Topic of Research Seminar: Conformal symmetry in f(R,T) perfect fluid spacetimes, the cases of planar and cylindrical geometries.

Abstract: Einstein’s well known theory for gravitation, General Relativity (GR), has been studied extensively over the past century. Its remarkable success up to the distance scale of the solar system makes it the most reliable description of gravity found so far. However, problems seem to surface upon increasing the distance scale beyond the solar system. In particular, GR falls short of explaining the galactic rotation curves. It also fails to yield cosmological models that achieve accelerated expansion in conformance with observation. The conclusion is that an accurate description of gravity is still lacking on the very large distance scale.

Two approaches to resolving this issue have surfaced over time. One of them, the Lambda-CDM paradigm, is an attempt to fix the gravity rule by fixing the matter content of the universe. The other thrives upon a geometric interpretation of this dark effect. This latter approach formulates the essence of Modified Gravity. Numerous variants of Einstein’s theory have been considered, inclusive of the equivalent Teleparallel formulation of GR and its variations, all of which thrive on torsion. The focus of our discussion however, will be a theory that relies on curvature: the f(R,T) theory. Here R is the scalar curvature of the spacetime and T is the trace of the stress tensor. The function f(R,T) is taken to be the vacuum action and a variational procedure yields the modified equations for gravity. We will consider polynomial gravity models and analyze non-static spacetimes in the presence of a perfect fluid, under the assumption of planar and cylindrical symmetry. Such geometries are important both from the astrophysical and cosmological viewpoints. We will discuss solutions to the modified gravity equations via algebraic classification of the spacetimes. The spacetime metrics, fluid parameters and gravity models will obtain in the process of solving the field equations. For the resulting spacetimes, we will explore the conformal symmetries. 

In summary, this discussion will address the development of exact solutions to the field equations for f(R,T) gravity, and achieve a subsequent study of the obtained spacetimes from the viewpoint of geometry.

Subject Field of Topic: General Relativity and Cosmology

Name of Speaker: Dr. Abu Bakar Mehmood

Professorial Rank of Speaker: Recently graduated from LUMS

Date and Venue: October 17, 2022 at 1530 hrs, School of Natural Sciences (SNS) New building CR # 205, NUST Islamabad Campus.