2012/09/30 by Peter Taylor · 4 citations
Mathematics · Physics and Astronomy · #Charge (physics) #Classical mechanics #Constant curvature #Cosmology and Gravitation Theories #Coupling (piping) #Coupling constant #Curvature #Geometry #Mathematical analysis #Mathematical physics #Mathematics #Physics #Quantum Electrodynamics and Casimir Effect #Quantum mechanics #Relativity and Gravitational Theory #Scalar (mathematics) #Scalar curvature #Scalar field #Sign (mathematics) #Space (punctuation) #Wormhole #gr-qc
paper · pdf · doi:10.1103/physrevd.87.024046
published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 87(2) (American Physical Society) · 6 pages, 1 figure, Significant changes/corrections made to previous version
arxiv created 2012/10/20 · openalex publication_date 2013/01/30 · arxiv updated 2013/05/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In this paper, we consider the problem of computing the self-force and self-energy for a static scalar charge in a wormhole space-time with throat profile r(\ensuremathρ)=√\ensuremathρ2+a2 for arbitrary coupling of the field to the curvature. This calculation has previously been considered numerically by Bezerra Khusnutdinovand [Phys. Rev. D 79, 064012 (2009)], while analytic results have been obtained in the special cases of minimal (\ensuremathξ=0) coupling [N. R. Khusnutdinov and I. V. Bakhmatov, Phys. Rev. D 76, 124015 (2007)] and conformal coupling [V. B. Bezerra and N. R. Khusnutdinov Phys. Rev. D 79, 064012 (2009)] (\ensuremathξ=1/8 in three dimensions). We present here a closed form expression for the static Green's function for arbitrary coupling and hence we obtain an analytic expression for the self-force. The self-force depends crucially on the coupling of the field to the curvature of the space-time and hence it is useful to determine the dependence explicitly. The numerical computation can identify some qualitative aspects of this dependence such as the change in the sign of the force as it passes through the conformally coupled value, as well as the fact that the self-force diverges for \ensuremathξ=1/2. From the closed form expression, it is straightforward to see that there is an infinite set of values of the coupling constant for which the self-force diverges, but we also see that there is an infinite set of values for which the self-force vanishes.