相关论文: Construction of explicit symplectic integrators in…

In this paper we study the effective gravitational potential of Schwarzschild, Kerr, Reissner-Nordstr\"om and Kerr-Newman black holes with the relativistic corrections to evaluate the circular orbits and the Innermost Stable Circular Orbits…

To have the correct picture of a black hole as a whole it is of crucial importance to understand its interior. The singularities that lurk inside the horizon of the usual Kerr-Newman family of black hole solutions signal an endpoint to the…

The evolution of any factorized time-reversible symplectic integrators, when applied to the harmonic oscillator, can be exactly solved in a closed form. The resulting modified Hamiltonians demonstrate the convergence of the Lie series…

We study how inexact nonlinear solvers lead to a loss of exact symplecticity in the Symplectic Euler (SE) and Stormer-Verlet (SV) schemes when applied to general nonseparable Hamiltonian systems. These schemes are implicit and require…

As a generalization and extension of our previous paper [Escobar-Ruiz and Azuaje, J. Phys. A: Math. Theor. 57, 105202 (2024)], in this work, the notions of particular integral and particular integrability in classical mechanics are extended…

Hamiltonian systems of ordinary and partial differential equations are fundamental mathematical models spanning virtually all physical scales. A critical property for the robustness and stability of computational methods in such systems is…

The dynamics of charged particles moving around a Kerr-Newman black hole surrounded by cloud strings, quintessence and electromagnetic field is integrable due to the presence of a fourth constant of motion like the Carter constant. The…

There is a growing interest in the study of regular black holes because they eliminate the problem of the singularity that conventional black hole models present. We analyze here the motion of different types of particles (without mass,…

Spherically symmetric (1D) black-hole spacetimes are considered as a test for numerical relativity. A finite difference code, based in the hyperbolic structure of Einstein's equations with the harmonic slicing condition is presented.…

Reliable studies of the long-term dynamics of planetary systems require numerical integrators that are accurate and fast. The challenge is often formidable because the chaotic nature of many systems requires relative numerical error bounds…

The purpose of this note is to point out that a naive application of symplectic integration schemes for Hamiltonian systems with constraints such as SHAKE or RATTLE which preserve holonomic constraints encounters difficulties when applied…

Thermodynamic Riemannian geometry provides great insights into the microscopic structure of black holes (BHs). One such example is the Ruppeiner geometry which is the metric space comprising the second derivatives of entropy with respect to…

In the paper, only Static Spherically Symmetric space-times in four dimensions are considered within modified gravity models. The non-singular static metrics, including black holes not admitting a de Sitter core in the center and…

The timelike structure of the five-dimensional Schwarzschild and Reissner-Nordstr\"om Anti-de Sitter black holes is studied in detail. Different kinds of motion are allowed and studied by using an adequate effective potential. Then, by…

In this paper, we are concerned with the construction and analysis of a new class of methods obtained as double jump compositions with complex coefficients and projection on the real axis. It is shown in particular that the new integrators…

We implement several symplectic integrators, which are based on two part splitting, for studying the chaotic behavior of one- and two-dimensional disordered Klein-Gordon lattices with many degrees of freedom and investigate their numerical…

We consider the process of black hole formation in particle collisions in the exactly solvable framework of 2+1 dimensional Anti de Sitter gravity. An effective Hamiltonian describing the near horizon dynamics of a head on collision is…

This article is concerned with analytic Hamiltonian dynamical systems in infinite dimension in a neighborhood of an elliptic fixed point. Given a quadratic Hamiltonian, we consider the set of its analytic higher order perturbations. We…

An effective Hamiltonian is derived in the case of the strong Hund coupling and on-site Coulomb interaction by means of a projective perturbation approach. A physical mechanism for charge ordering in half-doped manganites…

We derive specific properties of electromagnetism when gravitational effects are not negligible and analyze their impact on new physics at the horizons of black holes. We show that a neutral configuration of charges in a region of high…