I have a broad range of research interests which are all related in one form or another with mathematical aspects of gravitation. I have to admit that I do have a kink for nice physical ideas and alternative approaches. Beaten paths do not really get me excited. However I do like to stay within the realms of reality. That being said I like my spacetime to be 4 dimensional and I like my matter models to satisfy reasonable energy conditions.
In the past I have written papers related to black hole shadows, spacetime limits, cosmology and one related to black hole stability.
My current research projects that I am more or less actively working on:
Understanding Thermodynamic interpretations of General Relativity in the light of the theory of Causal Fermion Systems as an underlying description. In particular I would be keen to understand whether Padmanabhan’s considerations regarding the cosmological constant could be recovered in the setup of CFS and whether it can in fact be connected to our considerations for baryogenesis.
Baryogenesis in the Causal Fermion System framework. The Causal Fermion Systems framework was developed by Felix to give a unified description of the standard model and gravitation. Within this framework we showed that a new mechanism for baryogenesis arrises. In future work we want to quantify this effect in different spacetimes to bring the theory closer to falsifiability.
This is joint work with Felix Finster.
Marrying the Causal Fermion System framework with the idea of non-Riemannian measure theories. In fact in our recent paper we already argued, that Causal Fermion Systems is not only compatible with non-Riemannian measure theories but in fact requires them in the context of our mechanism for baryogenesis. The goal now is to understand the context in which deviations form Riemannian measures occure in Causal Fermion Systems in more detail. One specific aim is to figure out which phenomenological predictions made with non-Riemannian measure theories can be reproduced in the context of Causal Fermion Systems, thereby providing the first step towards phenomenology for the latter.
This is joint work with Felix Finster and Eduardo Guendelman.
T-Orthogonal trapping in stationary black hole spacetimes with positive surface gravity. This is a technical requirement for one possible approach to a proof of Kerr uniqueness. (aka the statement that the Kerr family represents all possible asymptotically flat stationary solutions to the Einstein Field Equations). This problem seems to become my white whale.
I have discussed various approaches but no specific project materialized at this point in time.
Because I have way more ideas then time and skill to work them out I decided to set up a separate section on my page here for my brainfarts and conjectures.