Last update: 08.2023

This document contains a list of possible thesis projects in the fields of gravitational waves, numerical relativity and computational physics for the MSc in theoretical physics.

Students will be involved in the activities of the group, that include seminars, journal club, and outreach.

For more information you can contact Sebastiano Bernuzzi via email or telephone [+49 (0)3641 9 47111].

**Projects list**

- Gravitational waves from coalescing black holes
- Black holes ringdown
- Relativistic stars
- Numerical solutions of relativistic hydrodynamics

Gravitational waves and black holes are one of the most fascinating predictions of general relativity. In 2015, the LIGO experiment has detected gravitational waves emitted by the collision of two stellar-mass black holes.

The goal of this project is to work out at leading post-Newtonian order the relevant formulas describing the gravitational waves emitted by coalescing compact object. These formulas will be then used to extract the characteristic (chirp) mass of the first observed event from an analysis of LIGO data.

The student will receive a basic training on the principles of general relativity and gravitational waves. The thesis work include analytical calculations and some computational aspects (basic data manipulation and plotting). Computations will be performed with `Python`

(no previous knowledge required).

Black holes respond to perturbations by resonating at characteristic complex frequencies determined by the hole's mass and spin. Similarly to the normal modes of a string, the imaginary part of these frequencies describes a proper oscillation frequency of the black hole spacetime. The black hole modes however are "quasi normal" modes, as the oscillations are damped (dissipated) by the emission of gravitational waves. The observation of the ringdown in the waves is, in turn, the signature of the black hole.

The goal of this project is to study the equation describing the perturbations of Schwarzschild (nonrotating) black holes. The equation is known as Regge-Wheeler equation and the problem is a boundary initial value problem similar to the classical wave equation or the Schroedinger equation in quantum mechanics in 1D.

The student will receive a basic training on the principles of general relativity and black hole solution. The thesis work include analytical calculations and/or some computational aspects. Computations will be performed with `Python`

(no previous knowledge required).

Neutron stars are compact stars with masses of the order of the solar mass and radii of tens kilometers. They are born as a result of gravitational collapse of massive stars. Their structure is determined by quantum mechanics (degenerate matter) and general relativity (strong gravity). Neutron stars can be observed as pulsars, due to the emission of radio and other electromagnetic pulses generated by large magnetic fields around them. They are also sources of gravitational waves.

The goal of this project is to study equilibrium configurations and the mass-radius diagram of neutron stars. The ordinary differential equations governing static hydrodynamics equilibria are called the Tolman-Oppenheimer-Volkoff. In order to obtain a solution, these equations must be supplemented by an equation of state for the dense matter. General features of equilibria sequences include a maximum mass and radially stable and unstable configurations.

The student will receive a basic training on the principles of general relativity and black hole solution. The thesis work include analytical calculations and/or some computational aspects. Computations will be performed with `Python`

(no previous knowledge required).

Relativistic hydrodynamics equations describe many phenomena from astrophysical plasmas to collisions of heavy ions. They are nonlinear equations and their solutions require efficient numerical methods able to handle features like shocks waves, jets and turbulence.

The goal of this project is to implement a solver for relativistic hydrodynamics equations and apply it to standard test problems. Modern numerical methods for such equations are finite-volume shock-capturing algorithms and discontinuous Galerking algorithms.

The student will receive a basic training on the relativistic Euler equations and the numerical methods employed for their solutions. The thesis work include computational aspects and the development of a hydrodynamics solver.