1202.4915 (Chethan N. Gowdigere et al.)

On the smoothness of multi-M2 brane horizons    [PDF]

Chethan N. Gowdigere, Siddharth Satpathy, Yogesh K. Srivastava

We calculate the degree of horizon smoothness of multi- $M2$-brane solution
with branes along a common axis. We find that the metric is generically only
thrice continuously differentiable at any of the horizons. The four-form field
strength is found to be only twice continuously differentiable. We work with
Gaussian null-like co-ordinates which are obtained by solving geodesic
equations for multi-$M2$ brane geometry. We also find different, exact
co-ordinate transformations which take the metric from isotropic co-ordinates
to co-ordinates in which metric is thrice differentiable at the horizon. Both
methods give the same result that the multi-$M2$ brane metric is only thrice
continuously differentiable at the horizon.

View original: http://arxiv.org/abs/1202.4915