All Questions
Tagged with gravity lagrangian-formalism
57
questions
2
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answers
32
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
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0
answers
26
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
74
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 ...
- 664
0
votes
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answers
59
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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
$$\mathcal{L}=[\frac{1}{16\pi}\alpha \phi^{\dagger}\phi R+ \frac{1}{2}\phi^{\dagger}_{;\mu}\phi^{;\mu}...
- 1
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What is the boundary action need for topological massive gravity (TMG)?
For pure Einstein gravity with Dirichilet boundary conditions, Gibbons-Hawking-York boundary action is needed to make the variational principle well defined. I am considering the case for topological ...
0
votes
0
answers
67
views
What is the Lagrangian for the interaction of graviphoton with matter?
There are some models that postulate the existence of graviphoton. What is the Lagrangian for the interaction of graviphoton with matter?
- 337
3
votes
0
answers
144
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Is there a Virial theorem in General Relativity?
I know that in Newtonian mechanics one can derive the virial theorem for $N$ gravitating particles
\begin{equation}
2\langle T\rangle=-\langle U\rangle
\end{equation}
where $T$ is the kinetic energy ...
- 4,827
0
votes
1
answer
99
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Extra equation missing in varying the Lagrangian w.r.t to Metric compared to directly applying the Einstein equation in Einstein-Maxwell-scalar theory
So I have been working on this lagrangian whose equations of motion I am trying to derive. The original paper contained six equations, which I found by varying the action to corresponding four fields ...
- 23
1
vote
0
answers
93
views
Yang-Mills-Dirac Lagrangian and Gravity
Let $M$ be a Lorentzian spin $4$ manifold, i.e. admits a spin structure $Spin^+(M)\rightarrow M$, which is just a principal $Spin^+(1,3)$ bundle over $M$, which is compatible with the bundle of ...
- 269
0
votes
1
answer
409
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Einstein-Hilbert Lagrangian in linearized gravity
The Einstein-Hilbert Lagrangian is:
$$\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
604
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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
340
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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?
...
- 1,538
2
votes
1
answer
585
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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
109
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}...
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