Choice of the Lagrangian density for the gravitational field.
Ruslan Sharipov. 1 ... 10 11 12 ... ru The Lagrangian L is included in the action integral, which we considered in the previous post " The Lagrangian approach to deriving the equations of gravity in the new theory ". The Lagrangian L itself is expressed in the form of a three-dimensional integral of the Lagrangian density. As we see from these formulas, the Lagrangian density is the sum of two terms — the Lagrangian density of the gravitational field and the Lagrangian density of matter. The Lagrangian density of matter describes the dynamics of matter. It depends on a specific type of matter that can be cosmic dust, gas, liquid, solid, or even dark matter. We will leave the choice of Lagrangian density of matter for later. Now let's consider the choice of the Lagrangian density for the gravitational field. The dynamic variables of the gravitational field in the new theory are a three-dimensional metric and a scalar function denoted by the letter g with two zeros.