The Geometry of Large Causal Diamonds and the No Hair Property of Asymptotically de-Sitter Spacetimes

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dc.creatorGibbons, G. W.
dc.creatorSolodukhin, S. N.
dc.date2007-06-05
dc.date2007-06-12
dc.date.accessioned2026-07-07T10:36:03Z
dc.date.available2026-07-07T10:36:03Z
dc.descriptionIn a previous paper we obtained formulae for the volume of a causal diamond or Alexandrov open set $I^+(p) \cap I^-(q)$ whose duration $τ(p,q) $ is short compared with the curvature scale. In the present paper we obtain asymptotic formulae valid when the point $q$ recedes to the future boundary ${\cal I}^+$ of an asymptotically de-Sitter spacetime. The volume (at fixed $τ$) remains finite in this limit and is given by the universal formula $V(τ) = {4\over 3}π(2\ln \cosh{τ\over 2}-\tanh^2{τ\over 2})$ plus corrections (given by a series in $e^{-t_q}$) which begin at order $e^{-4t_q}$. The coefficents of the corrections depend on the geometry of ${\cal I}^+$. This behaviour is shown to be consistent with the no-hair property of cosmological event horizons and with calculations of de-Sitter quasinormal modes in the literature.
dc.description13 pages, 2 figures, Latex; references added
dc.identifierhttps://arxiv.org/abs/0706.0603
dc.identifierhttp://arxiv.org/abs/0706.0603
dc.identifierPhys.Lett.B652:103-110,2007
dc.identifierdoi:10.1016/j.physletb.2007.06.073
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/179924
dc.subjectHigh Energy Physics - Theory
dc.subjectAstrophysics
dc.subjectGeneral Relativity and Quantum Cosmology
dc.subjectDifferential Geometry
dc.titleThe Geometry of Large Causal Diamonds and the No Hair Property of Asymptotically de-Sitter Spacetimes
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