Spinning gravimagnetic particles in Schwarzschild-like black holes

Abstract

We study the motion of a spinning particle with gravimagnetic moment in Schwarzschild-like spacetimes with a metric $d{s}^2=-f(r)d{t}^2+f^{-1}(r)d{r}^2+r^{2}d{\Omega }^2$, specifically we deal with Schwarzschild, Reissner-Nordstrom black holes as well as Ayon-Beato-Garcia and Bardeen regular spacetimes. First, we introduce the Hamiltonian system of equations which describes such kind of particles. In the case of null gravimagnetic moment, the equations are equivalent to the Mathisson-Papapetrou-Tulczyjew-Dixon (MPTD) equations. Working in the equatorial plane, using the constants of motion generated by the symmetries of the considered spacetimes and the Spin Supplementary Conditions (SSC), we change the problem of solving six differential equations for the momenta and the non-vanishing spin-tensor components to solving six algebraic equations. We show that the equation for the $P_0(r)$ component totally decouples, $P_0(r)$ can be found by solving a 6th order polynomial. We analyze the conditions for existence of solutions of this algebraic system for the relevant cases of gravimagnetic moment equal to unit, which corresponds to a gravimagnetic particle, and zero which corresponds to the MTPD system. A numerical algorithm to generate solutions of the momenta $P_{\mu }$ is provided and some solutions are generated.

arXiv comment19 pages, 14 figure

References in corpus (27)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
• Regular Black Hole in General Relativity Coupled to Nonlinear Electrodynamics
• The Bardeen Model as a Nonlinear Magnetic Monopole
• Dynamical Boson Stars
• Post-Newtonian corrections to the motion of spinning bodies in NRGR
• Chaos in Schwarzschild Spacetime : The Motion of a Spinning Particle
• Hamiltonian of a spinning test-particle in curved spacetime
• Equations of Motion of Spinning Relativistic Particle in External Fields
• Dynamical evolution of fermion-boson stars
• Growth of resonances and chaos for a spinning test particle in the Schwarzschild background
• Recent progress on the description of relativistic spin: vector model of spinning particle and rotating body with gravimagnetic moment in General Relativity
• Can gravitation accelerate neutrinos?
• Dynamical formation and stability of fermion-boson stars
• Lagrangian formulation for Mathisson-Papapetrou-Tulczyjew-Dixon (MPTD) equations
• Dynamics of test bodies with spin in de Sitter spacetime
• Frame-dragging effect in the field of non rotating body due to unit gravimagnetic moment
• Covariant hamiltonian spin dynamics in curved space-time
• Mathisson-Papapetrou-Tulczyjew-Dixon (MPTD) equations in ultra-relativistic regime and gravimagnetic moment
• Frenkel electron and a spinning body in a curved background
• Fermion-boson stars with a quartic self-interaction in the boson sector
• Ultra-relativistic spinning particle and a rotating body in external fields
• Relativistic effects due to gravimagnetic moment of a rotating body
• Gravitational Interaction of Spinning Bodies, Center-of-Mass Coordinate and Radiation of Compact Binary Systems
• Spinning bodies in curved space-time
• World-line geometry probed by fast spinning particle
• Geometric Constructions Underlying Relativistic Description of Spin on the Base of Non-Grassmann Vector-Like Variable

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