The large D black hole dynamics in AdS/dS backgrounds

We have constructed a class of perturbative dynamical black hole solutions in presence of cosmological constant. We have done our calculation in large number of dimensions. The inverse power of dimension has been used as the perturbation parameter and our calculation is valid upto the first subleading order. The solutions are in one to one correspondence with a dynamical membrane and a velocity field embedded in the asymptotic geometry. Our method is manifestly covariant with respect to the asymptotic geometry. One single calculation and the same universal result works for both dS and AdS geometry or in case of AdS for both global AdS and Poincare patch. We have checked our final answer with various known exact solutions and the known spectrum of Quasi Normal modes in AdS/dS.