Horizons cannot save the landscape

International audienceSolutions with anti-D3 branes in a Klebanov-Strassler geometry with positive charge dissolved in fluxes have a certain singularity corresponding to a diverging energy density of the Ramond-Ramond and Neveu-Schwarz-Neveu-Schwarz three-form fluxes. There are many hopes and arguments for and against this singularity, and we attempt to settle the issue by examining whether this singularity can be cloaked by a regular event horizon. This is equivalent to the existence of asymptotically Klebanov-Tseytlin or Klebanov-Strassler black holes whose charge measured at the horizon has the opposite sign to the asymptotic charge. We find that no such Klebanov-Tseytlin solution exists. Furthermore, for a large class of Klebanov-Strassler black holes we considered, the charge at the horizon must also have the same sign as the asymptotic charge and is completely determined by the temperature, the number of fractional branes and the gaugino masses of the dual gauge theory. Our result suggests that antibrane singularities in backgrounds with charge in the fluxes are unphysical, which in turn raises the question as to whether antibranes can be used to uplift anti-de Sitter vacua to deSitter ones. Our results also point to a possible instability mechanism for the antibranes