Marginally stable circular orbits in the Schwarzschild black hole surrounded by quintessence matter

Abstract.

Marginally stable circular orbits (MSCOs) of a massive test particle are investigated in the spacetime geometry of the Schwarzschild black hole surrounded by quintessence. For this matter we consider three important scenarios where the equation of state parameter, $\omega_{q}$, has one of the following forms: i) $\omega_{q} = -1$, ii) $\omega_{q} = -2/3$ and iii) $\omega_{q} - 1/3$. The existence of such marginally stable circular orbits in these scenarios depend on the range of the normalization factor $\alpha$. Briefly, we show that in the first case such orbits exist only if $0 < \alpha < 4/16875$. Moreover in the second case, which is a special Kiselev black hole, it is found that MSCOs exist when the value of the normalization factor satisfies $0< \alpha \leq 0.00536165238$. In the last case MSCOs are also shown to exist.