Spatial infinity in higher dimensional spacetimes

Tetsuya Shiromizu and Shinya Tomizawa
Phys. Rev. D 69, 104012 – Published 14 May 2004
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Abstract

Motivated by recent studies on the uniqueness or nonuniqueness of higher dimensional black hole spacetime, we investigate the asymptotic structure of spatial infinity in n-dimensional spacetimes (n>~4). It turns out that the geometry of spatial infinity does not have maximal symmetry due to the nontrivial Weyl tensor (n1)Cabcd in general. We also address static spacetime and its multipole moments Pa1a2as. Contrasting with four dimensions, we stress that the local structure of spacetimes cannot be unique under fixed multipole moments in static vacuum spacetimes. For example, we consider the generalized Schwarzschild spacetimes which are deformed black hole spacetimes with the same multipole moments as spherical Schwarzschild black holes. To specify the local structure of the static vacuum solution we need some additional information, at least the Weyl tensor (n2)Cabcd at spatial infinity.

  • Received 8 January 2004

DOI:https://doi.org/10.1103/PhysRevD.69.104012

©2004 American Physical Society

Authors & Affiliations

Tetsuya Shiromizu

  • Department of Physics, Tokyo Institute of Technology, Tokyo 152-8551, Japan
  • Department of Physics, The University of Tokyo, Tokyo 113-0033, Japan
  • Advanced Research Institute for Science and Engineering, Waseda University, Tokyo 169-8555, Japan

Shinya Tomizawa

  • Department of Physics, Tokyo Institute of Technology, Tokyo 152-8551, Japan

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Vol. 69, Iss. 10 — 15 May 2004

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