A recent study calculates, using a controlled slow-rotation expansion over the Hartle-Thorne metric, the heating energy and spin-up of a compact star accreting matter from a thin disc, showing that first-order rotational corrections can be relevant for millisecond pulsars. This Bachelor's Thesis will not reproduce that full calculation, which requires higher-order treatment and magnetic considerations beyond the scope of a Bachelor's Thesis, but rather its simplest limit and initial steps.
What you gain
The student learns to work with circular geodesics in Schwarzschild, reproduces the classical Novikov-Thorne accretion efficiency result (energy at the ISCO), and then adds the Lense-Thirring metric (slow rotation to first order) to calculate the frame-dragging correction to the specific energy and angular momentum of circular orbits. They compare their zero-order and first-order expressions with published results in the corresponding limiting case, using symbolic computation in Python (sympy).
What you need
General Relativity (optional, essential), Classical Mechanics, Mathematical Methods (tensor calculus), Python with sympy for symbolic computation.
Work plan
- Review of circular geodesics in Schwarzschild and derivation of specific energy and angular momentum40 h
- Reproduction of the Novikov-Thorne thin disc model and accretion efficiency at the ISCO45 h
- Introduction to the Hartle-Thorne metric and first-order expansion in rotation (Lense-Thirring)55 h
- Calculation of the frame-dragging correction to energy and spin-up, numerical comparison with the non-rotating case45 h
- Writing the thesis and preparing the defence45 h
Do not take it if
If the General Relativity elective has not been taken or the supervisor cannot oversee tensor calculus in detail, the Hartle-Thorne formalism will be unmanageable in the available time; in that case, it is advisable to limit the scope to the Schwarzschild case only (difficulty 1-2) or discard the topic.