On stability behaviors of 5D M-theory black objects

Abstract

Abstract Using N = 2 supergravity formalism, we investigate certain behaviors of five-dimensional black objects from the compactification of M-theory on a Calabi–Yau three-fold. The manifold has been constructed as the intersection of two homogeneous polynomials of degrees (ω + 2, 1) and (2, 1) in a product of two weighted projective spaces given by WP 4 ( ω , 1 , 1 , 1 , 1 ) × P 1 . First, we determine the allowed electric charge regions of the BPS and non BPS black holes obtained by wrapping M2-branes on appropriate two cycles in such a proposed Calabi–Yau three-fold. After that, we calculate the entropy of these solutions which takes a maximal value corresponding to ω = 1 defining the ordinary projective space P 4 . For generic values of ω, we show that the non BPS states are unstable. Then, we conduct a similar study of five-dimensional black strings. Concerning the allowed magnetic charge regions of the BPS and non BPS black stringy solutions derived from M5-branes on dual divisors, we calculate the tension taking a minimal value for P 4 . By determining the recombination factor, we show that the non-BPS black string states are stable in the allowed regions in the magnetic charge space.