SUSY in the sky

TL;DR

This paper explores new fermionic supersymmetries in curved space-time, especially in black-hole solutions, revealing conditions for their existence and algebraic structure, with implications for solving the Dirac equation.

Contribution

It provides a general framework for identifying supersymmetries generated by fermionic charges linked to bosonic constants of motion beyond the Hamiltonian.

Findings

Discovery of a new non-trivial supersymmetry in Kerr-Newman black holes

Identification of conditions for supersymmetry algebra closure

Connection between supersymmetries and Killing-Yano tensors

Abstract

Spinning particles in curved space-time can have fermionic symmetries generated by the square root of bosonic constants of motion other than the Hamiltonian. We present a general analysis of the conditions under which such new supersymmetries appear, and discuss the Poisson-Dirac algebra of the resulting set of charges, including the conditions of closure of the new algebra. An example of a new non-trivial supersymmetry is found in black-hole solutions of the Kerr-Newman type and corresponds to the Killing-Yano tensor, which plays an important role in solving the Dirac equation in these black-hole metrics.