I am interested in effective field theory approaches to quantum gravity, as well as modern methods from differential geometry. Find my list of literature here. What follows is a list of research projects I am currently pursuing:
Effective field theory approaches to quantum gravity
Short-distance modification of General Relativity in the framework of Poincaré gauge theory of gravity:
It can be shown that if spin is treated as a source of the gravitational field, there is a critical density where a gravity-induced four-fermion contact interaction becomes relevant. Similarly to Fermi's electroweak contact interaction, one can argue that this is the effective theory of massive gravitational gauge bosons. We explore this idea here.
Regularized black holes
The existence of the Schwarzschild singularity in General Relativity is a strong indication that this theory is UV incomplete. Hence, there are various so-called regularized black hole metrics presented in the literature, whose singularity is lifted by introducing a minimal length scale ℓ. This comes at a price: the metrics no longer solve the vacuum Einstein field equations. We are interested in understanding these regularized black holes better.
Force-free electrodynamics and black holes
In presence of a strong magnetic field, free charges in a plasma effectively screen the electric field, thereby making the corresponding field strength tensor degenerate. Thereby, the dynamics of the charges can be effectively integrated out, rendering the electromagnetic field the only free variable of the system. Using differential forms, we try to apply this technique to cosmic jets.
Gauge structures in gravity; Gravity as a gauge theory of the Poincaré group
Einstein's theory of General Relativity can be understood as a certain limit of a gauge approach to gravity, similar to Yang--Mills theory. Here, we explore various ramifications in this extended theory of gravity.
Algebraic properties of the curvature tensor in spacetimes with curvature and torsion
The Riemann curvature tensor of General Relativity has a set of algebraic properties that justify its decomposition into smaller pieces. In Poincaré gauge theory, the symmetries are somewhat reduced and give rise to new structures that we try to elucidate here. This is relevant because it allows for a more straightforward comparison between General Relativity and Poincaré gauge theory both on mathematical and physical grounds.
The symplectic potential of Poincaré gauge theory of gravity
If one is interested in obtaining the equations of motion in field theory, one is forced to integrate by parts due to the kinetic terms in the Lagrangian. The boundary term created thereby is called the symplectic potential, and it determines the Hamiltonian dynamics of the theory. In gauge theories, however, the symplectic potential is not necessarily invariant under gauge transformations, if the field theory is defined on a space with a boundary. Here, we explore the symplectic potential of Poincaré gauge theory of gravity.
- Quasi-normal modes of the BTZ black hole solution with torsion
Black holes in General Relativity
Exact solutions, curvature invariants, and analogies between gravity and electromagnetism
The so-called Plebanski–Demianski black hole is a very general black hole solution in General Relativity, and it can describe a massive, rotating, accelerating, electromagnetically charged black hole with cosmological constant and additional NUT parameter. We determine its curvature invariants exactly and point out similarities to electromagnetism. Moreover, we introduce a novel way of deriving the so-called Bel–Robinson 3-form, which is related to the superenergy of the gravitational field. Read more here.