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Title: Recessional velocities and Hubble's law in Schwarzschild-de Sitter space

Abstract

We consider a spacetime with empty Schwarzschild-de Sitter exterior and Schwarzschild-de Sitter interior metric for a spherical fluid with constant density. The fluid interior may be taken to represent a galaxy supercluster, for which the proper distance from the center of the supercluster to the cosmological horizon has the same order of magnitude as the Hubble radius derived from Friedmann-Robertson-Walker cosmologies. The fluid interior and surrounding vacuum may also be considered as a model of the Local Group of galaxies in the far future. Particle motion is subject both to the attractive gravity exerted by the fluid and the repelling cosmological constant. Using global Fermi coordinates for the central observer within the fluid, the Fermi velocity, the astrometric velocity, the kinematic velocity, and the spectroscopic velocity, relative to the central (Fermi) observer, of a radially receding test particle are calculated and compared. We find that the Fermi relative velocity can exceed the speed of light in this model, but the presence of a positive cosmological constant causes recessional speeds of distant high energy particles to decrease rather than increase. We derive a version of Hubble's law for this spacetime which might be applicable for the analysis of a receding massmore » within a great void adjacent to a supercluster, relatively isolated from gravitational sources other than the supercluster. We also compare some of our results to related behavior in Friedmann-Robertson-Walker cosmologies and consider implications to arguments regarding the expansion of space.« less

Authors:
 [1];  [2]
  1. Department of Mathematics, California State University, Northridge, Northridge, California 91330-8313 (United States)
  2. Department of Physics and Astronomy, California State University, Northridge, Northridge, California 91330-8268 (United States)
Publication Date:
OSTI Identifier:
21409382
Resource Type:
Journal Article
Journal Name:
Physical Review. D, Particles Fields
Additional Journal Information:
Journal Volume: 81; Journal Issue: 6; Other Information: DOI: 10.1103/PhysRevD.81.063518; (c) 2010 The American Physical Society; Journal ID: ISSN 0556-2821
Country of Publication:
United States
Language:
English
Subject:
79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; COMPARATIVE EVALUATIONS; COORDINATES; COSMOLOGICAL CONSTANT; COSMOLOGY; DE SITTER SPACE; DENSITY; EXPANSION; GALAXIES; GRAVITATION; HUBBLE EFFECT; MASS; METRICS; PARTICLES; SCHWARZSCHILD METRIC; SPACE-TIME; SPHERICAL CONFIGURATION; TEST PARTICLES; VELOCITY; CONFIGURATION; EVALUATION; MATHEMATICAL SPACE; PHYSICAL PROPERTIES; SPACE

Citation Formats

Klein, David, and Collas, Peter. Recessional velocities and Hubble's law in Schwarzschild-de Sitter space. United States: N. p., 2010. Web. doi:10.1103/PHYSREVD.81.063518.
Klein, David, & Collas, Peter. Recessional velocities and Hubble's law in Schwarzschild-de Sitter space. United States. doi:10.1103/PHYSREVD.81.063518.
Klein, David, and Collas, Peter. Mon . "Recessional velocities and Hubble's law in Schwarzschild-de Sitter space". United States. doi:10.1103/PHYSREVD.81.063518.
@article{osti_21409382,
title = {Recessional velocities and Hubble's law in Schwarzschild-de Sitter space},
author = {Klein, David and Collas, Peter},
abstractNote = {We consider a spacetime with empty Schwarzschild-de Sitter exterior and Schwarzschild-de Sitter interior metric for a spherical fluid with constant density. The fluid interior may be taken to represent a galaxy supercluster, for which the proper distance from the center of the supercluster to the cosmological horizon has the same order of magnitude as the Hubble radius derived from Friedmann-Robertson-Walker cosmologies. The fluid interior and surrounding vacuum may also be considered as a model of the Local Group of galaxies in the far future. Particle motion is subject both to the attractive gravity exerted by the fluid and the repelling cosmological constant. Using global Fermi coordinates for the central observer within the fluid, the Fermi velocity, the astrometric velocity, the kinematic velocity, and the spectroscopic velocity, relative to the central (Fermi) observer, of a radially receding test particle are calculated and compared. We find that the Fermi relative velocity can exceed the speed of light in this model, but the presence of a positive cosmological constant causes recessional speeds of distant high energy particles to decrease rather than increase. We derive a version of Hubble's law for this spacetime which might be applicable for the analysis of a receding mass within a great void adjacent to a supercluster, relatively isolated from gravitational sources other than the supercluster. We also compare some of our results to related behavior in Friedmann-Robertson-Walker cosmologies and consider implications to arguments regarding the expansion of space.},
doi = {10.1103/PHYSREVD.81.063518},
journal = {Physical Review. D, Particles Fields},
issn = {0556-2821},
number = 6,
volume = 81,
place = {United States},
year = {2010},
month = {3}
}