Open AccessA covariant gravitational field equation including the contribution of gravitational field
Author(s) -
Lou Tai-Ping
Publication year - 2006
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.55.1602
Subject(s) - physics , gravitational field , gravitational energy , covariant transformation , classical field theory , speed of gravity , gravitational constant , gravitational redshift , metric tensor , gravitation , gravitational acceleration , stress–energy tensor , einstein tensor , general relativity , gravitational potential , mathematical physics , field (mathematics) , linearized gravity , exact solutions in general relativity , classical mechanics , quantum mechanics , riemann curvature tensor , geometry , curvature , mathematics , pure mathematics , geodesic
Using the four-leg metric tensor λ(α)μ, a gravitational field 4-vector potential for index μ is defined as ω(α)μ≡-cλ(α)μ, and a covariant gravitational field equation that includes the gravitational field contribution is proposed as Rμν-gμνR/2+Λgμν=8πG(T(Ⅰ)μν+T(Ⅱ)μν)/c4, where Λ is Einstein's cosmic constant T(Ⅰ)μν and T(Ⅱ)μν are energy-momentum tensor of pure matter part and pure gravitational field part, respectively. The covariant energy-momentum tensor of gravitational field that belongs to the part of the gravitational source can be constructed as T(Ⅱ)μν=c2(D(α)μρDρν(α)-gμνD(α)τγDτγ(α)/4)/4πG, where D(α)μν≡ω(α)μ;ν-ω(α)ν;μ. The static spherically symmetric gravitational field, the missing mass and the gravitational field quantization are discussed.