### Relativistic interactions between a fast spinning neutron star and a massive black hole

Prof. Kinwah Wu

Strongly interacting gravitational systems often show interesting dynamical phenomena. Finite-size spinning objects in gravity do not follow geodesics in the space-time manifold. A fast spinning neutron stars or an orbiting neutron-star pair near a massive black hole would therefore exhibit complex spin and orbital behaviours arisen from relativistic coupling. For the bound systems, spin-curvature coupling would lead to non-planar neutron-star orbits, in addition to de-Sitter and Lense-Thirring precessions of the neutron star's spin. The spin-orbit and orbit-orbit coupling would also induce gravito-magnetism, which manifests in the complex nutation and precession of the spinning stars and/or the orbital vector. For the unbounded system, detectable memory effects could be induced by the fly-by encounters. Radio pulsar timing and gravitational wave observations are identified as the means to study the dynamics of these relativistic interacting systems. Black hole - neutron star systems are useful in the study of fundamental physics and of astrophysics. This is a theoretical project. It involves phenomenological modelling, algebraic computations 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.