1111.1897 (S. Kalyana Rama)

Static brane--like vacuum solutions in D \ge 5 dimensional spacetime with positive ADM mass but no horizon    [PDF]

S. Kalyana Rama

We solve D = n + m + 2, m \ge 2, n \ge 1, dimensional vacuum Einstein's equations for static, brane--like solutions. The general solution depends on f(r) and F(r), and the constants (a_0, a_i, M_\infty) obeying a_0 + \sum_i a_i = 1/2 and M_\infty > 0 . For 2 a_0 = 1 and a_i = 0, standard black n-brane solution e^F = f = 1 - \frac{M_\infty} {r^{m - 1}} follows. For a_0^2 + \sum_i a_i^2 > 1/4, the solutions have novel properties : as r decreases from \infty to 0, {\bf (i)} f decreases from 1, reaches a minimum, and increases to \infty, remaining strictly positive; {\bf (ii)} e^F decreases monotonically from 1 to 0; and {\bf (iii)} the `mass' function M = r^{m - 1} (1 - f) decreases monotonically from M_\infty to - \infty . All metric components remain non zero and finite for 0 < r \le \infty, hence there is no horizon or singularity in this range. The presence of the n-dimensional space is crucial for these properties. Such solutions may be naturally anticipated if Mathur's fuzzball proposal for black holes is correct.

View original: http://arxiv.org/abs/1111.1897