2006/06/26 by Shanxian Xu, Xu Shan-Xian, Jiliang Jing
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #De Sitter universe #General relativity #Hamiltonian (control theory) #Mathematical physics #Noncommutative and Quantum Gravity Theories #Physics #Quantum mechanics #Spacetime #Universe #gr-qc #hep-th
paper · pdf · doi:10.1088/0264-9381/23/14/007
published as Class.Quant.Grav. 23 (2006) 4659-4672 · 12 pages
openalex publication_date 2006/06/26 · arxiv created 2006/06/30 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The field equation with the cosmological constant term is derived and the energy of the general 4-dimensional stationary axisymmetric spacetime is studied in the context of the hamiltonian formulation of the teleparallel equivalent of general relativity (TEGR). We find that, by means of the integral form of the constraints equations of the formalism naturally without any restriction on the metric parameters, the energy for the asymptotically flat/de Sitter/Anti-de Sitter stationary spacetimes in the Boyer-Lindquist coordinate can be expressed as E=(1)/(8π)∫S dθ dφ(sinθ √gθθ+√gφφ-(1/√grr)(∂√g_ θθ gφφ/∂ r)). It is surprised to learn that the energy expression is relevant to the metric components grr, gθθ and gφφ only. As examples, by using this formula we calculate the energies of the Kerr-Newman (KN), Kerr-Newman Anti-de Sitter (KN-AdS), Kaluza-Klein, and Cveti\vc-Youm spacetimes.