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

TL;DR

This paper investigates the existence of marginally stable circular orbits around Schwarzschild black holes influenced by quintessence matter, analyzing how different equations of state affect orbit stability based on a normalization factor.

Contribution

It provides a detailed analysis of MSCO existence conditions in Schwarzschild black holes surrounded by quintessence for three specific equations of state, highlighting the dependence on the normalization factor.

Findings

MSCOs exist only within specific ranges of the normalization factor for each scenario.

In the case of , MSCOs exist if 0<<4/16875.

In the /3 case, MSCOs exist when 0<<0.00536165238.

Abstract

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 $\omega_{q}$, 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 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 satisfy $0<\alpha\leq 0.00536165238$. In the last case the MSCOs are also shown to exist.