of outermost minimal surfaces in geometrostatic manifolds whose ADM mass is small relative to the separation between the black holes and prove the Intrinsic Flat Stability of the Positive Mass Theorem in this setting.

We show that the maximal future development of asymptotically flat spherically symmetric black hole initial data for a self-gravitating nonlinear scalar field, also called a Higgs field, contains a connected, achronal marginally trapped tube which is asymptotic to the event horizon of the black hole, provided the initi…

Study shows formation of Kerr black holes with complete apparent horizons and proves Penrose inequalities.

Bayesian Neural Networks show unexpected collapse of epistemic uncertainty with large models and little data.

Method detects trajectory outliers using Hodge Laplacian embeddings.

Small deformations of marginally (outer) trapped surfaces are considered by using their stability operator. In the case of spherical symmetry, one can use these deformations on any marginally trapped round sphere to prove several interesting results. The concept of 'core' of a black hole is introduced: it is a minimal …

In 1985, Barnsley and Harrington defined a ``Mandelbrot Set'' $\mathcal{M}$ for pairs of similarities --- this is the set of complex numbers $z$ with $0<|z|<1$ for which the limit set of the semigroup generated by the similarities $x \mapsto zx$ and $x \mapsto z(x-1)+1$ is connected. Equivalently, $\mathcal{M}$ is the …

This paper explores charged black holes in 3+1 dimensions, finding limitations on their existence.

We establish the full global non-linear stability of the Kerr-de Sitter family of black holes, as solutions of the initial value problem for the Einstein vacuum equations with positive cosmological constant, for small angular momenta, and without any symmetry assumptions on the initial data. We achieve this by extendin…

We give conditions on a general stress-energy tensor T_{αβ} in a spherically symmetric black hole spacetime which are sufficient to guarantee that the black hole will contain a (spherically symmetric) marginally trapped tube which is eventually achronal, connected, and asymptotic to the event horizon. Price law decay p…

New memory effect discovered in gravitational wave behavior.

Ray-Singer torsion measures light degrees of freedom in black hole entropy.

Global existence and boundedness proved for quasilinear wave equations on Kerr black holes.

New data shows multiple black holes can form from modified vacuum data.

We study the relevant structure of so(2,n) which makes the BTZ black hole possible in the anti de Sitter space. We pay a particular attention of the reductive Lie algebra structures and Iwasawa decompositions and the way these structures evolves when one increases the dimension. The singularity is defined as the closed…

TIER uses extended strain data to improve gravitational wave detection sensitivity.

We directly connect topological changes that can occur in mathematical three-space via surgery, with black hole formation, the formation of wormholes and new generalizations of these phenomena. This work widens the bridge between topology and natural sciences and creates a new platform for exploring geometrical physics…

Constructs solutions of Einstein equations for black holes gluing along timelike geodesics.

Proposes a new VAE framework for anomaly detection in time series data.

New approach simplifies proof of wave equations on black holes.

We demonstrate the existence of spherically-symmetric truly naked black holes (TNBH) for which the Kretschmann scalar is finite on the horizon but some curvature components including those responsible for tidal forces as well as the energy density $\barρ$ measured by a free-falling observer are infinite. We choose a ra…

The study examines Morse diagrams and their behavior under Murasugi sums, leading to contact structure classifications.

In this paper, we prove the linear stability to gravitational and electromagnetic perturbations of the Reissner-Nordström family of charged black holes with small charge. Solutions to the linearized Einstein-Maxwell equations around a Reissner-Nordström solution arising from regular initial data remain globally bounded…

We investigate contrasting behaviours emerging when studying foliations on non-metrisable manifolds. It is shown that Kneser's pathology of a manifold foliated by a single leaf cannot occur with foliations of dimension-one. On the other hand, there are open surfaces admitting no foliations. This is derived from a quali…

We show a non existence result for solutions of the prescribed mean curvature equation in the product manifold $\mathbb{H}^2 \times \R$, where $\mathbb{H}^2$ is the real hyperbolic plane. More precisely we prove a-priori estimates for graphs with constant mean curvature $h \in (0, 1/2]$ on circular annuli of $\mathbb{H…

The paper connects Diophantine approximation to black hole behavior, proving blow-up conditions.

The present paper shows a solution to the problem of automatic distress detection, more precisely the detection of holes in paved roads. To do so, the proposed solution uses a weightless neural network known as Wisard to decide whether an image of a road has any kind of cracks. In addition, the proposed architecture al…

This paper proves a canonical foliation on null infinity for Kerr-like black holes.

Formally constructs metrics near timelike geodesics in vacuum spacetimes.

In the last few years, machine learning techniques, in particular convolutional neural networks, have been investigated as a method to replace or complement traditional matched filtering techniques that are used to detect the gravitational-wave signature of merging black holes. However, to date, these methods have not …

Over the past three decades, black holes have played an important role in quantum gravity, mathematical physics, numerical relativity and gravitational wave phenomenology. However, conceptual settings and mathematical models used to discuss them have varied considerably from one area to another. Over the last five year…

Polyhedra can be Rupert if they can be slightly rotated to fit inside each other.

We study some aspects of spherical symmetric dyonic non-supersymmetric black holes in $4d \; N=1$ supergravity coupled to chiral and vector multiplets on Kähler-Ricci solitons. Then, we have a family of dyonic non-supersymmetric black holes deformed with respect to the flow parameter related to the Kähler-Ricci soliton…

Proof of reverse isoperimetric inequality for black holes.

We construct new classes of exact solutions in metric--affine gravity (MAG) with string corrections by the antisymmetric $H$--field. The solutions are parametrized by generic off--diagonal metrics possessing noncommutative symmetry associated to anholonomy framerelations and related nonlinear connection (N--connection)…

This paper describes the black hole threshold in a moduli space of spherically symmetric spacetimes.