D-dimensional dilaton gravity

In D-dimensional dilaton gravitational model stationary Schwarzschild type solutions (centrally symmetrical solutions in vacuum) are obtained. They contain the two-parameter set of solutions: the first parameter is proportional to a central mass and the second one describes intensity of the dilaton field. If the latter parameter equals zero we have pure Schwarzschild solution with the black hole and constant dilaton field. But when the mentioned parameter is non-zero and the dilaton is non-constant, the black hole horizon vanishes. Introduction The considered dilaton gravitational model is the consequence of the string theory in the low-energy limit [1, 2]. Here we study the generalization of the Schwarzschild solution (that is stationary centrally symmetrical solution in vacuum) for D-dimensional dilaton gravity. We start from the following action [1]: