All Questions
Tagged with gravity lagrangian-formalism
9
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
$$ T_{EH}^{\mu\nu} = -2 \frac{\delta L_{EH}...
- 9,581
22
votes
1
answer
4k
views
Why is it so coincident that Palatini variation of Einstein-Hilbert action will obtain an equation that connection is Levi-Civita connection?
There are two ways to do the variation of Einstein-Hilbert action.
First one is Einstein formalism which takes only metric independent. After variation of action, we get the Einstein field equation.
...
- 5,971
5
votes
1
answer
634
views
Non-linearity and self-coupling of gravity
I have heard that non-linearity of Einstein's field equations has to do with the fact that gravity self-couples. What does non-linearity have to do with self-coupling?
- 857
2
votes
0
answers
529
views
Derivation of equations of motion in Nordstrom's theory of scalar gravity?
Nordstrom's theory of a particle moving in the presence of a scalar field $\varphi (x)$ is given by
$$
S = -m\int e^{\varphi (x)}\sqrt{\eta_{\alpha \beta}\frac{dx^{\alpha}}{d \lambda}\frac{dx^{\beta}}{...
- 6,564
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
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
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
$$
\mathcal{L}_M=\dfrac{1}{2g^2}F \...
4
votes
2
answers
354
views
Constraints on the Einstein-Hilbert action
The Einstein-Hilbert action is given by
$$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