2011/04/30 by Wessel Valkenburg
Physics and Astronomy · #Advanced Differential Geometry Research #Astrophysics #Black Holes and Theoretical Physics #Classical mechanics #Cosmological constant #Cosmology #Cosmology and Gravitation Theories #Curvature #Dark energy #Friedmann equations #Geometry #Mathematical physics #Metric (unit) #Metric expansion of space #Physics #Quantum mechanics #Scale factor (cosmology) #Spacetime #Theoretical physics #Universe #astro-ph.CO #gr-qc
paper · pdf · doi:10.1007/s10714-012-1405-9
published as Gen.Rel.Grav. 44 (2012) 2449-2476 · 23 pages, one figure. Numerical module for evaluation of the solutions released at http://web.physik.rwth-aachen.de/download/valkenburg/ColLambda/ Matches published version, published under Open Access. Note change of title
openalex publication_date 2012/07/03 · arxiv created 2012/07/23 · arxiv updated 2015/03/18 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We present elliptic solutions to the background equations describing the Lemaître–Tolman–Bondi metric as well as the homogeneous Friedmann equation, in the presence of dust, curvature and a cosmological constant Λ. For none of the presented solutions any numerical integration has to be performed. All presented solutions are given for expanding and collapsing phases, preserving continuity in time and radius; both radial and angular scale functions are given. Hence, these solutions describe the complete spacetime of a collapsing spherical object in an expanding universe, as well as those of ever expanding objects. In the appendix we present for completeness a solution of the Friedmann equation in the additional presence of radiation, only valid for the Robertson–Walker metric.