The effect of quintessence in black hole spacetime

A new method is introduced to study the classification of spacetime, and spacetime horizons and timelike geodesics are investigated in the background spacetime of Reissner-Nordstrom-(anti-)de Sitter black hole surrounded by the quintessence (Q-RN(A)dS). We find that, for Q-RNAdS metric, there are two types of black holes: two horizons and four horizons. In a black hole spacetime of two horizons, the angular precession of the aphelion per revolution increases with the increase of the quintessence parameter $r_\text{q}$; while the number of aphelion per revolution increases with the decrease of the quintessence equation of state parameter $w_\text{q}$. This shows that the quintessence parameters $r_\text{q}$ and $w_\text{q}$ can be determined by measuring the angular precession and number of aphelion per revolution, respectively. For Q-RNdS metric there are two cases: one horizon and three horizons. The Q-RNdS metric of one horizon describes the de Sitter-like spacetime, which has a naked singularity at $r=0$. It is interesting to note that any particle never reaches the singularity, since the effective potential is infinite at the point. On the other hand, the quintessence has no significant on the geodesics in de Sitter-like spacetime. It is worth pointing out that there are no bound states for the Q-RNAdS spacetime with four horizons and the Q-RNdS spacetime with three horizons.