Comments on the tethered galaxy problem

Abstract

In a recent paper Davis, Lineweaver, and Webb make the counterintuitive assertion that a galaxy held “tethered” at a fixed distance from our own could emit blueshifted light. This effect was derived from the simplest Friedmann-Robertson-Walker (FRW) spacetimes and the ΩM=0.3, ΩΛ=0.7 case, which is believed to be a good late time model of our universe. In this paper, we recover their results in a more transparent way, revise their calculations, and propose a formulation of the tethered galaxy problem based on radar distance rather than comoving “proper” distance. This formulation helps to remove the coordinate-dependent nature of the tethered galaxy problem and establishes consistency between the empty FRW model and special relativity. In the general case, we see that, although the radar distance tethering reduces the redshift of a receding object, it does not do so sufficiently to cause the blueshift as found by Davis, Lineweaver, and Webb. We also discuss some important issues raised by this approach relating to the interpretation of the redshift, velocity, and distance in relativistic cosmology.