The first-order symmetry operator on gravitational perturbations in the 5D Myers–Perry spacetime with equal angular momenta

Abstract It has been revealed that the first-order symmetry operator for linearized Einstein equation on a vacuum spacetime can be constructed from Killing–Yano 3-form. This might used to construct all or part of solutions field equation. In this paper, we perform mode decomposition metric perturbation Schwarzschild and Myers–Perry with equal angular momenta in 5 dimensions, investigate action specific modes concretely. We show that, such spacetimes, there is no transition between by operator, it ends up being linear combination infinitesimal transformations isometry.