Ongoing Projects
Ongoing Projects
Fluid Solutions in General Relativity
(Undergraduate Research)
In GR, spherically symmetric fluid solutions of Einstein field equations are used to build stellar models. My students and I are building such models with a cosmological constant term in the field equations. This will enable us to study the effect of accelerated expansion of the Universe on these stellar models. This is also interesting from a geometric/mathematical perspective. My students and I recently presented this work at the APS-MAS Fall 2023 meeting (see pictures in Gallery).
This work is being supported by an internal grant at St. Mary's College of Maryland.
Current Research Group
Alex Stornelli
Project: Polytropic stars in general relativity.
James Ripple
Project: Generalisation of Tolman VII solution.
Maxwell Esztergomi
Project: Charged Tolman IV space-time with a cosmological constant.
The Geometric Trinity of Gravity
The theory of general relativity (GR) is usually formulated in the framework of (pseudo-)Riemannian geometry. However, there exist equivalent formulations of GR where gravity can be described using quantities such as torsion and non-metricity. The underlying geometry of these formalisms is non-Riemannian. These three equivalent formulations of GR are referred to as the geometric trinity of gravity.
A few issues within such non-Riemannian theories of gravity that I have been working on are:
Generalised form of the kinematic equations Raychaudhuri equation.
Lagrangian formulation of Raychaudhuri equation and other kinematic equations.
Establishing the so-called gravito-electromagnetic analogy in these theories.
The Averaging Problem in Cosmology
The averaging problem in cosmology is a classic problem that stems from the difficulties encountered in defining a rigorous integration operation in non-Euclidean geometries. In the context of general relativity, the problem worsens due to the non-linear nature of the Einstein field equations (EFE). It has been posited that to take into account the effect of averaging, some extra terms should to be added to the EFE. These additional terms (or their effect) are sometimes called back-reaction.
In the past, with Mustapha Ishak, I have worked on calculating the effects of back-reaction on linear perturbations in cosmology. I have also analysed the modifications to observables in cosmology such as distances and growth of structure. Both of these were done in the covariant averaging framework of macroscopic gravity. Although I am not currently working on the averaging problem, I am still interested in it. Any new ideas or collaboration requests are welcome.
To enquire about vacancies in the group or a prospect of collaboration, contact me at anagashe@smcm.edu.