Covariant Formalism in General Relativity
In general relativity, the Riemann curvature tensor is split into the Ricci tensor and the Weyl curvature tensor. Moreover, the Weyl tensor can be can split into the electric part and the magnetic part. The electric part describes the tidal (Newtonian) force, while the magnetic part has no Newtonian analogy, the so-called gravitomagnetic field. General relativity predicts the presence of gravitomagnetic fields and gravitational waves. A binary system of massive compact objects can produce gravitational waves, while a rotating massive body such as supermassive black holes have been predicted to generate the gravitomagnetic field. The gravitomagnetic fields implies that the formation of the jets along angular momentum vector, which could be as a mechanism for the jet formation in quasars and AGNs.
Over 2008 Ashkbiz Danehkar worked as an early-stage researcher in a project on gravitational theories, which included courses on general relativity. He studied cosmological perturbations in general relativity using 1+3 and 1+1+2 covariant formalism and tetrad formalism in a relativistic cosmological model. The results show that cosmological models with only Newtonian field are inconsistent and obstruct sounding solutions. Therefore, both the electric and the magnetic part of the Weyl curvature are necessary for the nonlocal interaction of gravitation and the propagation of gravitational waves.
BRST-Antifield Formalism in Gauge Theory
Becchi, Rouet, Stora (1974,1975,1976), and Tyutin (1975) developed The BRST formalism to extend the gauge symmetry, which provides useful way of studying the consistent interactions in terms of the deformation to the solutions of the master equation. As the gauge symmetry can be made using a nilpotent derivation, the gauge action is invariant under the BRST symmetry. Replacing the gauge symmetry with the BRST symmetry introduces antifield, ghosts, and antighosts for each gauge variable. BRST cohomology was extended by the antifield formalism allowed to determine consistent interactions among the fields from coupling deformations of the master equation. Therefore, the BRST-antifield formalism presents an efficient tool to study the consistent interactions in gauge theory.
As an early-stage researcher in 2008, Ashkbiz Danehkar worked In a project on a dual linearized gravity coupled to a topological background (BF) field, which included courses on quantum field theory and constrained dynamics. During his time at University of Craiova, he learned about gauge and BRST symmtry in quantum field theory. Ashkbiz Danehkar studied BRST coupling between a dual formulation of linearized gravity and topological BF model, which could have some applications in cosmological models and dark energy.