Related papers: Generating spiky solutions of Einstein field equat…
The classical approach to spacetime singularities leads to a simplified dynamics in which spatial derivatives become unimportant compared to time derivatives, and thus each spatial point essentially becomes uncoupled from its neighbors.…
There are a number of publications on relativistic objects dealing either with black holes or naked singularities in the center. Here we show that there exist static spherically symmetric solutions of Einstein equations with a strongly…
We demonstrate a novel algorithm for generating stationary stochastic signals with a specified power spectral density (or equivalently, via the Wiener-Khinchin relation, a specified autocorrelation function) while satisfying constraints on…
Gravitational shockwaves are geometries where components of the transverse curvature have abrupt behaviour across null hypersurfaces, which are fronts of the waves. We develop a general approach to describe classical field theories on such…
Static spherically symmetric solutions to the Einstein-Dirac system were constructed numerically for the first time in 1999 by Finster, Smoller and Yau \cite{FSY1} in the case of two fermions. In 2020 this result was generalized by Leith,…
We study the Stokes phenomenon for the solutions of general homogeneous linear moment partial differential equations with constant coefficients in two complex variables under condition that the Cauchy data are holomorphic on the complex…
A quantum system subjected to a strong continuous monitoring undergoes quantum jumps. This very well known fact hides a neglected subtlety: sharp scale-invariant fluctuations invariably decorate the jump process even in the limit where the…
Finite difference method and pseudo-spectral method have been widely used in the numerical relativity to solve the Einstein equations. As the third major category method to solve partial differential equations, finite element method is much…
Motivated by applications in economics and finance, in particular to the modeling of limit order books, we study a class of stochastic second-order PDEs with non-linear Stefan-type boundary interaction. To solve the equation we transform…
Waves scattering from unbounded structures are always complicated problems for numerical simulations. For the case that the non-periodic incident field scattered by (locally perturbed) periodic surfaces, with the help of the Bloch…
We propose a model of an adaptive network of spiking neurons that gives rise to a hypernetwork of its dynamic states at the upper level of description. Left to itself, the network exhibits a sequence of transient clustering which relates to…
We construct rotating black holes in Einstein-scalar-Gauss-Bonnet theory with a quadratic coupling function. We map the domain of existence of the rotating fundamental solutions, we construct radially excited rotating black holes (including…
Vector-tensor theories beyond General Relativity have widely been studied in the context of ultraviolet completion of gravity, endowing a mass to the graviton and explaining dark energy phenomena. We here construct rotating black hole…
A methodology for solving two-point boundary value problems in phase space for Hamiltonian systems is presented. Using Hamilton-Jacobi theory in conjunction with the canonical transformation induced by the phase flow, we show that the…
We use a metric of the type Friedmann-Robertson-Walker to obtain new exact solutions of Einstein equations for a scalar and massive field. The solutions have a permanent or transitory inflationary behavior.
Spiking networks that perform probabilistic inference have been proposed both as models of cortical computation and as candidates for solving problems in machine learning. However, the evidence for spike-based computation being in any way…
We investigate properties of self-gravitating isorotating Skyrmions in the generalized Einstein-Skyrme model with higher-derivative terms in the matter field sector. These stationary solutions are axially symmetric, regular and…
Novel static black hole solutions with electric and magnetic charges are derived for the class of modified gravities: $f({\cal R})={\cal R}+2\beta\sqrt{{\cal R}}$, with or without a cosmological constant. The new black holes behave…
We introduce the Stable Physics-Informed Kernel Evolution (SPIKE) method for numerical computation of inviscid hyperbolic conservation laws. SPIKE resolves a fundamental paradox: how strong-form residual minimization can capture weak…
Emerging technologies are revealing the spiking activity in ever larger neural ensembles. Frequently, this spiking is far from independent, with correlations in the spike times of different cells. Understanding how such correlations impact…