5. The problem of the gravitational field of a point mass taking into account the mass of the field itself.
Consider the problem of the gravitational field of a point mass, taking into account the mass of the field itself. It is known that the energy density of the gravitational field is W=-g^2/G. That is, the density of the gravitational
the fields are negative and equal to-g^2/Gc^2. We write down Gauss's theorem for the gravitational field of a point mass
From here you can write a differential equation for the gravitational field strength, or the acceleration of free fall.
The solution to this equation is as follows
This formula can be written as follows
where
Schwarzschild radius.
For r>2Gm/r^2, an asymptotic approximation of Bessel functions can be used
and get the classical formula of Newton's law of gravity
If we assume that the mass of the gravitational field is not negative, but positive, that is, the density of the gravitational field is g^2/c^2
then the differential equation for the point mass field will take the form
And his decision will be
In it, the negative argument of the square root extraction function occurs three times, that is, for the positive mass of the gravitational field of the point mass
the differential equation has no solution.