# Grassmann-odd extra dimensions and gravity

Take a world with $D=3+n$ space-time dimensions, where $n$ are extra space-like dimensions.

With extra-dimensional newton gravity

$$F=G_N(D)\dfrac{Mm}{r^{2+n}}$$

Can $n$ affect IF the extra dimension is "Grassmann"-like or "time-like" instead "space-like"?

• To reopen this post (v1). consider to only ask one subquestion per post. – Qmechanic Sep 15 '18 at 11:41
• Reformulation with unified argument. – riemannium Sep 15 '18 at 11:42
• What type of dimensions are the first 3 in $D=3+n$? – Qmechanic Sep 15 '18 at 11:43
• Space-like, of course...I ask this, because...I know some bits of the answer...But I am curious of how others see the "issue" if "n" are not "space-like" dimensions... – riemannium Sep 15 '18 at 11:46
• The subquestion about multiple time dimensions seems to be a duplicate of physics.stackexchange.com/q/43322/2451 , physics.stackexchange.com/q/43630/2451 and links therein. – Qmechanic Sep 15 '18 at 11:48

## 1 Answer

Grassmann-odd dimensions have no topology or metric. One cannot assign a numerical value to the soul of a supernumber, cf. this related Phys.SE post.

So to answer the question what happen to gravity (in a non-relativistic limit) of some superfield theory, one can remove all the $\theta$-variables, and ask the same question in the corresponding component theory.