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Kostik's latest activity
Kostik
replied to the thread
A
Boundary conditions in ##\delta I=0## to derive Einstein's equations
.
They remain fixed so that the boundary term disappears in the integration by parts. I think we are speaking about different things...
Tuesday, 5:58 AM
Kostik
replied to the thread
A
Boundary conditions in ##\delta I=0## to derive Einstein's equations
.
You are misunderstanding my statement. In varying the action, the endpoints of all paths remain fixed. That is the boundary condition I...
Tuesday, 5:53 AM
Kostik
replied to the thread
A
Boundary conditions in ##\delta I=0## to derive Einstein's equations
.
The boundary condition requirement is used in varying the action. I’m not concerned with the E-L equations per se, which are local. I am...
Tuesday, 5:48 AM
Kostik
posted the thread
A
Boundary conditions in ##\delta I=0## to derive Einstein's equations
in
Special and General Relativity
.
Dirac derives Einstein's field equations from the action principle ##\delta I=0## where $$I=\int R\sqrt{-g} \, d^4x$$ (##R## is the...
Tuesday, 5:23 AM
Kostik
replied to the thread
A
Variation of CMFR mass density ##\rho## along a world line
.
Semantics. By "acts on" I am thinking of the object the external force physically acts on, not the change in its motion.
Friday, 10:35 AM
Kostik
replied to the thread
A
Variation of CMFR mass density ##\rho## along a world line
.
If ##\rho## is charged matter, the external force (an electric field) acts on ##\rho##. The divergence in ##v## is the result. In...
Friday, 10:29 AM
Kostik
replied to the thread
A
Variation of CMFR mass density ##\rho## along a world line
.
What does force act on?
Friday, 10:26 AM
Kostik
replied to the thread
A
Variation of CMFR mass density ##\rho## along a world line
.
The force acts on ##\rho## which is what alters ##v^\mu##.
Friday, 10:20 AM
Kostik
replied to the thread
A
Variation of CMFR mass density ##\rho## along a world line
.
I interpret ##d\rho/ds=-\rho {v^\mu}_{ ;\mu}## as the density being inversely proportional to the divergence of the world lines, which...
Friday, 2:00 AM
Kostik
replied to the thread
A
Variation of CMFR mass density ##\rho## along a world line
.
Is there a way to express ##d\rho/ds## in terms of ##f^\mu## in some explicit way?
May 2, 2024
Kostik
posted the thread
A
Variation of CMFR mass density ##\rho## along a world line
in
Special and General Relativity
.
Dirac ("GTR" p. 47) makes an interesting observation immediately after obtaining Einstein's field equations with the simple...
May 1, 2024
Kostik
replied to the thread
A
What does Dirac mean by "the suffixes would not balance"?
.
Yep I noticed that, sorry being very sloppy in this thread. Appreciate all the replies.
Apr 28, 2024
Kostik
reacted to
Orodruin's post
in the thread
A
What does Dirac mean by "the suffixes would not balance"?
with
Like
.
It should also be pointed out that both ##\epsilon## (as defined by Weinberg) are tensor densities of weight -1. The metric determinant...
Apr 28, 2024
Kostik
replied to the thread
A
What does Dirac mean by "the suffixes would not balance"?
.
I understand the issue, no need for worry. Just mentioning in passing the equation in Weinberg "Gravitation and Cosmology", on p. 100...
Apr 28, 2024
Kostik
replied to the thread
A
What does Dirac mean by "the suffixes would not balance"?
.
Oops, yes, I got the second derivative wrong. I see exactly what Dirac means by "the suffixes would not balance". Sloppy ... apologies.
Apr 27, 2024
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