Mass of asymptotically anti-de Sitter hairy spacetimes

TL;DR

This paper investigates how to properly define the mass of asymptotically anti-de Sitter spacetimes with scalar fields, showing that boundary conditions preserving symmetry are essential for consistent mass calculation.

Contribution

It demonstrates that the standard mass definition applies only under boundary conditions compatible with AdS symmetry in scalar field spacetimes.

Findings

Mass can be identified from the lapse function coefficient only with symmetry-compatible boundary conditions.

Some existing mass prescriptions fail when scalar fields break asymptotic AdS invariance.

Proper boundary conditions are crucial for consistent mass definitions in hairy AdS spacetimes.

Abstract

In the standard asymptotic expansion of four dimensional static asymptotically flat spacetimes, the coefficient of the first subleading term of the lapse function can be identified with the mass of the spacetime. Using the Hamiltonian formalism we show that, in asymptotically locally anti-de Sitter spacetimes endowed with a scalar field, the mass can read off in the same way only when the boundary conditions are compatible with the asymptotic realization of the anti-de Sitter symmetry. In particular, this implies that some prescriptions for computing the mass of a hairy spacetime are not suitable when the scalar field breaks the asymptotic anti-de Sitter invariance.