Stability of the spacetime of a magnetized compact object

Abstract

We investigate the stability of scalar perturbations around a magnetized stationary compact object in General Relativity. The considered object is one of the simplest exact solutions of Einstein electrovacuum equations corresponding to a spheroidal body endowed with a dipole magnetic moment. It is effectively constructed by imposing a perfect reflection (mirror) boundary condition on a central region of the Gutsunaev-Manko spacetime. A time-domain analysis of the perturbations reveals a quasinormal phase followed by a power-law decaying tail. Our findings suggest that the exterior region of the magnetized compact object is stable in the entire parameter space. Moreover, the system tends to become generically more stable the stronger the magnetization of the central object is. Such findings can be useful for the qualitative understanding of more realistic astrophysical situations involving highly magnetized sources.