The guidelines for this Speculations Forum mention the concept Wild Ass Guesswork (WAG). I rather favor a term I learned in the military, SWAG, sophisticated wild ass guess. Well, maybe not real sophisticated, but to at least some degree.
An ultimate goal of mine is this question: What would it mean if there is an upper limit to the size of a black hole? For now, I stop on the major concept and begin with a minor one that is important to the larger.
I have read widely about spacetime but not deeply. I am not good with mathematics. I am aware of and comfortable with the concept: “matter tells spacetime how to curve, and curved spacetime tells matter how to move.” But not much deeper.
Is there an equation that calculates how mass curves spacetime? Specifically, the question is how much a black hole, or any large mass, will draw in space time. I suspect it does, but am not positive this is a valid concept.
To be explicit, presume we stand off from a solar system in space and that we can see the lines of space and that we are not affected by changes. Presume we can see the lines where planets A, B, and C orbit the sun S. Just for a starting point, presume one solar mass. We replace sun S with one that is ten or a hundred times as massive. How would those circles for the orbits of the planets move? From our distant and unaffected location, my speculation is that we would see the line for each planet would move in closer to the sun and the closer ones would be affected more than those further away.
Do you think those orbit lines would move? If so, how much would they move? I suspect there are equations for this, but, not being mathematically endowed, I cannot recognize them and/or extract just the parts needed.
(Let’s ignore the sudden change on the planets themselves for several reasons.)
But how would we measure it? From our location, let’s say directly above the orbital plane of the planets, use Pythagorean’s theorem. Set the adjacent as the line to the sun, the hypotenuse as the line to each of the planets, and the opposite is the distance between the sun and the planet. And since this is a thought experiment, presume our visual lines of sight to the planets and the sun are not changed by the changes in mass and that we can see the changes instantly.
Is this a valid thought experiment? Your thoughts please