# Is the Hubble parameter different for each observer?

As the universe expands, galaxies disappear beyond the observable universe. So we could calculate the rate of expansion of the universe (the Hubble parameter) by estimating the rate of disappearance.

Now imagine if an astronaut leaves his spaceship and orbits around a black hole for a long time, and returns to the spaceship. Perhaps billions of years have elapsed for those on the spaceship, but only hundreds of years for the astronaut. They can both agree on how many galaxies were visible from the spaceship at the start and finish of the journey.

However, they both must disagree as to the rate of disappearance of the galaxies. The astronaut calculated that the missing galaxies disappeared over a few hundred years, but the spaceship observer says it was over a few billion years. Therefore they would have observed two different Hubble parameters while the astronaut was travelling. Is this wrong?

• Galaxies do not disappear over the horizon like that. When they get closer to the event horizon, they get redshifted towards infinity, but seem to never actually disappear out of view. At the same time, new galaxies will appear as the particle horizon expands, but these will also be increasingly redshifted wjen they appear. – Thriveth Mar 1 '17 at 3:21
• Also, the Hubble parameter is tied up, not n the observer but on the Universe. it is defined as the rate of change of the scale factor, which is the average distance between galaxies in the Universe at a given time in units of the current average distance (assuming the galaxies don't move or evolve over time). This does not depend on the astronauts perceived time. – Thriveth Mar 1 '17 at 3:25
• Thanks @Thriveth. So maybe the rate of change of the Hubble parameter is different for each observer? – Paul Mar 1 '17 at 14:39