Effect of dark energy models on the energy content of charged and rotating black holes
Abstract
Abstract The energy content of the charged-Kerr (CK) spacetime surrounded by dark energy (DE) is investigated using approximate Lie symmetry methods for the differential equations. For this, we consider three different DE scenarios: cosmological constant with an equation of state parameter , quintessence DE with an equation of state parameter , and a frustrated network of cosmic strings with an equation of state parameter . To study the gravitational energy of the CK black hole surrounded by the DE, we explore the symmetries of the 2nd-order perturbed geodesic equations. It is noticed, for all the values of ω , the exact symmetries are recovered as 2nd-order approximate trivial symmetries. These trivial approximate symmetries give the rescaling of arc length parameter s in this spacetime which indicates that the energy in the underlying spacetime has to be rescaled by a factor that depends on the black hole parameters and the DE parameter. This rescaling factor is compared with the factor of the CK spacetime found in [Hussain et al . Gen. Relativ. Gravit. (2009)] and the effects of the DE on it are discussed. It is observed that for all the three values of the equation of state parameter ω , the effect of DE results in decreased energy content of the black hole spacetime, regardless of values of the charge Q , spin a and the DE parameter α . This reduction in the energy content due to the involvement of the DE favours the idea of mass reduction of black holes by accretion of DE given by [Babichev et al . Phys. Rev. Lett. (2004)].