Asymptotically (anti)-de Sitter solutions in Gauss-Bonnet gravity without a cosmological constant

Abstract

In this paper we show that one can have asymptotically de Sitter (dS), anti-de Sitter (AdS) and flat solutions in Gauss-Bonnet gravity without any need to a cosmological constant term in field equations. First, we introduce static solutions whose 3-surfaces at fixed $r$ and $t$ have constant positive ($k=1$), negative ($k=-1$), or zero ($k=0$) curvature. We show that for $k=\pm 1$, one can have asymptotically dS, AdS and flat spacetimes, while for the case of $k=0$, one has only asymptotically AdS solutions. Some of these solutions present naked singularities, while some others are black hole or topological black hole solutions. We also find that the geometrical mass of these 5-dimensional spacetimes is $m+2\alpha |k|$, which is different from the geometrical mass, $m$, of the solutions of Einstein gravity. This feature occurs only for the 5-dimensional solutions, and is not repeated for the solutions of Gauss-Bonnet gravity in higher dimensions. We also add angular momentum to the static solutions with $k=0$, and introduce the asymptotically AdS charged rotating solutions of Gauss-Bonnet gravity. Finally, we introduce a class of solutions which yields an asymptotically AdS spacetime with a longitudinal magnetic field which presents a naked singularity, and generalize it to the case of magnetic rotating solutions with two rotation parameters.

13 pages, no figure

References in corpus (22)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• Measurements of Omega and Lambda from 42 High-Redshift Supernovae
• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters
• Cosmological Imprint of an Energy Component with General Equation of State
• The Case for a Positive Cosmological Lambda-term
• Cosmological Results from High-z Supernovae
• Gauss-Bonnet Black Holes in AdS Spaces
• A measurement by BOOMERANG of multiple peaks in the angular power spectrum of the cosmic microwave background
• DASI First Results: A Measurement of the Cosmic Microwave Background Angular Power Spectrum
• The Universe as a Domain Wall
• Black Hole Thermodynamics and Negative Entropy in deSitter and Anti-deSitter Einstein-Gauss-Bonnet gravity
• A High Spatial Resolution Analysis of the MAXIMA-1 Cosmic Microwave Background Anisotropy Data
• Topological black holes in the dimensionally continued gravity
• Cosmological Solutions of Horava-Witten Theory
• Anti-de Sitter Black Holes, Thermal Phase Transition and Holography in Higher Curvature Gravity
• Anti-de Sitter Black Hole Thermodynamics in Higher Derivative Gravity and New Confining-Deconfining Phases in dual CFT
• Black holes with topologically nontrivial AdS asymptotics
• Braneworld Cosmology in (Anti)--de Sitter Einstein--Gauss--Bonnet--Maxwell Gravity
• Charged Rotating Black Branes in anti-de Sitter Einstein-Gauss-Bonnet Gravity
• Magnetic Branes in Gauss-Bonnet Gravity
• De Sitter space versus Nariai Black Hole: stability in d5 higher derivative gravity
• Accelerated Expansion of the Universe in Gauss-Bonnet Gravity

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