Self-force as probe of internal structure

Abstract

The self-force 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) self-force when the body is a spherical ball of perfect fluid in hydrostatic equilibrium, under the assumption that its rest-mass density and pressure are related by a polytropic equation of state. The body is strongly self-gravitating, and all computations are performed in exact general relativity. The dependence on internal structure is best revealed by expanding the self-force in powers of 1/r, with r denoting the radial position of the charge outside the body. To the leading order, the self-force scales as 1/r^3 and depends only on the square of the charge and the body's mass; the leading self-force is universal. The dependence on internal structure is seen at the next order, 1/r^5, through a 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 self-force, and quadratically with the body's radius in the case of the electromagnetic self-force. In both cases we find that for a fixed mass and radius, the self-force is smaller if the body is more centrally dense, and larger if the mass density is more uniformly distributed.

18 pages, 6 figures, minor revisions before publication

References in corpus (5)

• Constraining neutron star tidal Love numbers with gravitational wave detectors
• Extracting equation of state parameters from black hole-neutron star mergers. I. Nonspinning black holes
• Evolution of inspiral orbits around a Schwarzschild black hole
• Dependence of Self-force on Central Object
• Self force of a static electric charge near a Schwarzschild Star

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• The hidden geometry of electromagnetism
• Self-force and the Schwarzschild star