Distribution of Energy-Momentum in a Schwarzschild-Quintessence Space-Time Geometry

An analysis of the energy-momentum localization for a four-dimensional Schwarzschild black hole surrounded by dark energy in the form of quintessence is presented in order to provide expressions for the distributions of energy and momentum. The calculations are performed by using the Landau–Lifshitz and the Weinberg energy-momentum complexes. It is shown that all the momenta vanish, while the expression for the energy depends on the mass M of the black hole, the state parameter w _q and the normalization factor c. The special case of $w_{q}=-\frac{2}{3}$ is studied and some limiting cases are examined.