Abstract:
The selfforce acting on a (scalar or electric) charge held in place outside a massive body contains information about the body's composition, and can therefore be used as a probe of internal structure. We explore this theme by computing the (scalar or electromagnetic) selfforce when the body is a spherical ball of perfect fluid in hydrostatic equilibrium, under the assumption that its restmass density and pressure are related by a polytropic equation of state. The body is strongly selfgravitating, and all computations are performed in the context of exact general relativity. The dependence on internal structure is best revealed by expanding the selfforce in powers of $r_0^{1}$, with $r_0$ denoting the radial position of the charge outside the body. To the leading order, the selfforce scales as $r_0^{3}$ and depends only on the square of the charge and the body's mass; the leading selfforce is universal. The dependence on internal structure is seen at the next order, $r_0^{5}$, through a multiplicative structure factor that depends on the equation of state. We compute this structure factor for relativistic polytropes, and show that for a fixed mass, it increases linearly with the body's radius in the case of the scalar selfforce, and quadratically with the body's radius in the case of the electromagnetic selfforce. In both cases we find that for a fixed mass and radius, the selfforce is smaller if the body is more centrally dense, and larger if the mass density is more uniformly distributed.
