### Complex dynamics of fast spinning neutron stars around a massive black hole

Prof. Kinwah Wu

Strongly bound gravitational systems often show interesting dynamical phenomena. Spinning finite-size objects in gravity would not follow geodesics in the space-time manifold. A fast spinning neutron stars or a neutron-star system orbiting around a black hole would exhibit complex spin and orbital behaviours due to various relativistic coupling. This project investigates two special classes of black hole - neutron star systems:

(1) a fast spinning NS orbiting around a BH, and

(2) a double neutron-star system 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 neutron star's spin. In (2) orbit-orbit coupling induces gravito-magnetism, which manifests in the complex orbital and spin motion of the double neutron-star system. Radio pulsar timing and gravitational wave observations will be able to study the dynamical properties of these systems. Black hole - neutron star systems are useful in the study of fundamental physics and in astrophysics. They can be used to map the space-time structure around black holes and to determine the masses and spins of the massive nuclear black holes in galaxies. This is a theoretical project. It involves phenomenological modelling, algebraic computation and numerical calculations.

### General Relativistic Radiative Transfer in Dynamical Space Time

Prof. Kinwah Wu

The current formulations for general relativistic radiative transfer are derived in a stationary space-time framework. In many astrophysical systems the gravitational fields, and hence the associated space-time, are not stationary. An example as such in the stellar scales is the coalescence of two very compact objects, such as two neutron stars, two black holes or a neutron star and a black hole. These systems are expected to be strong gravitational radiation sources.

The currently available general relativistic radiative transfer formulations are insufficient to calculate the electromagnetic radiations from these systems, which are crucial to provide the additional information in the gravitational radiation source identification and clarification. A more advance covariant radiative transfer formulation is therefore needed.

Note that ovariant radiative transport in dynamical space-time is not the same as time-dependent radiative transfer in general relativistic settings. In the latter, the space-time metric and the gravitational field are stationary. The radiative transfer equation, derived subject to the conservation of phase space density and photon number, incorporates the metric as a ``functional parameter''. The emitters, the observer and the media in between may have time-dependent properties, but at all instances they follow their world lines in a single stationary ``universal'' space-time manifold. The radiation (bundle of photons) is transported on the null geodesics in this space-time manifold, interacting with the media as it propagates. In a dynamical space-time, geodesic itself varies when the underlying space-time modulates. Determining the geodesics for photons and particles between a specific pair of emitter and observer and carrying out the radiative transfer calculation is therefore more technical challenging.

This project aims to develop a sensible and practical formulation for radiative transfer in non-stationary space-time. The student will carry out a global analyses of the structures of space-time for a specific evolving astrophysics system and determine the corresponding geodesics. The radiative transport equations are constructed along the derived geodesic, satisfying the invariance of particle number and the conservation of phase space density of the particles. Solution scheme is sought for the transfer equations in the astrophysical contexts.