On dimension of tetrads in effective gravity

G. E. Volovik

*Low Temperature Laboratory, Aalto University, School of Science and Technology, P.O. Box 15100, FI-00076 AALTO, Finland*

Landau Institute for Theoretical Physics, 142432 Chernogolovka, Russia

**Abstract**

Two different sources of emergent gravity lead to the inverse square of
length dimension of metric field, [g_{μν}]=1/[l]^{2}, as distinct
from the conventional dimensionless metric, [g_{μν}]=1, for c = 1. In both scenarios all the physical quantities, which obey
diffeomorphism invariance, such as the Newton constant, the scalar
curvature, the cosmological constant, particle masses, fermionic and
scalar bosonic fields, etc., are dimensionless.