Electromagnetic Fields in the Exterior of an Oscillating Relativistic Star -- I. General Expressions and application to a rotating magnetic dipole

TL;DR

This paper derives general relativistic expressions for electromagnetic fields around oscillating relativistic stars and applies them to a rotating magnetic dipole, revealing significant corrections to energy loss estimates compared to Newtonian models.

Contribution

It provides the first analytic general relativistic solutions for electromagnetic fields around oscillating stars and quantifies relativistic corrections to dipolar radiation energy loss.

Findings

Relativistic corrections increase energy loss estimates by a factor of 2-6.

Analytic expressions are derived for electromagnetic fields in general relativistic context.

Application to a rotating dipole demonstrates the impact on pulsar spin-down calculations.

Abstract

Relativistic stars are endowed with intense electromagnetic fields but are also subject to oscillations of various types. We here investigate the impact that oscillations have on the electric and magnetic fields external to a relativistic star in vacuum. In particular, modelling the star as a relativistic polytrope with infinite conductivity, we consider the solution of the general relativistic Maxwell equations both in the vicinity of the stellar surface and far from it, once a perturbative velocity field is specified. In this first paper we present general analytic expressions that are not specialized to a particular magnetic field topology or velocity field. However, as a validating example and an astrophysically important application, we consider a dipolar magnetic field and the velocity field corresponding to the rotation of the misaligned dipole. Besides providing analytic expressions for the electromagnetic fields produced by this configuration, we calculate, for the first time, the general relativistic energy loss through dipolar electromagnetic radiation. We find that the widely used Newtonian expression under-estimates this loss by a factor of 2-6 depending on the stellar compactness. This correction could have important consequences in the study of the spin evolution of pulsars.