Does an astronaut floating in space near the center of the galaxy, where the mass density is higher (let's ignore the dark matter halo for this example) have a clock that runs slower than an astronaut hovering in space near the edge of the galaxy? Let's say both astronauts are far from any stars and planets. I'm curious if the increased mass density at the center of the galaxy affects the astronaut's clock relative to the astronaut at the edge, even if neither of them are near any particular star or planet.
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