A Further Generalized Lagrangian Density and its Special Cases

Abstract

By summarizing and extending the Lagrangian densities of the general relativity and the Kibble's gauge theory of gravitation，a further generalized Lagrangian density for a gravitational system is obtained and analyzed in greater detail, which can be used for studying more extensive range of gravitation. Many special cases can be derived from this generalized Lagrangian density, their general characters and peculiarities will be briefly described.

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.…”

“…For the sake of simplicity, we shall use (4) as the Lagrangian density of gravitational field in this paper. For more complicated cases, please refer to [1,3].…”

“…Many general characters and peculiarities of (1) and (3) have been described and discussed in [1][2][3]. In this paper we shall discuss some other characters and peculiarities of (1) and (3) which was not discussed in [1][2][3] yet.…”

“…In this paper we shall discuss some other characters and peculiarities of (1) and (3) which was not discussed in [1][2][3] yet. The main topics to be discussed are:…”