Self-force of a scalar charge in the space-time of extreme charged anti-dilatonic wormhole

Abstract

The self-interaction for a static scalar charge in the space-time of extreme charged anti-dilatonic wormhole is calculated. We assume that the scalar charge is the source of massless scalar field with minimal coupling of the scalar field to the curvature of spacetime. I. INTRODUCTIONWormholes are topological handles in spacetime linking different universes or different parts of the same universe. Interest in these configurations dates back to at least 1916 [1] with revivals of activity following the works of Einstein and Rosen in 1935 [2] and the later series of works initiated by Wheeler in 1955 [3]. A fresh interest in this topic has been rekindled by the works of Morris and Thorne [4] and of Morris, Thorne and Yurtsever [5]. In classical general relativity, it is well known that traversable wormholes as solutions to the Einstein equations can only exist with exotic matter which violates the null energy condition T µνu µ u ν ≥ 0 for any null vector field u µ . Various models providing the wormhole existence include scalar fields [6,7]; wormhole solutions in Einstein-Gauss-Bonnet theory [8,9]; wormholes geometries induced by quantum effects [10,11]; wormhole solutions in semi-classical theory of gravity [12][13][14]; solutions in modified theories of gravity [15][16][17][18][19]; modified teleparallel theories [20] and their extensions [21], etc. The geometry of wormhole as well as a good introduction in the subject may be found in the Visser book [22] and in the review by Lobo [23] Static spherically symmetric wormholes would look observationally almost like black holes. One of the effects which can differ these two spacetimes is the self-interaction for the charge. Self-interaction effects in curved spacetime have been vigorously explored; for an extensive review, see [24][25][26][27]. The origin of this induced self-interaction resides on the nonlocal structure of the field caused by the space-time curvature or nontrivial topology. In flat space-time, the effect is determined by the derivative of acceleration of the charge. For electrically charged particles in flat spacetime, the self-force is given by the Abraham-Lorentz-Dirac formula [28,29]. In static curved space-times and space-times with nontrivial topology the self-force can be nonzero even for the charge at rest (here and below the words "at rest" mean that the velocity of charge is collinear to the timelike Killing vector which always exists in a static space-time). Results of this type were obtained for a static particle in flat spacetimes of the topological defects [30][31][32][33][34][35][36]. The formal expression for the electromagnetic self-force in an arbitrary curved space-time was first derived by DeWitt and Brehme [37] and a correction was later provided by Hobbs [38]. Mino, Sasaki, and Tanaka [39] and independently Quinn and Wald [40] obtained similar expressions for the gravitational self-force on a point mass. The self-force on a charge interacting with a massless minimally coupled scalar field was considered by Quinn [41]. More rec...

Simple black holes with anisotropic fluid

“…The anisotropic fluid can be used to study effectively the static matter fields. Traversable wormholes are widely studied recently [28,29] based on various gravity theories. The solutions require the existence of exotic materials which violate energy conditions and have (effective) negative anisotropic pressures.…”

Arbitrarily coupled massive scalar field in conical thin-shell spacetimes

“…Thus one cannot, in principle, expect the scalar self-force to behave as the electrostatic self-force. The scalar self-force on a static particle is a problem recently addressed in a large class of spherically symmetric spacetimes [26,27,28,29]. Much of this work was done in wormhole spacetimes, where some authors [30,31] noted that the self-force diverges for an infinite set of values of the curvature coupling ξ. Bezerra and Khusnutdinov [32] analyzed the anomalous behavior through an analogous problem in scattering theory by defining an effective potential in a non-relativistic quantum mechanical problem and identifying the poles of the self-interaction with the bound states for the wave function.…”