All Questions
Tagged with gravity lagrangian-formalism
57
questions
3
votes
1
answer
214
views
Deviation of light rays in a scalar gravity theory (simple modification of Nordström theory)
I'm considering a simple scalar theory of gravity in Minkowski spacetime, which isn't exactly the same as the old Nordström theory. The scalar gravity field $\phi$ and the electromagnetic field $A_a$ ...
- 7,592
0
votes
1
answer
152
views
Replacing $U(1)$ covariant derivative with $GL(4,\mathbb{R})$ covariant derivative... does it give quantum gravity?
I realize that many questions about deriving quantum gravity have been asked multiple times before on this forum, but it hasn't been asked exactly like I am doing here. I would like to know what ...
- 1,548
1
vote
1
answer
53
views
Consistency of substitution of a canonical variable from EoM back into (momentum-less) action
I was reading this answer, where the issue of substituting equations of motion (eoms) into the action is addressed. I am fine with the basic idea that the action principle is destroyed when the eoms ...
- 53
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
$$
\mathcal{S} = \frac{1}{2\pi}\int{d^2x\sqrt{-g}\...
- 2,035
0
votes
0
answers
177
views
Gibbons-Hawking-York (GHY) boundary term
In the Hilbert action, apart from the bulk term, there is a boundary term called GHY $\int d^{3}x\sqrt{h}K$. Why do we choose to calculate this on the $r=$constant hypersurface instead of the $t=$...
- 153
1
vote
0
answers
100
views
Einstein-Hilbert action on lattice
I am wondering how the Einstein-Hilbert action is written on lattice in Euclidean spacetime, and if the metric will still be diagonal if it is possible to write Einstein-Hilbert action on lattice.
- 153
3
votes
0
answers
287
views
Why can't we do a Fourier transform of Einstein-Hilbert action?
In QFT, going to the momentum space to extract the propagators and the vertices is a standard procedure. However, the same is not true for the Einstein-Hilbert action. I want to know the precise ...
- 1,200
4
votes
2
answers
354
views
Constraints on the Einstein-Hilbert action
The Einstein-Hilbert action is given by
$$S_{EH}=\frac{1}{2\kappa}\int\text{d}^4x\sqrt{-g}R$$
Let's say we want to replace it with an action that doesn't reproduce singularities for example $R\...
4
votes
1
answer
256
views
Calculation of gravitational Euclidean action of Schwartzchild BH
I am reading the paper of Gibbons and Hawking Action integrals and partition functions in quantum gravity, Phys. Rev. D 15 (1977) 2752 where they compute the gravitational action of black holes.
In ...
- 2,197
1
vote
1
answer
303
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Spin connection equations of motion from Einstein-Palatini action
I am working through "Supergravity" from Freedman and Van Proeyen. In exercise 8.11 one is tasked to vary the Einstein-Palatini action
$$ S = \frac{1}{2\kappa^2}\int d^Dx\ e e^\mu{}_a e^\nu{}...
- 91
0
votes
1
answer
161
views
Energy-momentum tensor and gravity [closed]
Calculating from a given action the energy-momentum tensor $ \tilde{T}_{\mu \nu} $ (differentiating respect to $ \delta g^{\mu \nu}) $ I can create gravity by a generalization of the Einstein field ...
- 496
1
vote
0
answers
88
views
Diagonalisation of a ghost Lagrangian
I have a ghost Lagrangian of the form
$\mathcal{L}= \bar{c}M_{11}c + \bar{c}M_{12}b + \bar{b}M_{21}c + \bar{b}M_{22}b$
where $c,b$ are the ghosts and $\bar{c}, \bar{b}$ the anti ghost fields, $M_{...
1
vote
1
answer
244
views
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
0
votes
0
answers
53
views
Tree level gravity + SM
Let's write the Standard Model action, replace the Lorentz metric with the GR metric, add the Einstein-Hilbert action, and expand the metric to the first order around the flat one. Do we get anything ...
- 2,921
1
vote
1
answer
246
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Action of a massive spin-2 field
I'm reading about gravitational waves at the moment (mainly using Maggiore's textbook). In it he gives the Pauli-Fierz action for a massive spin-2 field and the action contains the trace of the field. ...
- 420