Questions tagged [gauss-bonnet]
21 questions
18
votes
2 answers
How to show the Gauss-Bonnet term is a total derivative?
It is well-known that the Gauss-Bonnet term
$$\mathcal L_G =R^2 -4 R_{\mu\nu}R^{\mu\nu}+R_{\mu\nu\rho\sigma}R^{\mu\nu\rho\sigma}\tag 1$$
does not contribute to the equations of motion when adding it to the four-dimensional Einstein–Hilbert action.…
user146681
17
votes
2 answers
Deriving Gauss-Bonnet Gravity (Or just higher order corrections)
I have been working for some time now on deriving the equations of motion (EOM) for the Gauss-Bonnet Gravity, which is given by the action:
$$\int d^D x \sqrt{|g|} (R^2-4R_{ab}R^{ab}+R_{abcd}R^{abcd}).$$
I've tried for some time to derive the…
tanzhongm
- 480
10
votes
0 answers
Gauss-bonnet gravity constraints from string theory
Recently there have been advances in observational constraints of gravity theories that contain scalars coupled to the gauss-bonnet topological term:
http://arxiv.org/abs/0704.0175
http://arxiv.org/abs/1204.4524
my understanding (from what the above…
lurscher
- 14,933
5
votes
1 answer
Gauss-Bonnet term in Physics
Given a 4-dimensional compact manifold (torsion free), the Euler characteristic is defined as:
$$E_4 ~=~ \int \epsilon_{abcd}R^{ab} \wedge R^{cd}$$
with $R^{ab}$ is the curvature 2-form. Perturb the connection 1-form (represent by $\delta…
user109798
- 651
5
votes
1 answer
Gauss-Bonnet theorem in the Hawking/Ellis book
At the page 336 of Hawking, Ellis: The Large Scale Structure of Space-Time, the Gauss-Bonnet theorem is stated as
$$\int_H \hat{R}\ d\hat{S} = 2\pi \chi(H) \qquad (1)$$
with
$$\hat{R} = R_{abcd} \hat{h}^{ac} \hat{h}^{bd}$$
and induced metric on the…
Ivica Smolić
- 285
4
votes
0 answers
$\langle TT\rangle$ correlator of the boundary CFT from metric fluctuations in the bulk gravity
Is there a reference which explains how the $\langle TT\rangle $ correlation of the boundary conformal field theory (CFT) can be holographically calculated from the bulk gravity? (..I am often getting referred to some paper by Skenderis et. al but…
Student
- 4,611
3
votes
1 answer
Euler number of the world sheet
I have a question in the section 3.2 "The Polyakov path integral" in Polchinski's string theory p. 83.
Given
$$ \chi=\frac{1}{4 \pi} \int_M d^2 \sigma g^{1/2} R + \frac{1}{2 \pi} \int_{\partial M} ds \,\, k \,\,\,\, (3.2.3b) $$
It is said
We…
user26143
- 6,571
3
votes
0 answers
Graviton propagator, and Gauss-Bonnet gravity
Let's say we consider Einstein's Lagrangian from GR. In linearized gravity, we would expand the Ricci scalar to quadratic order in the perturbation parameter to find the propagator.
My question is as follows:
Let's say we consider the Gauss Bonnet…
Tushar Gopalka
- 1,212
3
votes
1 answer
Is the Palatini-Lovelock action of order $k$ topological in $2k$ dimensions?
I am interested in Lovelock actions in the metric-affine (or Palatini) formalism. It is well-known that the metric version (starting from the Levi-Civita curvature) of the Lovelock lagrangian of order $k$ is a topological term in $2k$ dimensions.…
Gravitino
- 567
- 4
- 19
3
votes
1 answer
What is the physical significance of Gaussian curvature in condensed matter physics?
In basic models concerning two-level systems, we deal with manifolds such as the Bloch sphere and torus. I believe that the Chern number is what dominates the theory in terms of ties to differential geometry, but what how could one look at the…
TribalChief
- 591
2
votes
0 answers
Calculating Gaussian Curvature for metric
I am trying to calculate Gaussian curvature of an optical metric
$$
d \sigma^2=\frac{r\left(\omega_{\infty}^2-\omega_e^2\right)+2 m \omega_e^2}{(r-2 m) \omega_{\infty}^2}\left(\frac{d r^2}{1-\frac{2 m}{r}}+r^2 d \varphi^2\right)
$$
The paper gives…
sabir ali
- 21
2
votes
0 answers
Gauss-Bonnet term in tetrad formalism
In eq. 4 of https://arxiv.org/abs/hep-th/9508128 it is stated that the Gauss-Bonnet term for gravity in 4d can be written as
$$
S=\frac{1}{4}\int d^{4}x\,\epsilon^{\mu\nu\alpha\beta}\epsilon_{abcd}R_{\mu\nu}^{\quad ab}R_{\alpha\beta}^{\quad…
user367349
- 21
2
votes
0 answers
Duality and corrections to second-order gravity without and with torsion terms
Recently, there appeared a paper by Giacomo Pollari, A Nieh-Yan-like topological invariant in General Relativity, where the action for gravity looks like:
$$S_g=S_{EHP}+S_{HO}+S_{PO}+S_{GB}+S_{NY}+S_{ET}$$
and where
$$S_{EHP}=\alpha_0\int e^I\wedge…
riemannium
- 6,843
2
votes
0 answers
Variation of the Gauss-Bonnet term
We have the Gauss-Bonnet term
$$L_{GB}=R^{2}-4R_{\mu\nu}R^{\mu\nu}+R_{\mu\nu\rho\sigma}R^{\mu\nu\rho\sigma}$$
where $R$, $R_{\mu\nu}$ and $R_{\mu\nu\rho\sigma}$ are the Ricci scalar, the Ricci tensor and the Riemann tensor respectively. The…
john
- 43
2
votes
0 answers
Gauss-Bonnet correction to Carnot's efficiency
Could anyone tell explicitly, how did the author get the $T_c$ vs. $\alpha$ plot given in Figure 3 in Gauss-Bonnet Black Holes and Holographic Heat Engines Beyond Large N.
user100419
- 31