Why aren't black holes the same as M2 branes?

Question

If there was an M2-brane with the topology of a sphere. Then I can't see why there are not the same thing?
They both have the same topology if we consider the black hole event horizon.
Both seem to have information stored on the surfaces.
But if they are the same thing it would mean an M2 brane acts like a hologram of a bunch of particles inside it's volume. (Due to the holographic principle). So an M2 brane would have to represent more than one particle unlike a string. Is this correct?
If so, then why aren't they considered the same thing?

Ramiro Hum-Sah · Accepted Answer

I offer two reasons:
1) The causal structure is not the same (there is no event horizon for the M2 solution). See equation 4) in "The eleven dimensional supermembrane revisited".
2) As you know, the number of degeneracies of an black hole of charge $Q$ grows exponentially with the charge. In contrast, the number of degrees of freedom  of a stack of $N$ supermembranes grows as $N^{frac{3}{2}}$ see page 10 in "Introductory Lectures on Multiple Membranes".
The $M2$ brane is more like a naked singularity, rather that a black hole. This can be seen from the fact that the value of the dilaton blows up as you in the geometric locus of the supermembrane.

Why aren't black holes the same as M2 branes?

One Answer

Add your own answers!

Ask a Question