# A 3d gravity

1. Oct 10, 2016

### shereen1

Dear all
can anyone help me to understand why gravity in 3 dim doesnt have local degree of freedom. How can i compute the degree of freedoms for gravity in and dimension D.
If i consider massless gravity in 3d is the graviton propagating

2. Oct 10, 2016

### haushofer

See e.g.Carlip's book on 2+1 quantum gravity. In three dimensions, the Riemann tensor is completely determined by the Ricci tensor and the metric. Hence the vacuum einstein eqns state the Riemann tensor vanishes. Hence no gravitational waves.

3. Oct 10, 2016

### shereen1

Thank you haushofer i will download the book and have a look on it.

4. Oct 11, 2016

### haushofer

Zwiebach's book onstring theory has a nice exposition of the counting of degrees of freedom in phase space. This amount is proportional to (D-3). So no graviton propagation for D=3.

5. Oct 11, 2016

### shereen1

I will download it to, i also find the book of Steven Carlip interesting too!