Schwarzschild-Type Solutions in Dilaton Gravity

Abstract

In the D-dimensional dilaton gravity model, we obtain and study stationary Schwarzschild-type solutions, i.e., centrally symmetric solutions in a vacuum. They form a two-parameter family of solutions: one of the parameters is an analogue of the gravitational radius, and the second parameter characterizes the intensity of the dilaton field. If the second parameter is zero, which means that the dilaton field is constant, then the expression obtained for the metric becomes the well-known Schwarzschild solution describing a black hole. But if this parameter is nonzero, then the black hole horizon does not appear. We find the parameters of quasielliptic orbits of test particles for the obtained solutions in the weak gravitational field limit.