Speaker
Description
This work serves as a sequel to our previous study, where, by assuming the existence of the canonical Killing tensor forms and applying a general null tetrad transformation, we obtained a variety of solutions (Petrov types D, III, N) in vacuum with cosmological constant $\Lambda$. Among those, there is a unique Petrov type D solution with a shear-free, diverging and non-geodesic null congruence which will be presented in full detail in the following sections. Additionally, in this work we will introduce a Petrov type I solution with a shear-free, diverging and non-geodesic null congruence, obtained by employing Lorentz transformations, within the concept of symmetric null tetrads, instead of the general null tetrad transformation. Building upon this and in line with the concept of symmetric null tetrads, which played a crucial role in deriving the most general Petrov type D solution ( Debever-Plebanski-Demianski solution), we propose a new directive. This directive suggests that, by assuming the canonical forms of Killing tensor and implying Lorentz transformations correlating the spin coefficients between themselves ($\pi=-\bar\tau, \kappa = - \bar\nu$, etc.) can yield a broader class of (algebraically) general solutions to Einstein's equations, rather than relying on boosts and spatial rotations.
