All Questions
Tagged with gravity lagrangian-formalism
57
questions
33
votes
8
answers
7k
views
Why does no physical energy-momentum tensor exist for the gravitational field?
Starting with the Einstein-Hilbert Lagrangian
$$ L_{EH} = -\frac{1}{2}(R + 2\Lambda)$$
one can formally calculate a gravitational energy-momentum tensor
$$ T_{EH}^{\mu\nu} = -2 \frac{\delta L_{EH}...
- 9,581
22
votes
1
answer
4k
views
Why is it so coincident that Palatini variation of Einstein-Hilbert action will obtain an equation that connection is Levi-Civita connection?
There are two ways to do the variation of Einstein-Hilbert action.
First one is Einstein formalism which takes only metric independent. After variation of action, we get the Einstein field equation.
...
- 5,971
8
votes
1
answer
11k
views
Minimal vs. Non-minimal coupling in General Relativity
What is the difference between Minimal vs. Non-minimal coupling in General Relativity? A brief introduction to Minimal Coupling in General Relativity could be useful too.
- 377
7
votes
1
answer
669
views
$\phi R$ term for scalar field in a curved background
Consider the following action for a free scalar field $\phi$ in a curved background
$$S=\int dx\Big( \frac12g^{\mu\nu}\partial_\mu\phi\partial_\nu\phi+\gamma \phi R\Big).$$
Here $g_{\mu\nu}$ is a ...
- 1,586
7
votes
1
answer
3k
views
How is the Lagrangian defined in GR?
Reading about the Schwarzschild metric in general relativity I see that sometimes $$L=g_{\mu\nu}\dot{x}^{\mu}\dot{x}^{\nu}$$ and sometimes $$L=\sqrt{g_{\mu\nu}\dot{x}^{\mu}\dot{x}^{\nu}}.$$
Which is ...
- 789
6
votes
2
answers
338
views
Variation of Maxwell action with respect to the vierbein - Einstein-Cartan Theory
I'm using the reference "Differential Geometry, Gauge Theories and Gravity" by M. Göckeler and T. Schücker and I am having trouble to vary correctly the lagrangian
$$
\mathcal{L}_M=\dfrac{1}{2g^2}F \...
5
votes
1
answer
634
views
Non-linearity and self-coupling of gravity
I have heard that non-linearity of Einstein's field equations has to do with the fact that gravity self-couples. What does non-linearity have to do with self-coupling?
- 857
5
votes
1
answer
708
views
How does General Relativity Emerge from Brans-Dicke Gravity with an Infinite Omega Parameter?
The action for the Brans-Dicke-Jordan theory of gravity is
$$
\\S =\int d^4x\sqrt{-g} \;
\left(\frac{\phi R - \omega\frac{\partial_a\phi\partial^a\phi}{\phi}}{16\pi} + \mathcal{L}_\mathrm{M}\right)....
- 668
4
votes
3
answers
605
views
Conceptual question Einstein-Hilbert action and QFT in curved spacetime
I have a conceptual question regarding the Einstein Hilbert action and QFT in curved spacetimes, both of which I am just about to learn in more depth.
To derive Einstein's equation from an action ...
4
votes
2
answers
354
views
Constraints on the Einstein-Hilbert action
The Einstein-Hilbert action is given by
$$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
200
views
Can the Solar System be assumed a single body concentrated in the Sun?
This question springs from a comment against my question posted on the Space SE
My questions may seem inane, or obvious to most of you real physics people too ...
Any number of sources put the peg ...
- 4,723
4
votes
2
answers
522
views
Why can't we insert gravity in the special relativistic lagrangian?
I am a math student and I have taken four-five lessons about special relativity in a course about Lagrangian and Hamiltonian mechanics, so be patient with me if my question is stupid. My teacher says ...
- 241
4
votes
1
answer
398
views
How to show the number of divergences in quantum gravity is infinite?
As is well known, Quantum Gravity is not renormalisable. How can I prove that for the Gravity tensor, there exists an infinite number of divergences? And why can this not be absorbed by mass or gauge ...
- 143
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
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