Abstract
Flat-space limit is well-defined for asymptotically AdS spacetimes written in coordinates called the BMS gauge. For the three-dimensional Einstein gravity with a negative cosmological constant, we calculate the quasi-local energy momentum tensor in the BMS gauge and take its flat-space limit. In defining the flat-space limit, we use the BMS/GCA correspondence which is a duality between gravity in flat-spacetime and a field theory with Galilean conformal symmetry. The resulting stress tensor reproduces correct values for conserved charges of three dimensional asymptotically flat solutions. We show that the conservation relation of the flat-space energy-momentum tensor is given by an ultra-relativistic contraction of its relativistic counterpart. The conservation equations correspond to Einstein equation for the flat metric written in the BMS gauge. Our results provide further checks for the proposal that the holographic dual of asymptotically flat spacetimes is a field theory with Galilean conformal symmetry.
Highlights
This method has met with some very interesting recent successes
In defining the flat-space limit, we use the BMS/GCA correspondence which is a duality between gravity in flat-spacetime and a field theory with Galilean conformal symmetry
Our results provide further checks for the proposal that the holographic dual of asymptotically flat spacetimes is a field theory with Galilean conformal symmetry
Summary
Instead of Fefferman-Graham gauge which is a common way of defining asymptotically AdS space-times one can write a generic solution of three dimensional Einstein gravity with cosmological constant, S. The parent CFT in the study of [1, 2] is on the plane and the contracted coordinate was the x-coordinate This assumptions dictated some restriction on the centrally extended algebra in such a way that in order to reproduce the known results of flat-space gravity the parent CFT must be non-unitary. Where CLL and CLM are the central charges which appear respectively in the [Lm, Ln] and [Lm, Mn] parts of the algebra (2.17).2 It was shown in [14] that (3.1) gives the correct entropy for the cosmological horizon of the three dimensional Einstein gravity solution which is the flat limit of BTZ black holes. This is an evidence in favour of the correctness of BMS/GCA correspondence
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