Gravitational entropy in Petrov type D spacetimes


My current interest is on gravitational entropy in the case of Petrov type D spacetimes. The Gregoris and Ong proposal in the case of LRS Bianchi type I spacetimes is my current interest, where the spacetime has local rotational symmetry and is of Petrov type D, i.e. the spacetime has a non-zero Weyl scalar $\Psi _{2}$ and we use the Cartan invariant to describe gravitational entropy. 
Related talks:
  • Does the Weyl invariant based proposal provide an accurate description of gravitational entropy? XI International conference on new frontiers in physics, Greece, 2022 (PDF   abstract)
  • Gravitational entropy, cosmology and black holes. Gravitational physics and astronomy conference, TBA (PDF   abstract)