All Questions
Tagged with gravity lagrangian-formalism
57
questions
2
votes
1
answer
374
views
$d$-dimensional Einstein equations
I am reading this paper https://arxiv.org/abs/2002.02577. On page 13, it is written that the $d$-dimensional Einstein equations are
$$G_{\mu\nu}+\frac{(d-1)(d-2)}{6}\Lambda g_{\mu\nu}=8\pi T_{\mu\nu}...
- 43
3
votes
1
answer
142
views
Boundary terms for stringy correction to GR
We know that there can be possible higher derivative corrections (stringy corrections) to the Einstein-Hilbert action. In GR, to ensure that we get the Einstein Field equations from varying the E-H ...
- 1,182
2
votes
1
answer
128
views
Hamiltonian of a quantum field that is minimally coupled to gravity
The action for the gravitational field is known as the Einstein-Hilbert action:
$$\begin{equation}
S_{G}=\int d^4 x \sqrt{|g|} R
\end{equation}$$
where $R$ is the Ricci scalar.
The ...
- 99
2
votes
1
answer
190
views
Experimental methods to identify C.O.G of a highly heterogeneous cube
While taking to a college about calculating the centre of gravity of multibody basic objects, the question was raised on how one would determine the C.O.G of a highly heterogeneous object of a given ...
- 121
3
votes
2
answers
85
views
How does $r$ depend on $\varphi$ in the Schwarzschild metric?
I am confused about the Wikipedia derivation of the equation
for geodesic motion in the Schwarzschild spacetime. The derivation of this equation involves variation with respect to the longitude $\...
- 311
7
votes
1
answer
669
views
$\phi R$ term for scalar field in a curved background
Consider the following action for a free scalar field $\phi$ in a curved background
$$S=\int dx\Big( \frac12g^{\mu\nu}\partial_\mu\phi\partial_\nu\phi+\gamma \phi R\Big).$$
Here $g_{\mu\nu}$ is a ...
- 1,586
4
votes
2
answers
522
views
Why can't we insert gravity in the special relativistic lagrangian?
I am a math student and I have taken four-five lessons about special relativity in a course about Lagrangian and Hamiltonian mechanics, so be patient with me if my question is stupid. My teacher says ...
- 241
2
votes
0
answers
116
views
The origin of action of the scalar-tensor theory of gravity
I just started a project on the scalar-tensor theory of gravity and read up few papers and books related to it. In most of the books the idea and need for this theory is explained and from there the ...
- 49
0
votes
1
answer
725
views
Energy Momentum Tensor for a Dirac Fermion coupled to external gravity
A small (and perhaps trivial :-() calculation is troubling me somewhat.
Consider the action of a right-handed Dirac fermion coupled to external gravity (a background gravitational field). The action ...
- 2,095
6
votes
2
answers
338
views
Variation of Maxwell action with respect to the vierbein - Einstein-Cartan Theory
I'm using the reference "Differential Geometry, Gauge Theories and Gravity" by M. Göckeler and T. Schücker and I am having trouble to vary correctly the lagrangian
$$
\mathcal{L}_M=\dfrac{1}{2g^2}F \...
4
votes
0
answers
230
views
Closed trajectories for Kepler problem with classical spin-orbit corrections?
Kepler problem explains closed elliptic trajectories for planetary systems or in Bohr's classical atomic model - let say two approximately point objects, the central one has practically fixed position,...
- 960
4
votes
1
answer
398
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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
0
votes
1
answer
90
views
Effective lagrangian in minisuperspace
I am driving the paper (http://arxiv.org/abs/gr-qc/0412089) as part of my research project, i have some problems to obtain the effective Lagrangian for Einstein Hilbert action the eq.(4). If any one ...
- 21
-1
votes
1
answer
69
views
why objects interacting through gravity come and rotate in a plane?
Imagine thee planets interacting through gravity, mathematically how should they come and rotate in a same plane, like planets and sun?
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