How far can observable relations determine a Robertson-Walker metric?

Ehlers, Jürgen; Rindler, Wolfgang

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How far can observable relations determine a Robertson-Walker metric?

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Ehlers, Jürgen
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

Rindler, Wolfgang
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Citation

Ehlers, J., & Rindler, W. (1987). How far can observable relations determine a Robertson-Walker metric? Astronomy and Astrophysics, 174(1-2), 1-4.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-5D9E-4

Abstract

The use of observable relations (kinematic information) to determine a relativistic model of the universe is examined. The relations between the apparent luminosity of distant galaxies as a function of redshift, S(z), the number of galaxies per unit solid angle up to redshift, N(z), the average cross-sectional area of a galaxy orthogonal to the line of sight, the intrinsic luminosity of a standard galxay, L(t), and the proper number density of galaxies in the past, n(t), are studied. The calculation of the expansion factor and curvature of the Robertson-Walker metric using the S(z) and N(z) combined with L(t) and n(t) is described, and the necessary equations are provided.