Energy of homogeneous cosmologies

Abstract

An energy for the homogeneous cosmological models is presented. More specifically, using an appropriate natural prescription, we find the energy within any region with any gravitational source for a large class of gravity theories-namely those with a tetrad description-for all 9 Bianchi types. Our energy is given by the value of the Hamiltonian with homogeneous boundary conditions; this value vanishes for all regions in all Bianchi class A models, and it does not vanish for any class B model. This is so not only for Einstein's general relativity but, moreover, for the whole 3-parameter class of tetrad-teleparallel theories. For the physically favored one parameter subclass, which includes the teleparallel equivalent of Einstein's theory as an important special case, the energy for all class B models is, contrary to expectation, negative.

Quasi-Local Energy-Momentum and Angular Momentum in General Relativity

“…One such list for the energy-momentum and mass, based mostly on [176, 143] and the properties of the quasi-local energy-momentum of the matter fields of Section 2.2, might be the following: The quasi-local energy-momentum must be a future-pointing nonspacelike vector (assuming that the matter fields satisfy the dominant energy condition on some Σ for which , and maybe some form of the convexity of should be required) (‘positivity’). must be zero iff D (Σ) is flat, and null iff D (Σ) has a pp -wave geometry with pure radiation (‘rigidity’). must give the correct weak field limit. must reproduce the ADM, Bondi-Sachs and Abbott-Deser energy-momenta in the appropriate limits (‘correct large-sphere behaviour’).For small spheres must give the expected results (‘correct small sphere behaviour’): in nonvacuum and kr 5 T abcd t b t c t d in vacuum for some positive constant k and the Bel-Robinson tensor T abcd .For round spheres must yield the ‘standard’ Misner-Sharp round-sphere expression.For marginally trapped surfaces the quasi-local mass must be the irreducible mass . For a different view on the positivity of the quasi-local energy see [391]. Item 1.7 is motivated by the expectation that the quasi-local mass associated with the apparent horizon of a black hole (i.e., the outermost marginally-trapped surface in a spacelike slice) be just the irreducible mass [176, 143].…”

“…(11.7) in the tetrad approach to general relativity, is calculated for arbitrary two-surfaces lying in the hypersurfaces of the homogeneity in all the Bianchi cosmological models in [391] (see also [340]). In these calculations the tetrad field was chosen to be the geometrically distinguished triad, being invariant with respect to the global action of the isometry group, and the future-pointing unit timelike normal of the hypersurfaces; while the vector field K a was chosen to have constant components in this frame.…”

On the Energy of Charged Black Holes in Generalized Dilaton-Axion Gravity

“…In the recent years, a wide interest have been focused on numerous efficient and precise tools, such as superenergy-tensors [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16], energy-momentum complexes, quasi-local expressions [17][18][19][20] and the tele-parallel theory of gravitation [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35] for the study of energymomentum localization.…”

Energy–momentum Distributions of Five-Dimensional Homogeneous-Anisotropic Universes

“…65 In TG, Nester et al presented energy of homogeneous cosmologies. 66 So and Vargas displayed energy of Bianchi type-I and type-II universes in TG. 67 Total energy and total momentum of the FRW-universe in TG was obtained by Liu et al 68 Also, Gad considered solution of field equations with stiff fluid matter using equation of state and energy-momentum densities in both gravitation theories.…”