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

Journal Article · Mon Mar 15 00:00:00 EDT 2010 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.81.063518· OSTI ID:21409382

Klein, David ^[1]; Collas, Peter ^[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)

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.

• OSTI ID: 21409382
• Journal Information: Physical Review. D, Particles Fields, Vol. 81, Issue 6; Other Information: DOI: 10.1103/PhysRevD.81.063518; (c) 2010 The American Physical Society; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

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