SELF-INTERACTION AND QUANTUM EFFECTS NEAR A POINT MASS IN 3-DIMENSIONAL GRAVITATION

We determine some gravitational effects in the classical and quantum m assive scalar field theories near a point mass in the Einstein theory in three dimensions and near a particular spinning point mass in the t opologically massive gravity. Classically, we find the expression, to a first-order approximation in the deficit angle of the conical spacet ime, for the self-force acting on a scalar charge at rest. Within quan tum field theory, we obtain the vacuum expectation value of the energy -momentum operator for a massive scalar field by determining the Eucli dean Green function. We provide an explicit expression for the vacuum energy-momentum tensor to first order in the deficit angle for an arbi trary coupling parameter. Near a point mass in the Einstein theory, we calculate the gravitational force on a massive test particle due to t he backreaction of the vacuum energy-momentum tensor. For the minimal and conformal couplings, we show that the gravitational force is alway s attractive. Near the particular spinning point mass in the topologic ally massive gravity, we can prove that the gravitational force is alw ays attractive for a massless scalar field.