On Stability Behaviors of 5D M-theory Black Objects

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 $(\omega+2,1)$ and $(2,1)$ in a product of two weighted projective spaces given by $\mathbb{WP}^{4}(\omega,1,1,1,1) \times\mathbb{P}^{1}$. 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 $\omega=1$ defining the ordinary projective space $\mathbb{P}^{4}$. For generic values of $\omega$, 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 $\mathbb{P}^{4}$. 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.