Stability of the spacetime of a magnetized compact object

TL;DR

This study analyzes the stability of scalar perturbations around a magnetized compact object in General Relativity, finding that such objects are generally stable and become more stable with increased magnetization.

Contribution

It introduces a new stability analysis of a spheroidal, magnetized compact object modeled by a specific exact solution with boundary conditions, extending understanding of magnetized astrophysical objects.

Findings

Exterior region is stable across all parameters.

Stability increases with stronger magnetization.

Perturbations exhibit quasinormal ringing followed by decay.

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.