A tale of two theories of gravity in asymptotically Anti-de Sitter spacetime

A tale of two theories of gravity in asymptotically Anti-de Sitter spacetime

Blog Article

Abstract We consider two BF formulations of the theory of gravity with a negative cosmological constant, of Plebanski and of MacDowell-Mansouri.Both give the standard Einstein grandpas best equations in the bulk but differ in expressions of edge charges.We compute the asymptotic charges explicitly in both theories for AdS-Schwarzschild, AdS-Kerr, and AdS-Taub-NUT solutions.We find that while in the case of the Plebanski theory the charges are divergent, they are finite for MacDowell-Mansouri theory.Furthermore, we show that in the case of the arbitrary asymptotically AdS here spacetimes, MacDowell-Mansouri asymptotic charges, action, and symplectic form are all finite.

Therefore MacDowell-Mansouri theory of gravity in asymptotically AdS spaces does not need any counterterms.