Related papers: Interior Kerr solutions with the Newman-Janis algo…
Most linear algebra kernels in interior point methods for linear programming require the solution of linear systems of equation with the matrix $N = A^TD^{-1}A$ (or $AD^{-1}A^T$), where $A$ denotes the constraint matrix of the linear…
A distributional method to solve the Einstein's field equations for thin shells is formulated. The familiar field equations and jump conditions of Darmois-Israel formalism are derived. A carefull analysis of the Bianchi identities shows…
We formulate the Dirac equation for a massive neutral spin-half particle on a rotating black hole spacetime, and we consider its (quasi)bound states: gravitationally-trapped modes which are regular across the future event horizon. These…
In this paper we address the numerical solution of the quadratic optimal transport problem in its dynamical form, the so-called Benamou-Brenier formulation. When solved using interior point methods, the main computational bottleneck is the…
Stiff differential equations pose a major challenge for Physics-Informed Neural Networks (PINNs), often causing poor convergence. We propose a simple, hyperparameter-free method to address stiffness by normalizing loss residuals with the…
We study the Dirac equation in a spacetime that represents the nonlinear superposition of the Schwarzchild solution to an external, stationary electromagnetic Berttoti-Robinson solution. We separate the Dirac equation into radial and…
A family of spacetimes suitable for describing the interior of a non-rotational black hole is constructed. The stress-energy tensor is that of a spherically symmetric vacuum, as commonly assumed nowadays. The problem of matching the…
With the help of Newman-Janis method new spinning black hole (BH) solution for a non-local gravity model was obtained. We show how to account the quantum gravitational correction part in BH shadows modelling using spinning BH metrics with a…
The Dirac equation is solved in the $z=0$ Lifshitz black hole ($Z0$LBH) spacetime. The set of equations representing the Dirac equation in the Newman-Penrose (NP) formalism is decoupled into a radial set and an angular set. The separation…
We investigate static and rotating charged spherically symmetric solutions in the framework of $f({\cal R})$ gravity, allowing additionally the electromagnetic sector to depart from linearity. Applying a convenient, dual description for the…
In this paper, we recall some basic facts about the Kerr--Newman--(anti) de Sitter (KNdS) spacetime and review several formulations and integration methods for the geodesic equation of a test particle in such a spacetime. In particular, we…
We obtain rotating black hole solutions to the Einstein-Maxwell equations with the cosmological constant. There are eight parameters in the solutions. They are the physical mass $M$, the electric charge $Q$, the specific angular momentum…
In this paper, binary systems of unequal Kerr-Newman black holes located on the axis and apart by a massless strut are investigated. After adopting a fitting parametrization, the conditions on the axis and the one eliminating the individual…
We show how (at least in principle) one can construct electrically and magnetically charged slowly rotating black hole solutions coupled to non-linear electrodynamics (NLE). Our generalized Lense-Thirring ansatz is, apart from the static…
We obtain the Kerr-anti-de-sitter (Kerr-AdS) and Kerr-de-sitter (Kerr-dS) black hole (BH) solutions to the Einstein field equation in the perfect fluid dark matter background using the Newman-Janis method and Mathematica package. We discuss…
We investigate the properties of a closed-form analytic solution recently found by Manko et al. (2000) for the exterior spacetime of rapidly rotating neutron stars. For selected equations of state we numerically solve the full Einstein…
Starting from Newton's gravitational theory, we give a general introduction into the spherically symmetric solution of Einstein's vacuum field equation, the Schwarzschild(-Droste) solution, and into one specific stationary axially symmetric…
Rapidly rotating black hole solutions in theories beyond general relativity play a key role in experimental gravity, as they allow us to compute observables in extreme spacetimes that deviate from the predictions of general relativity. Such…
We carry out the Kerr/CFT correspondence in a four-dimensional extremal rotating regular black hole with a non-linear magnetic monopole (NLMM). One problem in this study would be whether our geometry can be a solution or not. We search for…
We address the problem of finding a local solution to a nonconvex-nonconcave minmax optimization using Newton type methods, including interior-point ones. We modify the Hessian matrix of these methods such that, at each step, the modified…