Tagged Questions
0
votes
1answer
95 views
proper variation of action term
I have a term I want to vary by a field, $\phi$.
$$
`S' = \frac{-1}{2}\,\sqrt{-g}\,g^{\mu\,\nu}\,\delta\left[h(\phi)\,\partial_{\mu}\phi\,\partial_{\nu}\phi \right].
$$
Is it correct to get this?
...
4
votes
1answer
447 views
Lagrangian for Relativistic Dust derivation questions
In most GR textbooks, one derives the stress energy tensor for relativistic dust:
$$
T_{\mu\nu} = \rho v_\mu v_\nu
$$
And then one puts this on the right hand side of the Einstein's equations. I ...
1
vote
1answer
478 views
2nd order variation of Hilbert-Einstein action + Gibbons-Hawking-York boundary term
While the first order metric variation of Hilbert-Einstein action plus Gibbons-Hawking-York boundary term is well-known and takes the form:
$\delta S_{HE}+\delta S_{GHY}=-\frac{1}{16\pi G}\int d^3x ...
8
votes
1answer
1k views
Explicit Variation of Gibbons-Hawking-York Boundary Term
Are there any references that present the explicit variation of the Hilbert-Einstein action plus the Hawking-Gibbons-York boundary term, and demonstrate the cancellation of the normal derivatives of ...
