Keplerian black holes and gravitating goldstones

In classical Newtonian physics, the two-body problem, like the Earth orbiting the Sun, results in simple elliptical orbits. This is because of the large symmetry in the mathematical description of the system. However, when we consider relativistic effects (as described by Einstein’s theory of relativity), these orbits tend to precess, or shift, because one of the symmetries is lost.

In his thesis, Dijs de Neeling explores whether it’s possible to create relativistic systems that still follow classical dynamics, maintaining the symmetrical, elliptical orbits. He demonstrates that this is achieved for a specific class of Hamiltonians (mathematical functions used to describe the total energy of a system). Some physical examples of the Hamiltonians are given and they are shown to be interconnected through a concept known as the classical double copy, a relation between classical solutions of theories of very different forces.

De Neeling found that these relativistic Hamiltonians, which resemble the classical Kepler problem (describing planetary motion), can be related to the original problem through adjustments of the time parameter. To a certain order of approximation, these Hamiltonians are the also shown to be the only ones that preserve the Keplerian symmetry. Additionally, he extended this relationship between Newtonian and Einsteinian physics to more complex systems with multiple centers of attraction. 

De Neeling also explored another version of the double copy, showing how certain scalar theories are linked through a duality between flavour and kinematics. One of these theories involves Goldstone bosons, massless particles that arise in the context of spontaneous symmetry breaking, interacting through gravity.

Dissertation: https://hdl.handle.net/11370/26bfc392-c16f-4d2d-9a2d-1c7ea2592f50