Abstract:
Considering the Schwarzschild - de Sitter space-time, many authors have explored a range of
cosmological events and effects. But, the effects of the cosmological constant () on energy and
angular momentum in the Schwarzschild – de Sitter space-time are not studied in depth in comparison
to the Schwarzschild space-time.
In this study, we obtain the expressions for total energy per unit rest mass ( ) and for angular
momentum per unit rest mass ( ) not only in the Schwarzschild - de Sitter space-time but also in the
Schwarzschild space-time considering a particle moving in a circular path. Then, we discuss the
conditions for the possibility of circular orbits. Finally, we plot the graphs for and for against the
coordinate radius of the circle for different low and high values of the central mass ( ) for positive
and negative cosmological constants for the Schwarzschild - de Sitter space-time in comparison with
the Schwarzschild space-time. Also, we plot the graphs for when is negative.
Considering the plotted graphs, we conclude that the effects introduced by the cosmological constant
on and are negligible with the present value of the cosmological constant. But, for higher
cosmological constant values, the effects on and are known to be significant. However, affects
and indeed when a particle moves in a circle.
According to this study, positive creates a repulsive field and when it is negative it creates an
attractive field. Accordingly, in the nonappearance of a central mass there is no possibility of circular
motion when is positive as a repulsive field would not give rise to circular motion. In the case of the
Schwarzschild - de Sitter space-time and for a particle moving in a circle are less (greater) than
that in the case of the Schwarzschild space-time when is positive (negative).
