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Mass of asymptotically anti–de Sitter hairy spacetimes

Andrés Anabalón, Dumitru Astefanesei, and Cristián Martínez
Phys. Rev. D 91, 041501(R) – Published 13 February 2015

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. Since the mass is determined only by the spatial metric and the scalar field, the above effect appears by considering not only the constraints, but also the dynamic field equations, which relate the spatial metric with the lapse function. In particular, this result 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.

  • Received 16 August 2014

DOI:https://doi.org/10.1103/PhysRevD.91.041501

© 2015 American Physical Society

Authors & Affiliations

Andrés Anabalón1,*, Dumitru Astefanesei2,3,†, and Cristián Martínez4,‡

  • 1Facultad de Artes Liberales and Facultad de Ingeniería y Ciencias, Departamento de Ciencias, Universidad Adolfo Ibáñez, Avenida Padre Hurtado 750 Viña del Mar, Chile
  • 2Instituto de Física, Pontificia Universidad Católica de Valparaíso, Casilla 4059 Valparaíso, Chile
  • 3Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut, 14476 Golm, Germany
  • 4Centro de Estudios Científicos (CECs), Avenida Arturo Prat 514 Valdivia, Chile

  • *andres.anabalon@uai.cl
  • dumitru.astefanesei@ucv.cl
  • martinez@cecs.cl

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Issue

Vol. 91, Iss. 4 — 15 February 2015

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