Lorentz invariance and diffeomorphism invariance in modified gravity

Research Area: Mathematical Physics

A large number of modified theories of gravity has been proposed and studied in the last decade. Amongst those are modified teleparallel gravity models. In a suitable limit these theories become equivalent to Einstein's theory of General Relativity (GR) in which case one speaks of the teleparallel equivalent of general relativity (TEGR). While GR is, by construction, invariant under local Lorentz transformations, TEGR is only quasi-invariant in the sense that its action is locally Lorentz invariant only up to a boundary term. This does not affect the field equations of the theory which are equivalent to those of GR.

This project aims to develop an in depth understanding of the role of local Lorentz transformations and local coordinate transformations in the context of modified gravity models.

In the first 6-12 months the student will study various modified theories of gravity. These will contain models which are not locally Lorentz invariant or not invariant under coordinate transformations.

In year 2 the student will derive the equations of motion for some of these theories and for models not previously studied. An important milestone will be to show that these equations reduce to previously studied models in a certain limit.

Next, these equations will be studied in the context of spherical symmetry and in cosmology. The student will work on constructing some explicit solutions to these equations and their properties will be investigated.

This investigation leads to the following interesting questions the student can study: First, the existence of regular cosmological models where the initial singularity is removed. Second, the existence of regular black hole solution.