My Master research has two major foci:
- Oscillations (pulsations) of compact objects, e.g. neutron stars or quark stars, which can generate gravitational waves (analogous to playing drums: the membrane oscillates and generates sound waves);
- Universalities between the fundamental oscillations, moment of inertia, quadrupole moment, and tidal Love number, e.g. the I-Love-Q relation, which are useful for disentangling the effects of the equations of state and the alternative theories of gravity.
For the first part, we have derived an accurate Cowling approximation (that ignores perturbations in spacetime) for fundamental modes in fully relativistic equations. We have applied the Chandrasekhar’s variational formula for the fundamental modes in incompressible stars to other kinds of compact stars, and found a very good agreement with numerical calculations.
For the second part, we have found that the incompressible limit is the underlying reason for those universalities and have derived their analytic approximations through the post Newtonian and post Minkowskian expansions. We also found a universal relation (i.e. independent of the equation of state) for the frequency of fundamental mode, tidal love number and moment of inertia.
Our list of publications on these topics.