Tunneling between de Sitter and anti-de Sitter black holes in a noncommutative D 3 -brane formalism

We obtain de Sitter (dS) and anti-de Sitter (AdS) generalized Reissner-Nordstrom\char21{}like black hole geometries in a curved ${\mathrm{D}}_{3}$-brane framework, underlying a noncommutative gauge theory on the brane world. The noncommutative scaling limit is explored to investigate a possible tunneling of an AdS vacuum in string theory to dS vacuum in its low energy gravity theory. The Hagedorn transition is invoked into its self-dual gauge theory to decouple the gauge nonlinearity from the dS geometry, which in turn is shown to describe a pure dS vacuum.