On a regular modified C-metric

A particular form of the C-metric is investigated, giving it a non-standard interpretation and removing any singularity at r = 0. In the weak field limit of the accelerating black hole, the proper acceleration A of a static observer is constant and the geometry becomes conformally-flat (anti de Sitter). The stress tensor is of ?-type (Lambda = -3a(2)/8 pi G) and its energy density is negative. We propose that is responsible of inertial forces that appear in uniformly accelerated systems (far from the accelerating source m and for r << 1/a the dominant term in the expression of a(r) is -a cos theta). The components of the stress tensor and all invariants of the conformally-flat Schwarzschild spacetime are regulated by means of the exponential factor exp(-k/r), k > 0.