All Questions
Tagged with gravity lagrangian-formalism
57
questions
2
votes
1
answer
365
views
Gravity in $d$ spacetime dimensions
Given the following action
$$S=\frac{1}{16\pi G}\int d^4x \sqrt {-g}(R+aR^2+bR_{\mu\nu}R^{\mu\nu}+cR_{\mu\nu\lambda\sigma}R^{\mu\nu\lambda\sigma}),$$
which is in 4D.
How to we generalise this ...
user67742
0
votes
1
answer
218
views
How to prove that the nonlinear completion of free massless spin-2 action must be Einstein-Hilbert action?
There is a saying that the nonlinear completion of free massless spin-2 action in Minkovski spacetime (that is Fierz-Pauli action) must be Einstein-Hilbert action up to Lovelock invariants.
I find a ...
- 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
3
votes
2
answers
861
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How would gravitons couple to the Stress-Energy tensor?
How would gravitons couple to the Stress-Energy tensor $T^{\mu\nu}$? How did physicists arrive at this result? I've read that it follows from the analysis of irreducible representations of the 4-...
1
vote
0
answers
320
views
Relation between $f(R)$ gravity and Tensor–vector–scalar (TeVeS) gravity
We know that there is a relation between f(R) gravity and scalar-tensor gravity. By applying the Legendre-Weyl transform, we can receive brans-dicke gravity from $f(R)$ gravity.
If we start with the ...
- 119
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
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
$$
S = -m\int e^{\varphi (x)}\sqrt{\eta_{\alpha \beta}\frac{dx^{\alpha}}{d \lambda}\frac{dx^{\beta}}{...
- 6,564
4
votes
1
answer
200
views
Can the Solar System be assumed a single body concentrated in the Sun?
This question springs from a comment against my question posted on the Space SE
My questions may seem inane, or obvious to most of you real physics people too ...
Any number of sources put the peg ...
- 4,723
33
votes
8
answers
7k
views
Why does no physical energy-momentum tensor exist for the gravitational field?
Starting with the Einstein-Hilbert Lagrangian
$$ 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
2
votes
2
answers
309
views
Is the gravitational constant G a minimum value in some sense?
Assume a central body of mass $M$, and call $a$ the acceleration of a test
body at a distance $r$ due to any interaction whatsoever with the central
body. Is is correct to say that the ratio $a r^2/ M$...
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