A Gravitational Stress Tensor for Asymptotically AdS Spaces from Holography

Abstract

This thesis presents a study of the quasilocal stress tensor proposed by Brown and York in 1993 from the perspective of the AdS/CFT correspondence which was carried out by Kraus and Balasubramanian in 1999. The thesis begins with a quick review of the essential ideas of AdS/CFT. The subsequent chapter explains the variational principle for the gravitational action and explains the need for introducing the Gibbons-Hawking-York boundary term and the nondynamical counterterm in the action. The chapter following this elucidates the challenges involved in describing a local stress-energy tensor for the metric of a spacetime and describes the earlier mentioned proposal by Brown and York. Later, we work out in detail and confirm the expressions for quasilocal stress tensor for asymptotically AdS spacetimes in various dimensions and also show that these lead to the right masses and momenta for various spacetimes as shown by Kraus and Balasubramanian. The interpretation of the quasilocal stress tensor from the CFT side is also discussed. We verify the result obtained by Brown and Henneaux and also make a key observation that for metrics that satisfy the fall-offs suggested by them, one may be able to drop the GHY term in the action thus leading to a modified stress tensor that could potentially give the same (correct) results for mass and momenta of various spacetimes.