Does mass draw in space time?

[Bryan Kelly]

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

[swansont]

20 minutes ago, Bryan Kelly said:

The guidelines for this Speculations Forum mention the concept Wild Ass Guesswork (WAG).

Yes, to say that we expect something above that level.

[Markus Hanke]

5 hours ago, Bryan Kelly said:

I suspect it does, but am not positive this is a valid concept.

It’s meaningless, and thus not a valid concept.

[Mordred]

4 hours ago, Bryan Kelly said:

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. 

 

 First off strong piece of advise. Don't think of spacetime as some materialistic fabric. I mention this as its a very common misconception. Mass energy does tell spacetime how to curve. This is correct, but one detail to recognize is this describes geodesic paths through spacetime due to relativistic effects. Mathematically speaking we describe spacetime using geometry but one of the tenets of GR is invariance of geometric choice. There is also invariant properties to all observer example proper distance etc. However Observer affects also affect how we measure the variant properties ( time dilation, length attraction etc).  Is there a limit to the mass energy term  that causes curvature such as a BH. Well we simply don't know what the limit is assuming there is one. Example the true singularity condition of a BH at R=0. An example of a variant property is infinite redshift at the EH of a BH.  Trying to describe this as "drawing in spacetime" doesn't make sense. Its more accurate to describe, the geodesics paths due to curvature. Past the EH all spacetime paths lead towards R=0 and never escape the EH.

Yes there is equations to support this. Under GR one uses the Einstein field equations

 

[Bryan Kelly]

“… one of the tenets of GR is invariance of geometric choice.”

I don’t understand that invariance concept.  I presume that BH means Black Hole.

There are several things that lead me to the conclusion that mass draws in spacetime.  The first is the quote about mass curves spacetime and spacetime tells mass how to move.  While cute quotes and sayings may not be technically true, there seems to be much to this one.

Another is the concept of the universe expanding.  Some 13 billion years in the past the universe was much smaller.  It expanded so fast that light could not keep up with the expansion. 

How did the universe become much smaller?  Some effect, some thing, made it smaller.

If this is so, then space must be something more substantial that just empty void.  It can be shrunk down and can be expanded.

What can cause it to be shrunk down?  To at least some degree, that is mass.  The more mass per unit of volume, the more space is made smaller, it is shrunk by mass.

When something is in the presence of mass, even time slows down.  I take this as another indicator that spacetime can be made smaller and can be made larger.  The current expansion of the universe appears to support this concept.

And thank you for the two links.  Regarding the first, I see the opportunities to change parameters, but don't know what i am changing or how to interpret the results.  Regarding the second, wow, there is a lot there and I will be looking there for quite a while.  Days, weeks, or more.

Thank you.

Edited June 29 by Bryan Kelly

[Bryan Kelly]

From an earlier post I get to here:  http://www.phinds.com/balloonanalogy/

From there are these links:

And here is an excellent discussion: Misconceptions About the Big Bang                good site

A couple of other good ones:

a brief history of cosmology --- two pages on your computer screen                     MS Edge reports cannot reach this page

a history of cosmology theories from the Greeks to now --- a considerably more extensive discussion      page not found

Sean Carroll's Cosmology Primer --- an extensive discussion            This page doesn’t seem to exist

errors in some popular attacks on the big bang --- may dispel any misconceptions you might have, looks OK

Does anyone know of anyone who might be in a position to make some updates?