Title:
Dynamics of fast spinning neutron stars around a massive black hole" 

Abstract: 
Strongly bound gravitational systems often show interesting dynamical phenomena. 
Fast spinning objects orbiting around a black hole exhibit complex spin precessions and orbital behaviours due to relativistic coupling. I shall show my recent work on two types of black hole (BH) - neutron star (NS) systems: 
(1) a fast spinning NS orbiting around a BH, and
(2) a double neutron star system (DNS) orbiting around a BH (which is a hierarchical 3-body system). 
In (1) spin-curvature coupling leads to non-planar NS orbits, in addition to de-Sitter and Lense-Thirring precessions of the NS's spin. In (2) orbit-orbit coupling induces gravito-magnetism, which manifests in the complex orbital and spin dynamics of the DNS. I shall discuss applying the findings of (1), together with (ms-)pulsar timing, to determine the masses of BHs and hence to establish a precise method for the BH mass measurement at the low end of M-sigma relation for spheroids in galaxies. I shall also discuss how gravito-magnetism in DNS could be detected in pulsar timing observation and gravitational wave observations, and the possible applications of the techniques developed in studying these systems in other scientific and non-scientific 
disciplines.