The geometry of null-like disformal transformations

Understand

Motivated by the hindrance of defining metric tensors compatible with the underlying spinor structure, other than the ones obtained via a conformal transformation, we study how some geometric objects are affected by the action of a disformal transformation in the closest scenario possible: the disformal transformation in the direction of a null-like vector field.

• Subsequently, we analyze symmetry properties such as mutual geodesics and mutual Killing vectors, generalized Weyl transformations that leave the disformal relation invariant, and introduce the concept of disformal Killing vector fields.
• In most cases, we use the Schwarzschild metric, in the Kerr-Schild formulation, to verify our calculations and results.
• We also revisit the disformal operator using a Newman-Penrose basis to show that, in the null-like case, this operator is not diagonalizable.