On the energy of the de Sitter-Schwarzschild black hole

Using Einstein’s and Weinberg’s energy complex, we evaluate the energy distribution of the vaccum nonsingularity black hole solution. The energy distribution is positive everywhere and be equal to zero at origin. PACS No.:04.20.-q, 04.50.+h E-mail:[email protected] 1 There are two reasons for evaluting the energy of a system in general relativity. First, the conserved qualitities, like total energy etc., play important roles in solving the equation of motion. Second, the energy distribution must be positive if attractive force only. In particular positions, r = 2M and r = 0, the Schwarzschild solution will be degenerate. The value r = 2M is a removable coordinate singularity, however, the singularity at the origin is indeed irremoved. All of the physical laws are not holden at the singularity, hence we can’t predict the evolution of singularity. The energy distribution at the singularity can’t be prediction, therefore, the gravity theory without singularity is inevitable. Many theories, which are like Brans-Dicke theory, Einstein-Cartan theory etc., try to avoid the existence of the singularity, but they can not do it. With considering the action in which pure gravity term adds to cosmological constant term, the first vacuum nonsingularity solution is written down by de Sitter [1] in 1917. The de Sitter geometry is generated by a vacuum with nonzero energy density ε = Λ 8π , described by the stress-energy tensor Tαβ = εgαβ, (1) with the equation of state p = −ε. (2) Recent, Dymnikova [1] shows that the spherically symmetric vacuum can generate a black hole solution which is regular at r = 0 and everywhere else.