Deriving Friedmann Robertson Walker metric and Hubble’s law from gravitational collapse formalism

• Published in: Results in physics Vol. 2; pp. 45 - 49
• Main Author: Mitra, Abhas
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 2012
• Subjects: Cosmology: miscellaneous; Cosmology: theory; FRW metric; General relativity; Gravitational collapse; Cosmology: miscellaneous; FRW metric; Cosmology: theory; Gravitational collapse; General relativity
• ISSN: 2211-3797; 2211-3797
• DOI: 10.1016/j.rinp.2012.04.002

In general relativity, one is supposed to derive the metric by solving the relevant Einstein equations. However, the metric for the Friedmann–Lemaitre–Robertson–Walker (FLRW) metric has so far been obtained by starting from Weyl’s postulate and eventually by geometric considerations alone. But here, instead, we rigorously derive the same by solving the Einstein equations appropriate for gravitational collapse/expansion of a perfect fluid. The fact that FLRW metric can indeed be obtained by solving a Einstein equations shows the physical correctness of the Weyl postulate. This exercise thus complements rather than rivals the traditional derivation of the FLRW metric. During this exercise, we derive rather than merely obtain the Hubble’s law. This exercise also confirms that the total energy of the FLRW universe, including matter and gravitation, is indeed given by the well known “Misner-Sharp mass”. With this firm identification, we confirm the intuitive idea that while the “closed model” is gravitationally bound, the “open model” is gravitationally unbound.
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