Field Equations and Conservation Laws Derived from the Generalized Einstein’s Lagrangian Density for a Gravitational System and Their Influences upon Cosmology

Abstract

Through discussions on the fundamental properties of the generalized Einstein's Lagrangian density for a gravitational system, the theoretical foundations of the modified Einstein's field equations and the Lorentz and Levi-Civita's conservation laws are systematically studied. The theory of cosmology founded on them is discussed in detail and some new properties and new effects of the cosmos are deduced; these new properties and new effects could be tested via future experiments and observations.

A Further Generalized Lagrangian Density and its Special Cases

“…(84,85) might be better than Einstein's conservation laws Eq. (86) [9,12]] and could be tested by future experiments and observations. Eq.…”

“…(4,6) (10) and Eqs. (8,9) represent the gravitational fields. This further generalized Lagrangian density is significantly more general than the Lagrangian densities denoted by Eqs.…”

“…(4,6) and Eqs. (8,9) It must be indicated that, apart from describing a gravitational system with torsion, this further generalized Lagrangian density (i.e. Eqs.…”

Further Study on the Conservation Laws of Energy-Momentum Tensor Density for a Gravitational System

“…In (3), √ −gT μ (M)α is also the energy-momentum tensor density for matter field, which has the same definition as in (1); √ −gt ∼μ (G)α is the energy-momentum pseudo tensor density for gravitational field, which is not tensor density! The relationship between √ −gt ∼μ (G)α of (3) and √ −gT μ (G)α of (1) can be determined by the Lagrangian density of gravitational field √ −g(x)L G (x).…”

“…If the Lagrangian density of gravitational field (4), the definition of u λμ (G)α is different from that in (5) [1,3]. Equation (4) is a simple Lagrangian density of gravitational field which is close to the original formulation of general relativity.…”