The tag has no wiki summary.

learn more… | top users | synonyms

3
votes
3answers
117 views

The Hole Argument

I have read explanations of this but haven't really understood. Given a spacetime $(M,g)$ I have read that if I represent the metric in some coordinates $(x,y,z,t)$ as $g(x,y,z,t)$ and then in another ...
5
votes
1answer
93 views

Kac-Moody algebras in 5 dimensional Kaluza-Klein theory

I am trying to make sense to the issue of how does the Kac-Moody algebra encode the symmetries of the non-truncated theory. Let's contextualize a little bit. Ok, so in the 5 dimensional Kaluza-Klein ...
2
votes
1answer
117 views

Are diffeomorphisms a proper subgroup of conformal transformations?

The title sums it pretty much. Are all diffeomorphism transformations also conformal transformations? If the answer is that they are not, what are called the set of diffeomorphisms that are not ...
5
votes
1answer
118 views

Supergravity, torsion and diffeomorphism invariance

The action for $N=1$ supergravity in an $4$ spacetime dimenions is $$ S= \int e\left( R + \overline{\psi}_a \gamma^{abc} D_b \psi_c \right) $$ Here $R$ is the scalar curvature, $e=\det(e_{a\mu})$, ...
2
votes
0answers
51 views

General covariance and global Poincaré algebras

Reading an article (page 7) I read this: Just as ordinary general covariance may be regarded as the local gauge symmetry corresponding to the global Poincare algebra and local gauge invariance ...
4
votes
2answers
161 views

Hilbert action's invariance under general coordinate changes

In an article, when considering invariance of the Hilbert action under a general coordinate change this formula appears for how the metric changes ...
2
votes
2answers
177 views

What transformation is the metric of general relativity invariant under?

My limited understanding of metrics comes from Cartan. From there, I understand that a metric is something invariant under certain transformations, e.g. Lorentz in special relativity. But with the ...
4
votes
1answer
122 views

Field action of linearized gravity associated with spin-2 particle in Thorne book

In MTW book there is one exercise in which there was proposed to discuss linearized tensor gravity, which is represented as $$ g_{\mu \nu} = \eta_{\mu \nu} + h_{\mu \nu}, \quad \eta_{\mu \nu} = ...
5
votes
1answer
336 views

6 independent Einstein field equations?

I can't understand the comment on page 409, Gravitation, by Misner, Thorne, Wheeler It follows that the ten components $G_{\alpha\beta} =8\pi T_{\alpha\beta}$ of the field equation must not ...
2
votes
1answer
117 views

Are background independence and diffeomorphism invariance the same?

What is the difference between background independence, which loop quantum gravity formalism claims to have, and diffeomorphism invariance?
6
votes
1answer
436 views

Diffeomorphism Invariance of General Relativity

I'm sorry I know this has been asked before, but I'm still a bit confused. I understand that an active diffeomorphism $\varphi:M\to M$ can be equivalently viewed as a coordinate transformation so that ...
9
votes
1answer
624 views

The Role of Active and Passive Diffeomorphism Invariance in GR

I'd like some clarification regarding the roles of active and passive diffeomorphism invariance in GR between these possibly conflicting sources. 1) Wald writes, after explaining that passive ...
6
votes
0answers
112 views

Time diffeomorphisms breaking in inflation

I am currently working on the topic of inflation. It seems that at the stage of inflation, the universe can be described as a de Sitter space. In such a space, all spacetime diffeomorphisms are ...
12
votes
2answers
560 views

Gauge invariance and diffeomorphism invariance in Chern-Simons theory

I have studied Chern-Simons (CS) theory somewhat and I am puzzled by the question of how diff. and gauge invariance in CS theory are related, e.g. in $SU(2)$ CS theory. In particular, I would like to ...
4
votes
1answer
413 views

failing to see the conundrum in the Einstein hole argument

I've been reading about the Einstein hole argument, and i fail to understand what makes active diffeomorphisms "special" compared to passive diffeomorphismsm also known as good old coordinate ...
11
votes
2answers
614 views

argument about fallacy of diff(M) being a gauge group for general relativity

I want to outline a solid argument (or bulletpoints) to show how weak is the idea of diff(M) being the gauge group of general relativity. basically i have these points that in my view are very solid ...
2
votes
0answers
265 views

composition of space expansion and movement as a gauge invariance

suppose i have a space-time where we have one point-like object* which we will call movement space probe or $\mathbf{M}_{A}$ for short, and it will be moving with constant velocity $V^A_{\mu}$ in ...
4
votes
2answers
409 views

Diff(M) and requirements on GR observables

This question is kind of inspired in this one: Diff(M) as a gauge group and local observables in theories with gravity The conundrum i'm trying to understand is how is derived the (quite) ...