Consider the following line element, ds^2 = −dt^2 + a^2(t) (dx^2 + dy^2) + b^2(t) dz^2, where a(t) and b(t) are distinct functions. State whether or not this line element obeys the Cosmological Principle, if applied to describe the universe on large scales. Justify your answer.

Consider the following line element, ds^2 = −dt^2 + a^2(t) (dx^2 + dy^2) + b^2(t) dz^2, where a(t) and b(t) are distinct functions. State whether or not this line element obeys the Cosmological Principle, if applied to describe the universe on large scales. Justify your answer.

Stars and Galaxies (MindTap Course List)

10th Edition

ISBN:9781337399944

Author:Michael A. Seeds

Publisher:Michael A. Seeds

Chapter18: Modern Cosmology

Section: Chapter Questions

Problem 12RQ

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Question

Consider the following line element,
ds^2 = −dt^2 + a^2(t) (dx^2 + dy^2) + b^2(t) dz^2,
where a(t) and b(t) are distinct functions. State whether or not this line element obeys the Cosmological Principle, if applied to describe the universe on large scales. Justify your answer.

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