A Note on Separability of Field Equations in Myers-Perry Spacetimes

TL;DR

This paper investigates the separability of scalar, vector, and tensor fields in 5D Myers-Perry black holes with equal angular momenta, revealing decoupled equations for zero modes and providing a basis for stability analysis.

Contribution

It introduces a group theoretical method with a twist to reduce field equations to ordinary differential equations in Myers-Perry spacetimes with enhanced symmetry.

Findings

Vector and tensor field equations reduced to coupled ODEs.

Decoupled master equations obtained for zero modes.

Formalism facilitates stability studies of Myers-Perry black holes.

Abstract

We study separability of scalar, vector and tensor fields in 5-dimensional Myers-Perry spacetimes with equal angular momenta. In these spacetimes, there exists enlarged symmetry, $U(2) \simeq SU(2) \times U(1)$. Using the group theoretical method with a twist, we perform the dimensional reduction at the action level and show that both vector and tensor field equations can be reduced to coupled ordinary differential equations. We reveal the structure of couplings between variables. In particular, we have obtained the decoupled master equations for zero modes of a vector field. The same analysis can be done for zero modes of a tensor field. Therefore, our formalism gives a basis for studying stability of Myers-Perry black holes.