All Questions
Tagged with gravity lagrangian-formalism
57
questions
2
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0
answers
33
views
Second-order equations of motion for higher derivative gravity?
We know that Lovelock gravity is the most general theory of gravity possible for Lagrangians which depend only on the metric tensor and the Riemann tensor
\begin{equation*}
L = L \left(g_{\alpha\beta},...
- 1,588
0
votes
0
answers
27
views
Detailed derivation of ESCK gravity and Extended Friedmann Equations with Torsion
Do you know a textbook on the Einstein-Cartan-Sciama-Kibble theory of Gravitation and its application to derive Extended Friedmann Equations with Torsion, which shows the calculations in detail?
2
votes
0
answers
75
views
Variational description of modified Einstein equations
Let us suppose that we have an Einstein equation of the form
$$ R_{(\mu \nu)}-\frac{1}{2} g_{\mu \nu} R=8\pi T_{\mu \nu},$$
where $R$ is an affine connection, which differs from the Levi-Civita ...
- 689
0
votes
0
answers
62
views
Equation of motion for gravity in scalar-tensor theory
I'm trying to derive equation of motion in Higgs scalar-tensor theory with the Lagrangian given by
$$\mathcal{L}=[\frac{1}{16\pi}\alpha \phi^{\dagger}\phi R+ \frac{1}{2}\phi^{\dagger}_{;\mu}\phi^{;\mu}...
- 1
0
votes
0
answers
19
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What is the boundary action need for topological massive gravity (TMG)?
For pure Einstein gravity with Dirichilet boundary conditions, Gibbons-Hawking-York boundary action is needed to make the variational principle well defined. I am considering the case for topological ...
0
votes
0
answers
67
views
What is the Lagrangian for the interaction of graviphoton with matter?
There are some models that postulate the existence of graviphoton. What is the Lagrangian for the interaction of graviphoton with matter?
- 357
3
votes
0
answers
146
views
Is there a Virial theorem in General Relativity?
I know that in Newtonian mechanics one can derive the virial theorem for $N$ gravitating particles
\begin{equation}
2\langle T\rangle=-\langle U\rangle
\end{equation}
where $T$ is the kinetic energy ...
- 4,827
0
votes
1
answer
100
views
Extra equation missing in varying the Lagrangian w.r.t to Metric compared to directly applying the Einstein equation in Einstein-Maxwell-scalar theory
So I have been working on this lagrangian whose equations of motion I am trying to derive. The original paper contained six equations, which I found by varying the action to corresponding four fields ...
- 23
1
vote
0
answers
93
views
Yang-Mills-Dirac Lagrangian and Gravity
Let $M$ be a Lorentzian spin $4$ manifold, i.e. admits a spin structure $Spin^+(M)\rightarrow M$, which is just a principal $Spin^+(1,3)$ bundle over $M$, which is compatible with the bundle of ...
- 269
0
votes
1
answer
419
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Einstein-Hilbert Lagrangian in linearized gravity
The Einstein-Hilbert Lagrangian is:
$$\mathcal{L}_{EH}=\sqrt{-g} R$$
where $g={\rm Det}[g_{\mu\nu}]$ and $R$ is the Ricci scalar. In linearized gravity $g_{\mu\nu}=\eta_{\mu\nu}+h_{\mu\nu}$ and
$$\...
user255856
4
votes
0
answers
110
views
Effective field theories in curved spacetime
Loosely speaking, in flat spacetime, one defines the effective Lagrangian by writing down all possible operators compatible with the symmetries and suppressed by some energy scale, and one usually ...
- 305
4
votes
3
answers
605
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Conceptual question Einstein-Hilbert action and QFT in curved spacetime
I have a conceptual question regarding the Einstein Hilbert action and QFT in curved spacetimes, both of which I am just about to learn in more depth.
To derive Einstein's equation from an action ...
2
votes
1
answer
342
views
Gravity = Yang-Mills squared? What is the Lagrangian?
In the following comment and references, it is mentioned that gravity can be understood as yang mills squared. What is the Lagrangian of a Yang Mills squared theory? Can anyone provide a quick primer?
...
- 1,548
2
votes
1
answer
596
views
Lagrangian of a graviton
Recently in an interview for a phd program I was asked how would you write the lagrangian of a graviton. I answered that since graviton is a massless particle it's lagrangian should be similar to the ...
user321957
3
votes
0
answers
110
views
"Correct" gauge for Chern-Simons terms in 5d?
Consider 5d Einstein-Maxwell-Chern-Simons gravity with action
$$S=\frac{1}{16\pi G}\int d^5x\sqrt{-g}\left[R-\frac{1}{4}F_{\mu\nu}F^{\mu\nu}-\frac{1}{12\sqrt{3}}\frac{\epsilon^{\mu\nu\rho\sigma\lambda}...
- 1,055
3
votes
1
answer
214
views
Deviation of light rays in a scalar gravity theory (simple modification of Nordström theory)
I'm considering a simple scalar theory of gravity in Minkowski spacetime, which isn't exactly the same as the old Nordström theory. The scalar gravity field $\phi$ and the electromagnetic field $A_a$ ...
- 7,592
0
votes
1
answer
152
views
Replacing $U(1)$ covariant derivative with $GL(4,\mathbb{R})$ covariant derivative... does it give quantum gravity?
I realize that many questions about deriving quantum gravity have been asked multiple times before on this forum, but it hasn't been asked exactly like I am doing here. I would like to know what ...
- 1,548
1
vote
1
answer
53
views
Consistency of substitution of a canonical variable from EoM back into (momentum-less) action
I was reading this answer, where the issue of substituting equations of motion (eoms) into the action is addressed. I am fine with the basic idea that the action principle is destroyed when the eoms ...
- 53
0
votes
0
answers
91
views
Variation of the effective two-dimensional action
I am trying to derive the Einstein equations in section 3.1 of Andrew Strominger- Les Houches lectures on Black Holes
where one has to vary the action
$$
\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
views
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