Encounter between an extended hyperelastic body and a Schwarzschild black hole with quadrupole-order effects

Abstract

We model the general relativistic interaction of a small hyperelastic sphere with a Schwarzschild black hole as it follows an initially marginally-bound orbit through a close encounter. While the interaction reveals effects that are encoded by the Mathisson-Papapetrou-Dixon (MPD) multipolar equations through quadrupole order, the calculation is made using an independent general relativistic finite element scheme that we described earlier (Phys.~Rev.~D 108(8):084020, October 2023). The finite element calculation is done in Schwarzschild coordinates, following a large and scalable number of mass elements in interaction with each other through elastic forces derived from a potential energy function and with the spacetime geometry. After the fact, we analyze the dynamics using a local Fermi coordinate system, computing (1) the deviation of the center of mass of the body relative to the initial marginally-bound orbit, (2) changes in orbital and spin angular momenta, and (3) the decrease in orbital energy and accompanying deposition of energy into internal elastic dynamics. The interaction leads to the capture of the small body into a highly eccentric orbit ($e\simeq 0.99998$ in a sample calculation).

arXiv commentv2: Added ancillary supplementary video; updated journal reference/DOI (accepted for publication in Phys. Rev. D)

References in corpus (28)

• Tidal Love numbers of neutron stars
• The motion of point particles in curved spacetime
• Self-force and radiation reaction in general relativity
• Approximate Universal Relations for Neutron Stars and Quark Stars
• Post-Newtonian corrections to the motion of spinning bodies in NRGR
• On the evolution of ultra-massive white dwarfs
• Relativistic Elasticity
• Spinning test-body orbiting around Schwarzschild black hole: circular dynamics and gravitational-wave fluxes
• Mechanics of extended masses in general relativity
• Evolution of small-mass-ratio binaries with a spinning secondary
• Center of mass, spin supplementary conditions, and the momentum of spinning particles
• Self-Force Calculations with a Spinning Secondary
• Spinning test-body orbiting around a Kerr black hole: circular dynamics and gravitational-wave fluxes
• Post-1-Newtonian equations of motion for systems of arbitrarily structured bodies
• Elastic Stars in General Relativity: II. Radial perturbations
• On Relativistic Material Reference Systems
• Relativistic effects in the tidal interaction between a white dwarf and a massive black hole in Fermi normal coordinates
• Elastic Stars in General Relativity: III. Stiff ultrarigid exact solutions
• Tidal deformations of compact stars with crystalline quark matter
• Elastic stars in general relativity: IV. Axial perturbations
• Spin and quadrupole contributions to the motion of astrophysical binaries
• Elasticity Theory in General Relativity
• Extended-body motion in black hole spacetimes: What is possible?
• Hyperbolic-like elastic scattering of spinning particles by a Schwarzschild black hole
• Covariant Equations of Motion Beyond the Spin-Dipole Particle Approximation
• Extended body dynamics in general relativity: hyperelastic models
• Extended bodies with spin induced quadrupoles on circular equatorial orbits in Kerr spacetime
• Continuous body dynamics and the Mathisson-Papapetrou-Dixon equations