When a star is said to live for 1 billion years, is that relative to the 'average cosmological time unit' or local time in the star's gravitational field? Also, if the sun is said to have 5 billion more years left in its lifetime, is that in cosmological time as well?
I've been reading through some of the discussions on physicsSE about the age of the universe as I have always wondered what the time units for that actually meant. I now have the idea that it is calculated in a sort of average frame of reference avoiding strong gravitational fields. And so I'm wondering what the age of the universe would be as judged by an atomic clock carried by an observer moving around from star to star, observing each star for it's entire lifespan. Since time slows for that observer, would they measure a much shorter time than 14 billion years? What could be the maximum deviation? Maybe stars are never so massive as to change the measurement more than a few hundred million years.
Time slows down for an observer in a strong gravitational field. If an observer was born alongside a very massive star and lived a lifespan equal to the star's (1 billion years), would that observer then think 1 billion years has elapsed relative to their own reference frame (i.e. by using a local atomic clock) and a greater length of cosmological time would have elapsed?
For our sun, 5 billion years of cosmological time would actually be a shorter length as measured by a local atomic clock in the sun's gravitational field, yes? So if the sun is to last 5 billion more years, either (a) it is as measured by local time and hence is longer length in cosmological time, or (b) it is as measured by cosmological time and is a shorter length in local time. Am I thinking about this reasonably?
I'm sure you get so many non-experts asking silly/annoying questions on this site, so please forgive me as I'm a mathematician not a physicist but have studied some advanced physics topics formally. Mathematical and informal explanations are equally appreciated.