Self-interaction and quantum effects near a point mass in three-dimensional gravitation

Abstract

The authors determine some gravitational effects in the classical and quantum massive scalar field theories near a point mass in the Einstein theory in three dimensions and near a particular spinning point mass in the topologically massive gravity. Classically, they find the expression, to a first-order approximation in the deficit angle of the conical spacetime, for the self-force acting on a scalar charge at rest. Within quantum field theory, they obtain the vacuum expectation value of the energy-momentum operator for a massive scalar field by determining the Euclidean Green function. They provide an explicit expression for the vacuum energy-momentum tensor to first order in the deficit angle for an arbitrary coupling parameter. Near a point mass in the Einstein theory, they calculate the gravitational force on a massive test particle due to the backreaction of the vacuum energy-momentum tensor. For the minimal and conformal couplings, they show that the gravitational force is always attractive. Near the particular spinning point mass in the topologically massive gravity, they can prove that the gravitational force is always attractive for a massless scalar field.

Multiplicative noise in Euclidean Schwarzschild manifold

“…Since both contributions are divergent, to regularize this divergent quantities we are following Refs. [56,57,58]. We define the renormalized two-point correlation function of coincident points as…”

The Self-Energy of a Charged Particle in the Presence of a Topological Defect Distribution

“…The presence of a density of defects in the continuum medium changes the field lines of a charged particle making the particle interact with its own electrical field, resulting in the self-energy of the particle. Outside the defect, from (19), (25) and (9), the self-energy is given by…”

“…A variety of studies involving self-forces on charge distributions due to topological defects have appeared in the recent literature [17,18,19,20,21,22,23,24].…”

Induced vacuum bosonic current in a compactified cosmic string spacetime

“…Due to its lack of global flatness, the cosmic string spacetime modifies the vacuum fluctuations associated with quantum fields. In this sense it has been shown a non-vanishing results for the renormalized vacuum expectation value (VEV) of physical observables, like the energymomentum tensor, considering scalar and fermionic quantum fields in [16][17][18][19][20] and [21][22][23][24], respectively. Moreover, if we take into consideration the presence of a magnetic flux running along the string's core, additional contributions to the above VEVs associated with charged fields takes place.…”