The Schwarzschild solution in the small region limit is a non-inertial system in the Minkowski space. This means that the gravitational field is not true:
Почему решение Шварцшильда не является истинным гравитационным полем
Dear Stefan,
We knew that. But now it is also a disposable field. This news is not unexpected for us.
Best regards, Valery
You can illustrate the above with a picture. The Schwarzschild solution in the small volume limit is an accelerated frame of reference in ordinary pseudo-revolutionary coordinates. While for the true gravitational field, the picture is an approximation using tangent spaces.
Note that for the Schwarzschild solution sqrt (-1) = 1, which will exclude the true gravitational field from the solutions of the Einstein equation
Preprint Exact equation of gravity field based on Einstein's separati...
Dear Stefan,
I disagree with that. You have no convincing arguments. With or without lambda, the gravitational field of solutions to the Einstein equation is not true, there is no local conservation law and there is a singularity. Renaming lambda to field energy philology.
Best regards, Valery
Dear Stefan,
Gik = 0 occurs because the condition sqrt (-1) turns off the gravitational field. This is how one can explain why the gravitational field given by Einstein's equation (5) is not true. The introduction of Lambda in (5) does not change anything.
Only eliminating sqrt (-1) from the equation corrects this situation.
Best regards, Valery
"Einstein's field equations with the cosmological constant and without the restriction sqrt(-g) = 1 form in their mixed-tensor representation the conservation law of total energy, momentum, and stress."
he point is that the condition sqrt (-g) = 1 is ALWAYS contained in the Einstein equation. See einstein_skpaw_844_15.pdf, eq (6)+(3a) .
Best regards, Valery
The lambda term is another term in the conservation law (see the last equation). Nothing more.
Equation conditions without sqrt (-g) = 1 becomes meaningful when administered tensor gravitational field energy-momentum
Dear Stefan, "The point is that the condition sqrt (-g) = 1 is NOT ALWAYS contained in the Einstein equation."
Give an example. Equation (5) is Einstein's vacuum equation. This automatically implies that sqrt (-g) = 1.
Best regards, Valery
Dear Stefan, "Does the Schwarzschild metric have the determinant g = -1, so that sqrt(-g)=1? Of course not."
Of course yes! Count it, it's simple.
Best regards, Valery
The Schwarzschild solution in the small region limit is a non-inertial system in the Minkowski space. This means that the gravitational field is not true.
Einstein's equations in chronological order
Equation 1 states the property of all solutions sqrt (-g) = 1. Those. solution of the Einstein equation has removable gravitational fields.
Equation 1means that any solution of the Einstein equation for a certain choice of coordinates has a determinant g = -1. This is shown by Schwarzschild. In this case, in the small-volume approximation, the solution turns out to be a field of inertia in flat space, i.e., this solution is not a true gravitational field.
Dear Stefan,
"So you see, that Einstein's field equations with the condition sqrt (-g) = 1 are a very special case, that is not always comfortable." This is the usual Einstein equation, just like any other. And has the same solutions.
Best regards, Valery
Solutions with the same determinant.
and the Schwarzschild metric
gik=diag(-B,A,r²,r²sin² theta),
and the Minkowski metric
g'ik=diag(-1,1,r²,r²sin² theta),
In Einstein's equation, the gravitational field is off. There is no gravitational field as a source.
In addition, solutions to the Einstein equation have the same determinant as the Minkowski metric.
"So you see, that Einstein's field equations with the condition sqrt (-g) = 1 are a very special case, that is not always comfortable."
So what? The solutions of the Einstein equation have the determinant of the Minkowski space. Always.
Best regards, Valery
Dear Stefan,
I claim that Einstein's equation is in the form (5). The complete Einstein equation for fixed coordinates. Gravitational field equation (7). Includes the gravitational energy tensor and is accurate.
Best regards, Valery
Equation (7). Satisfies all Einstein's requirements for the gravitational field equation. While Einstein's equation does not contain the energy tensor of the gravitational field as a source.
The singularity in the solution of equation (7) disappeared. What changes the idea of objects called "black holes". (dotted line singular Schwarzschild solution)
Preprint Exact equation of gravity field based on Einstein's separati...
Dear Stefan,
I see no point in internal decisions, it has nothing to do with physics.
I don't see any other exact solution like (7).
Best regards, Valery
Уравнение Эйнштейна. История с продолжением
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