Stationary electromagnetic fields in the exterior of a slowly rotating relativistic star: a description beyond the low-frequency approximation

Abstract

We investigate the electromagnetic fields in the vacuum exterior to a rotating relativistic star endowed with a magnetic dipole moment, and with the stellar surface behaving as a perfect conductor. While the stellar rotation is treated in the slow approximation of general relativity, we do not restrict our attention to slowly rotating electromagnetic fields, and take our analysis beyond the low‐frequency approximation considered so far. When the dipole moment is misaligned with the rotational axis, our approach does not yield analytic solutions, but determines the properties of the electromagnetic fields approximately and semi‐analytically by computing the coefficients of simple expressions for the fields through the numerical solution of two partial differential equations. Because our approach provides a solution that is in principle valid throughout space, we can evaluate the accuracy and/or invalidity of previously known analytic expressions at different distances from the stellar surface. Overall, the solutions found in this way represent an efficient way of bridging in a single semi‐analytic formalism the strongly relativistic and the asymptotic regimes for which analytic solutions have been found.

General-relativistic electromagnetic fields around a slowly rotating neutron star: time-dependent pseudo-spectral simulations

“…Rezzolla & J. Ahmedov (2004) then deduced the associated Poynting flux. Kojima et al (2004) solved numerically the equations for the oblique rotator in vacuum in general relativity. They essentially retrieved Rezzolla et al (2001) results close to the surface and the Deutsch solution for distances larger than the light cylinder radius.…”

Electromagnetic fields in the exterior of an oscillating relativistic star - I. General expressions and application to a rotating magnetic dipole

“…Here, however, to validate the expressions derived and to provide a comparison with known results, we consider a background magnetic dipole and the simplest of the perturbation velocity fields: the one produced by the uniform rotation of the dipole. In the near zone, the comparison of the derived expressions for the electric and magnetic fields can be compared with the solutions calculated by Rezzolla et al (2001a) and Kojima et al (2003), while, in the wave zone, the new components of the electromagnetic fields can be used to calculate the general relativistic expression for the electromagnetic energy loss through dipolar radiation. This validating test is also useful to reveal that the well‐known Newtonian expression commonly used to estimate the rotational energy loss through dipolar radiation in pulsars (Pacini 1968; Gunn & Ostriker 1969a,b; Shapiro & Teukolsky 1983) underestimates this loss by a factor of 6 if the star is very compact or by a factor of 2 if the star is less compact.…”

Theory of pulsar magnetosphere and wind

“…Muslimov & Harding (1997) and Sakai & Shibata (2003) were concerned about particle acceleration around polar caps in curved space-time. Kojima, Matsunaga & Okita (2004) looked for approximate analytical solutions to the oblique rotator problem in vacuum in general relativity. They furnished an approximate numerical solution, expanded to first order.…”