Is Galaxy Dark Matter a Property of Spacetime?

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We describe the motion of a particle in a central field in an expanding universe. Use is made of a double expansion in 1/c and 1/τ, where c and τ are the speed of light and the Hubble time. In the lowest approximation the rotational velocity is shown to satisfy v4 = ⅔ GMcH0, where G is Newton's gravitational constant, M is the mass of the central body (galaxy), and H0 is the Hubble constant. This formula satisfies observations of stars moving in spiral and elliptical galaxies, and is in accordance with the familiar Tully–Fisher law.

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