Does an universally valid definition of time exist?

I carry this question with me for several years now. Today, my interest raised to a level, at which I would like to go further and get more information about this topic.

Currently, I guess most people (even me) are defining time, as a dependency from the position of earth, related to sun and the moon. Of course, this makes sense and is a useful method. Regarding the changing revolution of moon and sun, this method makes some inaccuracies visible. Using an atomic clock is useful, to make it more independent, but even this method depends on other factors (time dilatation).

Here an imaginary, but probably more demonstrative situation: Three people exist. Person A is near to a classical black hole, Person B is living on earth and Person C is in a different galaxy, just somewhere in "empty" space. Each of them talks with each other in real time. Person A and B are submitting there currently measured time and Person C notices that the submitted numbers (=the time) are equal to his own measured time.

Is there an equation, that considers physical factors (e.g. gravity) to calculate a normalised time for every location?

Three people exist. Person A is near to a classical black hole, Person B is living on earth and Person C is in a different galaxy, just somewhere in "empty" space. Each of them talks with each other in realtime.

Well here's the first problem : they can't communicate in real time (using the common sense meaning of that expression).

Nothing can travel faster than light so there is no way for them to communicate over large distances in any real-time sense.

Person A and B are submitting there currently measured time and Person C notices that the submitted numbers (=the time) are equal to his own measured time.

Almost certainly impossible simply because they can't communicate like this because of the speed of light limitation.

Even if they were, they're in different gravitational fields so they would be likely to see time pass at different rates. So they'd all be likely to have different numbers.

Is there an equation, that considers physical factors (e.g. gravity) to calculate a normalised time for every location?

There is a specific problem with relativity in terms of different observers having different views of simultaneity. So "syncing" three independent entities in relativity may not make sense, and I think you're trying to do that.