Marginally Stable Circular Orbits in Schwarzschild Black Hole Surrounded by Quintessence Matter

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

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