Results of precise measurements of the periods of pulsars discovered i
n the central regions of globular clusters are shown to be approaching
the capabilities of testing the existence of a central black hole. Fo
r example, in the case of M 15 the available data on two pulsars PSR 2
129+1210A and PSR 2129+1209D seem to exclude the existence of a black
hole, the presence of which was instead supported by recent Hubble Spa
ce Telescope data on surface brightness profile (Yanny et al. 1994). T
he fluctuations of the gravitational field caused by the stars of the
system are enough to explain the acceleration observed for both pulsar
s. In the case of the Galactic center, additional data are needed for
similar definite conclusions.