Complete solutions to the metric of spherically collapsing dust in an expanding spacetime with a cosmological constant

Abstract

We present semi-analytical solutions to the background equations describing the Lemaître-Tolman-Bondi (LTB) metric as well as the homogeneous Friedmann equations, in the presence of dust, curvature and a cosmological constant Lambda. 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. Hence, these solutions describe the complete space time of a collapsing spherical object in an expanding universe. In the appendix we present for completeness a solution of the Friedmann equations in the additional presence of radiation, only valid for the Robertson-Walker metric.

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

References in corpus (24)

• The Hubble Constant: A Summary of the HST Program for the Luminosity Calibration of Type Ia Supernovae by Means of Cepheids
• Confronting Lemaitre-Tolman-Bondi models with Observational Cosmology
• Lemaitre-Tolman-Bondi model and accelerating expansion
• On cosmological observables in a swiss-cheese universe
• Observational constraints on inhomogeneous cosmological models without dark energy
• Testing the Void against Cosmological data: fitting CMB, BAO, SN and H0
• Can we avoid dark energy?
• Mapping Luminosity-Redshift Relationship to LTB Cosmology
• Local Void vs Dark Energy: Confrontation with WMAP and Type Ia Supernovae
• The Cosmic Microwave Background in an Inhomogeneous Universe - why void models of dark energy are only weakly constrained by the CMB
• Reconciling the local void with the CMB
• Swiss Cheese and a Cheesy CMB
• Observational constraints on the LLTB model
• Large scale structure simulations of inhomogeneous LTB void models
• Large-scale inhomogeneities may improve the cosmic concordance of supernovae
• LTB solutions in Newtonian gauge: from strong to weak fields
• Effects of inhomogeneities on apparent cosmological observables: "fake" evolving dark energy
• Residual Hubble-bubble effects on supernova cosmology
• CMB observations in LTB universes: Part II: the kSZ effect in an LTB universe
• Corrections to the apparent value of the cosmological constant due to local inhomogeneities
• The spherical symmetry Black hole collapse in expanding universe
• The Metric of the Cosmos from Luminosity and Age Data
• The Great Attractor and the Shapley Concentration
• Density profiles and voids in modified gravity models

Cited by in corpus (32)

• Cosmology and Fundamental Physics with the Euclid Satellite
• Cosmology and fundamental physics with the Euclid satellite
• Cosmic variance and the measurement of the local Hubble parameter
• Testing the Copernican principle by constraining spatial homogeneity
• Can a supervoid explain the Cold Spot?
• Exploring the evidence for a large local void with supernovae Ia data
• Probing spatial homogeneity with LTB models: a detailed discussion
• Exact spherically-symmetric inhomogeneous model with n perfect fluids
• The Copernican principle in light of the latest cosmological data
• A void in the Hubble tension? The end of the line for the Hubble bubble
• Perceiving the equation of state of Dark Energy while living in a Cold Spot
• Uncertainty on w from large-scale structure
• Cosmic Matter Flux May Turn Hawking Radiation Off
• Redshift drift in a pressure-gradient cosmology
• Invariant characterization of the growing and decaying density modes in LTB dust models
• Relativistic virialization in the Spherical Collapse model for Einstein-de Sitter and ΛCDM cosmologies
• Intrinsic uncertainty on the nature of dark energy
• Lensing in the Geodesic Light-Cone coordinates and its (exact) illustration to an off-center observer in Lemaître-Tolman-Bondi models
• Cosmological black holes: the spherical perfect fluid collapse with pressure in a FRW background
• CMB seen through random Swiss Cheese
• Gravitational entropy of local cosmic voids
• A non-linear approximation for perturbations in ΛCDM
• Towards the geometry of the universe from data
• Euclid: Testing the Copernican principle with next-generation surveys
• CMB sky for an off-center observer in a local void I: framework for forecasts
• Inverse Construction of the $\Lambda$LTB Model from a Distance-redshift Relation
• Charged cosmological black hole
• Relativistic virial relation for cosmological structures
• The history of the universe is an elliptic curve
• Analytic auto-differentiable $\Lambda$CDM cosmography
• Linear perturbations in spherically symmetric dust cosmologies including a cosmological constant
• Shear-dependent Pressure in a Lemaître-Tolman-Bondi Metric