Gravity in spacetimes with cosmological constants

Abstract

This thesis is composed of two parts: gravity in the spacetime with a negative/positive cosmological constant. The first part, which is the negative case, devotes to constructing the IIB supergravity dual solution in AdS/CFT correspondence for N = (1, 0) and N = (1/2, 0) non-anticommutative deformed super Yang-Mills theory. The non-anticommutativity is realised on N D3-branes in certain constant self-dual RR 5-form background fields. These background fields can be sourced by a set of additional D3-branes intersecting the N D3's. By taking the near horizon limit to the brane configurations, the supergravity solutions are obtained. The mapping between the bulk scalar fields and the boundary operators for N = (1, 0) case is investigated, and it is found that the spectrum of a particular class of the BPS operators is not deformed by the non-anticommutativity. The second part is for the positive cosmological constant case. In this part, a black fusiform solution with appositive cosmological const in d =5, N = 4 de Sitter supergravity is constructed. The solution is obtained via the braneworld Kaluza-Klein reduction ansatz, and preserves half of the de Sitter supersymmetry. It is static, with the gravitational contraction being balanced by the cosmological repulsion. The black fusiform has an event horizon and a cosmological horizon, and is asymptotically non-de Sitter. The horizons are of an in x S(^2) topology, and contain singularities at the opposite ends due to the nature of the reduction ansatz. Despite the singularities, the solution exhibits some physically properties compatible with that of the regular asymptotically de Sitter spacetimes. The entropy and mass observe the N-bound proposal and the maximal mass conjecture respectively. It also carries a charge which contributes to the 1st law of black hole mechanics.