We find simple expressions for velocity of massless particles in dependence
of the distance r in Schwarzschild coordinates. For massive particles these
expressions put an upper bound for the velocity. Our results apply to static
spherically symmetric metrics. We use these results to calculate the velocity
for different cases: Schwarzschild, Schwarzschild-de Sitter and
Reissner-Nordstr\"om with and without the cosmological constant. We emphasize
the differences between the behavior of the velocity in the different metrics
and find that in cases with naked singularity there exists always a region
where the massless particle moves with a velocity bigger than the velocity of
light in vacuum. In the case of Reissner-Nordstr\"om-de Sitter we completely
characterize the radial velocity and the metric in an algebraic way. We
contrast the case of classical naked singularities with naked singularities
emerging from metric inspired by noncommutative geometry where the radial
velocity never exceeds one. Furthermore, we solve the Einstein equations for a
constant and polytropic density profile and calculate the radial velocity of a
photon moving in spaces with interior metric. The polytropic case of radial
velocity displays an unexpected variation bounded by a local minimum and
maximum.Comment: 20 pages, 5 figure
