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5
questions
0
votes
0
answers
91
views
Variation of the effective two-dimensional action
I am trying to derive the Einstein equations in section 3.1 of Andrew Strominger- Les Houches lectures on Black Holes
where one has to vary the action
$$
\mathcal{S} = \frac{1}{2\pi}\int{d^2x\sqrt{-g}\...
- 2,035
1
vote
0
answers
100
views
Einstein-Hilbert action on lattice
I am wondering how the Einstein-Hilbert action is written on lattice in Euclidean spacetime, and if the metric will still be diagonal if it is possible to write Einstein-Hilbert action on lattice.
- 153
1
vote
1
answer
244
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Demonstration of the Brans-Dicke's Lagrangian
The Lagrangian in general relativity is written in the following form:
$$
\begin {aligned}
\mathcal {L} & = \frac {1} {2} g ^ {\mu \nu} \nabla_{\mu} \phi \nabla_{\nu} \phi-V (\phi) \\
& = R + \...
user87745
7
votes
1
answer
3k
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How is the Lagrangian defined in GR?
Reading about the Schwarzschild metric in general relativity I see that sometimes $$L=g_{\mu\nu}\dot{x}^{\mu}\dot{x}^{\nu}$$ and sometimes $$L=\sqrt{g_{\mu\nu}\dot{x}^{\mu}\dot{x}^{\nu}}.$$
Which is ...
- 789
3
votes
2
answers
861
views
How would gravitons couple to the Stress-Energy tensor?
How would gravitons couple to the Stress-Energy tensor $T^{\mu\nu}$? How did physicists arrive at this result? I've read that it follows from the analysis of irreducible representations of the 4-...
