Imagine two stars with the same mass but different densities and thus diameters, do these two stars curve space-time differently?

Yes.

Witty Rejoinder said:

Imagine two stars with the same mass but different densities and thus diameters, do these two stars curve space-time differently?

I’d say yes and beg off with a point at atmospheric forcing.

Thanks.

Yes.

Reductio ad absurdum, Witty.

What if one of the masses was a black hole.

sibeen said:

Reductio ad absurdum, Witty.

What if one of the masses was a black hole.

Slow down poindexter… ATM I have forgotten why I wanted to ask this question. Tomorrow I may take it up again.

Witty Rejoinder said:

ATM I have forgotten why I wanted to ask this question. Tomorrow I may take it up again.

…and people complain that I have a drinking problem!

if the sun suddenly turned into a blackhole the earth would continue to orbit as if nothing had changed. this leads me to believe that spacetime curvature will be the same and just the tidal? (or what the proper term would be) effects would change.

sibeen said:

…and people complain that I have a drinking problem!

It’s blasphemy I know but alas i’m merely weary and stone cold sober.

JudgeMental said:

if the sun suddenly turned into a blackhole the earth would continue to orbit as if nothing had changed. this leads me to believe that spacetime curvature will be the same and just the tidal? (or what the proper term would be) effects would change.

The plot thickens!

Witty Rejoinder said:

JudgeMental said:

if the sun suddenly turned into a blackhole the earth would continue to orbit as if nothing had changed. this leads me to believe that spacetime curvature will be the same and just the tidal? (or what the proper term would be) effects would change.

The plot thickens!

Doh… I really am too tired to be thinking this over.

Outside the surface of any spherical mass gravity behaves as though the mass were concentrated at the centre, so I’d say the answer is:

NO.

The Rev Dodgson said:

Outside the surface of any spherical mass gravity behaves as though the mass were concentrated at the centre, so I’d say the answer is:

NO.

define surface?

don’t have to define surface, just go far enough away for it to make no difference.

Postpocelipse said:

The Rev Dodgson said:

Outside the surface of any spherical mass gravity behaves as though the mass were concentrated at the centre, so I’d say the answer is:

NO.

define surface?

I’d have to agree with you if surface is measured as the gravitational radius of a body

> Imagine two stars with the same mass but different densities and thus diameters, do these two stars curve space-time differently?

You need PM2Ring to give you a definitive answer to this one. I’ve calculated the Newtonian gravitational potential from two stars with the same mass but different densities (it’s a surprisingly difficult calculation) and found that at any radius greater than the maximum radius of the two stars the gravitational potential is identical.

But what I did doesn’t take into account frame dragging or the Lense–Thirring effect. I suspect that the “black hole has no hair” theorem ensures that effects such as frame dragging are the same outside the maximum radius of the two stars but I don’t want to dip into the book “Gravitation” to find out.

Postpocelipse said:

Postpocelipse said:

The Rev Dodgson said:

Outside the surface of any spherical mass gravity behaves as though the mass were concentrated at the centre, so I’d say the answer is:

NO.

define surface?

I’d have to agree with you if surface is measured as the gravitational radius of a body

But then you have to consider that everything within that radius is bent to the particular density of the mass

fixed

I’d have to agree with you if surface is measured as the gravitational radius of a body

word salad. gravity goes to infinity so the “gravitational radius” would be infinite.

Please keep you “pet” theories to your own threads.

JudgeMental said:

I’d have to agree with you if surface is measured as the gravitational radius of a body

word salad. gravity goes to infinity so the “gravitational radius” would be infinite.

Please keep you “pet” theories to your own threads.

I’m only attempting to illustrate that density does differentiate mass providing it with varying potentials. That is established theory.

JudgeMental said:

Please keep you “pet” theories to your own threads.

bit trigger happy.

Witty Rejoinder said:

Imagine two stars with the same mass but different densities and thus diameters, do these two stars curve space-time differently?

From a distance the effects would be minimal but up close the smaller and denser star would have a stronger gradient

with little knowledge

if we take the heavy balls on a rubber sheet analogy

a small ball but very heavy will cause a bend on the sheet that would be like a spike in the sheet

a large football just as heavy would cause a wider shallower depression , whether it would be shallower I don’t know

wookiemeister said:

with little knowledge

if we take the heavy balls on a rubber sheet analogy

a small ball but very heavy will cause a bend on the sheet that would be like a spike in the sheet

a large football just as heavy would cause a wider shallower depression , whether it would be shallower I don’t know

The depth of the depression is total density. The width of the depression is total mass.

The depth of the depression is total density. The width of the depression is total mass.

wrong.

Postpocelipse said:

The Rev Dodgson said:

Outside the surface of any spherical mass gravity behaves as though the mass were concentrated at the centre, so I’d say the answer is:

NO.

define surface?

The surface is the distance at which the mass of the object is negligible beyond the sphere through that radius.

JudgeMental said:

The depth of the depression is total density. The width of the depression is total mass.

wrong.

glad your about. My next thread is dedicated to you. While I’m preparing that you might point out how that is the wrong way round.

Dropbear said:

Witty Rejoinder said:

Imagine two stars with the same mass but different densities and thus diameters, do these two stars curve space-time differently?

From a distance the effects would be minimal but up close the smaller and denser star would have a stronger gradient

Only if you were close enough to the smaller star that you would be inside the larger one.

it would be better for you to cogitate upon it and work it out for yourself. you might learn that way.

Postpocelipse said:

JudgeMental said:

The depth of the depression is total density. The width of the depression is total mass.

wrong.

glad your about. My next thread is dedicated to you. While I’m preparing that you might point out how that is the wrong way round.

It’s not the wrong way round, it’s just wrong.

The “depression” doesn’t have a width, it is infinite.
The depth of the depression depends on the mass, not the density.

What do you mean by “total density” anyway? Density is mass per unit volume.

It might be better to simply ignore Postpocelipse in this thread.

Witty Rejoinder said:

It might be better to simply ignore Postpocelipse in this thread.

Feel free to.

I enjoy chatting with Postpoc.

The “depression” doesn’t have a width, it is infinite.

yes, which has already been mentioned, postie.

The Rev Dodgson said:

Postpocelipse said:

The Rev Dodgson said:

Outside the surface of any spherical mass gravity behaves as though the mass were concentrated at the centre, so I’d say the answer is:

NO.

define surface?

The surface is the distance at which the mass of the object is negligible beyond the sphere through that radius.

Fair evaluation I say. ;)

The Rev Dodgson said:

Postpocelipse said:

JudgeMental said:

The depth of the depression is total density. The width of the depression is total mass.

wrong.

glad your about. My next thread is dedicated to you. While I’m preparing that you might point out how that is the wrong way round.

It’s not the wrong way round, it’s just wrong.

The “depression” doesn’t have a width, it is infinite.
The depth of the depression depends on the mass, not the density.

What do you mean by “total density” anyway? Density is mass per unit volume.

Until I have entirely digest the equations Mollwollfumble provided I cannot provide a clearly measurable analysis of your question.

The Rev Dodgson said:

Postpocelipse said:

JudgeMental said:

The depth of the depression is total density. The width of the depression is total mass.

wrong.

glad your about. My next thread is dedicated to you. While I’m preparing that you might point out how that is the wrong way round.

It’s not the wrong way round, it’s just wrong.

The “depression” doesn’t have a width, it is infinite.
The depth of the depression depends on the mass, not the density.

What do you mean by “total density” anyway? Density is mass per unit volume.

it’s like “total” recall or “strictly ballroom”

Witty Rejoinder said:

Imagine two stars with the same mass but different densities and thus diameters, do these two stars curve space-time differently?

The Rev Dodgson said:

Outside the surface of any spherical mass gravity behaves as though the mass were concentrated at the centre, so I’d say the answer is:

NO.

Correct.

However, we do have to consider the total energy of each star to determine its gravitational mass, it’s not just simply down to how much matter they contain. Thus if we have two stars containing an identical amount of matter but one is spinning faster than the other the one with more spin contains more energy than the other, so it will have higher gravity. And as Mollwollfumble alluded, the faster spinning star will cause more twisting of spacetime in its vicinity.

I should also mention that while gravity adds linearly in Newtonian physics that’s not exactly true in GR. But we can ignore that if our two stars are sufficiently far from other gravitational sources, i.e. if the local spacetime in the vicinity of each star would be essentially flat if the star weren’t there.

Dropbear said:

From a distance the effects would be minimal but up close the smaller and denser star would have a stronger gradient

True.

The Rev Dodgson said:

Only if you were close enough to the smaller star that you would be inside the larger one.

Correct again.

mollwollfumble said:

You need PM2Ring to give you a definitive answer to this one. I’ve calculated the Newtonian gravitational potential from two stars with the same mass but different densities (it’s a surprisingly difficult calculation) and found that at any radius greater than the maximum radius of the two stars the gravitational potential is identical.

But what I did doesn’t take into account frame dragging or the Lense–Thirring effect. I suspect that the “black hole has no hair” theorem ensures that effects such as frame dragging are the same outside the maximum radius of the two stars but I don’t want to dip into the book “Gravitation” to find out.

I’m pretty sure that both linear frame dragging and Lense–Thirring effects will be identical, assuming the stars have identical static mass & angular momentum (and charge).

Thanks PM.

Witty Rejoinder said:

Thanks PM.

+1

very informative assessment.

The Rev Dodgson said:

The surface is the distance at which the mass of the object is negligible beyond the sphere through that radius.

After a little consideration I can provide the reason I took the approach I did in this discussion. From the approach I have taken ‘surface’ is not an automatically physically definable quantity. Surface is the point at which relative accelerations equilibrate. The resolving present moment would be defined as the surface. From this perspective above the surface is considerable as the future and below is the observable light cone of the past. This I would justify as the future provides the only perpendicular line that leads to infinity. The perpendicular measurement of the past only extends to 14 billion years.

Might provide some fuel to the discussion I was seeking. I hope this is in line with the subject of the thread. If not I apologise to Witty for misdirecting his question.

Has absolutely nothing to do with the question and isn’t even science.

ChrispenEvan said:

Has absolutely nothing to do with the question and isn’t even science.

So I’ve walked into Argument rather than Discussion? My mistake. I’m sure I read 446 on the door. Have a good day….

ChrispenEvan said:

Has absolutely nothing to do with the question and isn’t even science.

My comment was actually addressed to Rev. I was intending to examine the definition of surface he provided to understand exactly how standard theory has defined the term.

Hah!!! I’ve figured out the communication confusion I encounter. I’m in the building trade but painters get taught a different approach to any other trade onsite. The builders technique is established as, ‘outside-in, bottom to top’. A painter is taught to assess from, ‘top to bottom, inside-out AND back to front’. I entirely understand the requirement for standard theory to be presented as it is but my method of analysing it has approached it from the end back to the beginning.

I’m working closer with builders atm so possibly my vocabulary will become less misdirecting.