Solutions of Penrose's Equation
E.N. Glass (Department of Physics, University of Michigan, Ann Arbor,, MI), Jonathan Kress (School of Mathematics, Statistics, University of, Sydney, Australia)
TL;DR
This paper explores solutions to Penrose's equation, a conformal Killing-Yano equation, analyzing their existence in various spacetime types and demonstrating the absence of solutions for the axial Killing vector in Kerr spacetime.
Contribution
It provides a detailed analysis of solutions to Penrose's equation across different Petrov types and clarifies the non-existence of solutions in Kerr spacetime for certain Killing vectors.
Findings
Solutions exist in Petrov type O, D, or N spacetimes.
No Killing potential exists for the axial Killing vector in Kerr spacetime.
Penrose's equation is characterized as a conformal Killing-Yano equation.
Abstract
The computational use of Killing potentials which satisfy Penrose's equation is discussed. Penrose's equation is presented as a conformal Killing-Yano equation and the class of possible solutions is analyzed. It is shown that solutions exist in spacetimes of Petrov type O, D or N. In the particular case of the Kerr background, it is shown that there can be no Killing potential for the axial Killing vector.
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