β Scribed by Jeffrey M Cohen; Edward T Toton
No coin nor oath required. For personal study only.
The effect of slow rotation on the dipole magnetic field of neutron stars is studied. It is shown that the differential rotation of inertial frames produced by the effect of "dragging of inertial frames" induces an additional component of electric field outside the star. This new component, as well as the usual electromagnetic components, vanishes as in the limit of collapse of a star to its Schwarzschild radius. For typical neutron stars, the electric quadrupole moment is about half that obtainable from a flat space analysis.
The discovery of pulsars, characterized by the emission of radio pulses at extremely regular intervals [14] has led to the belief that pulsars are rotating neutron stars [13] with frozen-in magnetic fields.
Owing to the high density and compactness of neutron stars [9, lo] the space exterior to the star can show appreciable departure from the flat space of newtonian mechanics. Not only can the spatial curvature in the vicinity of the star be significant, but the magnetic fields themselves can be altered from their special relativistic counterpart. In fact an investigation of the effect of the gravitational field exterior to a star on its magnetic multipole moments has shown that each magnetic multipole varies as a hypergeometric function of radius [2] rather than as r-(z+2). These functions, which can be expressed in terms of Legendre functions of the second kind, have the feature that each magnetic multipole vanishes in the limit as the radius of the star approaches its Schwarzerschild radius.
A second appreciable effect of a dense, compact, spinning star on the neighboring space is the dragging of inertial frames [4, 61. A rotating star is capable of inducing a rotation of local inertial frames relative to an inertial frame at infinity.
As the star becomes increasingly massive, the rotation rate of the local inertial frames increases and becomes comparable to the star's angular velocity for massive stars [3, 9, lo].
π SIMILAR VOLUMES
The magnetic configuration in the plasma-sphere surrounding a neutron star is described in terms of a model equation that is constructed to be valid from the surface of the star to distances of the order of the light speed cylinder and beyond. Significant asymptotic solutions of this equation, that