Speaker
Description
The theory of General Relativity (GR) stands on two of Einstein's most celebrated ideas: the Equivalence Principle and the statement that "gravity is geometry". The former implements Special Relativity (SR) and forces the geometry of spacetime to be Lorentzian, thus turning the previous statement into "gravity is Lorentzian geometry". It may not be obvious that these two ideas, yet closely related, are completely independent. Indeed, if willing to give up SR, one could in principle require that spacetime exhibit a local symmetry other than Lorentzian, and still work out a geometric theory of gravity. For instance, imposing local Galilean symmetry leads to Newton-Cartan geometry, pioneered by É. Cartan
in 1923. The result is a non-relativistic geometric theory of gravity.
In this work we study the recently discovered covariant formulation of non-relativistic gravity (NRG), obtained from an appropriate large speed of light expansion of GR, with the ultimate goal of obtaining its linearised spectrum. This involves, as a preliminary step, rewriting GR in terms of a timelike vielbein, a spatial metric and a torsionful connection, which in turn allows to write the Einstein-Hilbert Lagrangian in a so-called pre-non-relativistic form. This is proven to be the most suitable form in order to perform the aforementioned expansion. In addition, we also review Newton-Cartan geometry, as the natural geometrical framework of NRG, as well as related state-of-the-art techniques such as the obtention of relevant geometric fields via gauging procedures.
Building on this knowledge, and in analogy with the obtention of gravitational waves as a solution to the linearised Einstein field equations in GR, we aim to obtain the linearised spectrum of NRG from its action and corresponding equations of motion when considering small perturbations of the geometric fields around a flat Newton-Cartan background.
| Field of study | Quantum Physics |
|---|---|
| Supervisor | Niels Obers |
