2017/12/31 by Ben David Normann, Sigbjørn Hervik, Angelo Ricciardone +1
Mathematics · Physics and Astronomy · #Attractor #Black Holes and Theoretical Physics #Cosmological constant #Cosmology and Gravitation Theories #Equation of state #Friedmann–Lemaître–Robertson–Walker metric #Gauge (firearms) #Mathematical analysis #Mathematical physics #Orthonormal basis #Perfect fluid #Physics #Pulsars and Gravitational Waves Research #Quantum mechanics #Tetrad #Type (biology) #Universe #astro-ph.CO #gr-qc #hep-th #math-ph #math.MP
paper · pdf · doi:10.1088/1361-6382/aab3a7
published as Class. Quantum Grav. 35 (2018) 095004 · 42 pages, 6 figures, 6 tables in text. V2: minor changes, matches the version published in CQG
openalex created_date 2018/01/05 · openalex publication_date 2018/03/02 · arxiv created 2018/04/09 · arxiv updated 2018/04/10 · openalex updated_date 2026/08/05
Abstract In this paper the dynamics of free gauge fields in Bianchi type I–VII h space-times is investigated. The general equations for a matter sector consisting of a p -form field strength ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mstyle displaystyle="false"> <mml:mi>p</mml:mi> <mml:mspace width="thinmathspace"/> <mml:mo>∈</mml:mo> <mml:mspace width="thinmathspace"/> <mml:mo stretchy="false"></mml:mo> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mn>3</mml:mn> <mml:mo stretchy="false"></mml:mo> </mml:mstyle> </mml:math> ), a cosmological constant (4-form) and perfect fluid in Bianchi type I–VII h space-times are computed using the orthonormal frame method. The number of independent components of a p -form in all Bianchi types I–IX are derived and, by means of the dynamical systems approach, the behaviour of such fields in Bianchi type I and V are studied. Both a local and a global analysis are performed and strong global results regarding the general behaviour are obtained. New self-similar cosmological solutions appear both in Bianchi type I and Bianchi type V, in particular, a one-parameter family of self-similar solutions, ‘Wonderland ( λ )’ appears generally in type V and in type I for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mstyle displaystyle="false"> <mml:mi>λ</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> </mml:mstyle> </mml:math> . Depending on the value of the equation of state parameter other new stable solutions are also found (‘The Rope’ and ‘The Edge’) containing a purely spatial field strength that rotates relative to the co-moving inertial tetrad. Using monotone functions, global results are given and the conditions under which exact solutions are (global) attractors are found.