Physics
Scientific paper
Apr 2010
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2010acasn..51..219h&link_type=abstract
Acta Astronomica Sinica, vol. 51, no.2, p. 219-220
Physics
Relativistic Processes, Gravitational Waves, Methods: Numerical
Scientific paper
It is well known that spinning compact binaries are one of the most important research objects in the universe. Especially, EMRIs (extreme mass ratio inspirals) involving stellar compact objects which orbit massive black holes, are considered to be primary sources of gravitational radiation (GW) which could be detected by the space-based interferometer LISA. GW signals from EMRIs can be used to test general relativity, measure the masses and spins of central black holes and study essential physics near horizons. Compared with the situation without spin, the complexity of extreme objects, most of which rotate very fast, is much higher. So the dynamics of EMRI systems are numerically and analytically studied. We focus on how the spin effects on the dynamics of these systems and the produced GW radiations. Firstly, an ideal model of spinning test particles around Kerr black hole is considered. For equatorial orbits, we present the correct expression of effective potential and analyze the stability of circular orbits. Especially, the gravitational binding energy and frame-dragging effect of extreme Kerr black hole are much bigger than those without spin. For general orbits, spin can monotonically enlarge orbital inclination and destroy the symmetry of orbits about equatorial plane. It is the most important that extreme spin can produce orbital chaos. By carefully investigating the relations between chaos and orbital parameters, we point out that chaos usually appears for orbits with small pericenter, big eccentricity and orbital inclination. It is emphasized that Poincaré section method is invalid to detect the chaos of spinning particles, and the way of systems toward chaos is the period-doubling bifurcation. Furthermore, we study how spins effect on GW radiations from spinning test particles orbiting Kerr black holes. It is found that spins can increase orbit eccentricity and then make h+ component be detected more easily. But for h× component, because spins change orbital inclination in a complicated way, it is more difficult to build GW signal templates. Secondly, based on the scalar gravity theory, a numerical relativistic model of EMRIs is constructed to consider the self-gravity and radiation reaction of low-mass objects. Finally, we develop a new method with multiple steps for Hamilton systems to meet the needs of numerical researches. This method can effectively maintain each conserved quantity of the separable Hamilton system. In addition, for constrained system with a few first integrals, we present a new numerical stabilization method named as adjustment-stabilization method, which can maintain all known conserved quantities in a given dynamical system and greatly improve the numerical accuracy. Our new method is the most complete stabilization method up to now.
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