The shape of space-time around a star

[RayYates]

Gravity around star is often depicted as the curvature if spacetime or a 'dimple" in a flat sheet.

What would happen to space-time around a star if the star were to instantly disapear? Would the fabric of space time snap back to flat space or would it reverberate, expanding then contracting then expanding again?

 

[WannabeNewton]

The space - time around a spherically symmetric, static star (which many stars are to a good approximation) has similar properties to a 4 - sphere; if you looked at a constant radius, constant time section of the geometry then it will be equivalent to that of the 2 - sphere. It isn't a flat sheet by any means, that analogy hurts more than it helps. Your question, unfortunately, requires extrapolation of a situation that is physically impossible. You can't just make a star disappear out of nowhere even in principle.

 

[Dale]

Hi RayYates, welcome to PF!

As WannabeNewton says the problem is that the star simply disappearing is a violation of the Einstein Field Equations. And those are the very equations which we would use to determine the curvature of the spacetime.

However, you could imagine that the star suddenly turns into a spherically symmetric ball of light going outwards. The shape of the spacetime outside of the ball of light would be the same as before, but I don't know what the shape would be inside. I think that it would be flat.

 

[RayYates]

This is a though experiment so please, ignore the fact the a star can not disapear.

I understand the two dimensional representation of a ball on a "flat" sheet as curved space time is only poor representation of gravity.

I'm trying to understand, if mass can cause space time to curve toward the mass, (lets call that a positive curvature of space time) can space time have a negative curvature?

Will the sheet bounce / reverberate if the ball were suddenly removed?

Would the space-time effect called gravity alternate from positive to negative or would it simple return to center? And further more, would there be a "gravity wave"

 

[Drakkith]

Well, I think something similar to a gravitational wave would be released. We cannot remove a star instantly, but we can imagine a high mass object moving at near c velocity past us. It would move through space and the curvature would follow it with the resulting changes propagating through space at c as a wave. That is about as close to a massive object "dissapearing" that I can imagine.

 

[WannabeNewton]

Even in a thought experiment you cannot just violate physical laws. The notion of positive and negative curvature does exist as an intrinsic measure for manifolds and this property is called Gaussian curvature. But again, your scenario just isn't possible even in principle.

 

[Dale]

This is a though experiment so please, ignore the fact the a star can not disapear.

You are in essence asking, if 1+6 were 19, what would 3+2 be. How do you expect us to answer when the question violates the rules that we would use to answer?

 

[RayYates]

Well then...

Thanks Drakkith for ignoring my lame example, I'll just ask the main question.

If mass can cause space time to curve toward the mass, (lets call that a positive curvature of space time) are there any reason space time can not have a negative curvature?

I'm not speculating on what would cause this, only if there are any laws that would prevent it.

 

[WannabeNewton]

There is nothing in the EFEs that prevents that. In fact, the Friedman metric with negative curvature index describes hyperbolic space, at each instant of time, which has a negative Gaussian curvature.

 

[RayYates]

Ok back to speculation...

What might cause a negative curve?

 

[DrGreg]

If mass can cause space time to curve toward the mass, (lets call that a positive curvature of space time) are there any reason space time can not have a negative curvature?

I think you have a misunderstanding of the terminology. Positive curvature means curvature like a spherical surface. Negative curvature means curvature like a saddle.

I think you mean something different, essentially "concave" and "convex" curvature. Well, there is no difference. You have to remember that when you picture 4-dimensional spacetime curving in 5-dimensional space, the 5th dimension doesn't really exist, it's just an analogy to help you picture the geometry.

 

[RayYates]

Your correct DrGreg, I'm sure I have the terminology wrong. Physics is an armchair interest not my profession.

My understanding of the space-time around massive objects like a black hole is that space is compressed and time slows. I have a pretty clear mental picture of this if not the language.

It occurs to me that the opposite effect must also be possible, or even probable.

 

[pervect]

This is a though experiment so please, ignore the fact the a star can not disapear.

Unfortunately, sometimes one cannot make a bad initial premise dissappear, even if it's a thought experiment.

This is one of those times.

If you've ever seen a mathematical proof that uses the "reducto ad absurdum" method, you can perhaps appreciate why.

The standard "reducto ad absurdum" proof goes "make a bad assumption, get nonsense, which then proves your initial assumption was bad'.

Note that it's important to realize that you get nonsense, if you don't realize this, you can spend a lot of non-productive time arising from false initial assumptions.

I understand the two dimensional representation of a ball on a "flat" sheet as curved space time is only poor representation of gravity.

I'm trying to understand, if mass can cause space time to curve toward the mass, (lets call that a positive curvature of space time) can space time have a negative curvature?

Positive and negative curvatures exist, but they don't have anything to do with whether the sheet goes up or down. The shape is the same.

Will the sheet bounce / reverberate if the ball were suddenly removed?

As was mentioned previously, the only honest answer to that question is "that can't happen". However, other sorts of disturbances can cause gravity waves, which you can think of as ripples in space-time, or in your analogy ripples passing along the sheet.

 

[RayYates]

Thanks everyone. That's what I was trying to understand. I was trying to get to gravity waves without knowing the correct terminology.

Would a super nova generate gravity waves? If so would they be large enough to detect?

 

[WannabeNewton]

Yes a super - nova could generate gravitational waves (note that gravity waves are different). If the collapse of the star happened to be spherical then no gravitational waves would be produced but if there was a non - spherical collapse then the non - spherical parts will be radiated away as gravitational waves. The collapse of a star is a complex process so the amplitude of the gravitational waves could probably only be found numerically (too many self - interactions to use the non - linear EFEs to find a solution for the gravitational waves with a collapsing star as the source term) so I can't do it for you with a pen and paper but try googling it, there might be published papers on the amplitude of gravitational waves released from non - spherical collapse of stars (or maybe an adviser/mentor already has a resource ready).

 

[RayYates]

After reading a bit more about gravitational waves http://en.wikipedia.org/wiki/Gravitational_wave I have a follow up question.

How would light passing through a radiating gravitational wave behave?

 

[pervect]

After reading a bit more about gravitational waves http://en.wikipedia.org/wiki/Gravitational_wave I have a follow up question.

How would light passing through a radiating gravitational wave behave?

I wouldn't expect anything dramatic to happen, but I can't say I've ever seen an analysis complete enough to rule out something non-intuitive from happening.

 

[RayYates]

As light bends toward the gravity well of large mass objects, wouldn't a beam of light bend first toward then away from an oncoming gravitational wave?

 

[cephron]

Interesting point! Behaving similarly to as if it were refracting through a layer of something with higher optical density, perhaps? So the ultimate effect of the gravity wave (if they do in fact affect light in this manner) would be to leave the light traveling in the same direction, but its course would be shifted slightly sideways.

 

[Dale]

How would light passing through a radiating gravitational wave behave?

This is the operating principle behind the LIGO and LISA projects:
https://www.advancedligo.mit.edu/summary.html
http://list.caltech.edu/doku.php?id=mission_documents

 

[nitsuj]

This is the operating principle behind the LIGO and LISA projects:
https://www.advancedligo.mit.edu/summary.html
http://list.caltech.edu/doku.php?id=mission_documents

I thought those programs/experiments were scrapped.

Is LISA still gunna happen? (this decade).

 

[Dale]

I don't know if they are actually going to happen at all. I certainly doubt this decade, too much bad economy and too much cost overruns from the Webb telescope.

 

[RayYates]

Thanks DaleSpam for the links. So this is being studied and experiments constructed. I'll finish reading these in a moment.

After the big bang, did the cosmic inflation of space occur as a gravitational wave?

 

[debojoti]

RayYates...u can obiously think of the relative position of the space-time curve...now if a star has already created a depression... if now due to loss of its triple fusion elements (say) helium...it can just convert into a white dwarf that can cause the reduction of the overall mass and releaving the 'strech' in the space time fabric...similarly if the electron degeneration pressure get pass the chandrashekar limits....it may convert into a neutron star or a black hole...thus increasing the mass...thus now the curvature could be more than the one produced by the original star and thus we can see the movement of the fabric in a realtive manner to the mean position of the curvature which u could infer as the 'positive or the 'negetive' as u may look at it...

 

[Drakkith]

RayYates...u can obiously think of the relative position of the space-time curve...now if a star has already created a depression... if now due to loss of its triple fusion elements (say) helium...it can just convert into a white dwarf that can cause the reduction of the overall mass and releaving the 'strech' in the space time fabric...similarly if the electron degeneration pressure get pass the chandrashekar limits....it may convert into a neutron star or a black hole...thus increasing the mass...thus now the curvature could be more than the one produced by the original star and thus we can see the movement of the fabric in a realtive manner to the mean position of the curvature which u could infer as the 'positive or the 'negetive' as u may look at it...

There is no loss or gain of mass when an object turns into a white dwarf. A neutron star or black hole will have lost some mass during the collapse process, but not that much. And they definitely don't gain mass during this collapse. The curvature of space is identical no matter the object that occupies it as long as they have the same mass.

For example, let's assume we have a white dwarf with exactly the same mass as the Sun. Let us say that the distance from the center of the wite dwarf is 5,000 km. (Just making that number up for the example) For comparison the Sun's surface is about 700,000 km from it's center on average.

If we observe how the sun curves spacetime, from a distance of 700,000 km or greater from either the Suns center of the white dwarf's center, the effects are identical. It is only once we observe how the Sun curves spacetime from closer than this, which would be under its surface, that the curvature is different. From 700,000 km to 5,000 km from the white dwarf's center the curvature increases. The gradiant is larger for a white dwarf because it is much more dense than the Sun. A neutron star would have a similar effect as would a black hole.

 

[ZealScience]

Well, actually in Einstein's equations, conservation law of energy and momentum is necessary. Otherwise the energy/momentum tensor would not have a covariant derivative of zero, where it is closely related to curvature tensors and scalars. Therefore you cannot solve the equations to get curvature.

Just suppose it vanishes some how, to my perspective, it would generate great deal of gravitational waves, as the change of mass is too great. Well, as an amateur, just some stupid guesses.

 

[RayYates]

Follow up question for the experts:

In the Newtonian world and explosion causes a shock wave through the atmosphere that distorts the light passing through it. You can capture that wave on camera.

My understanding of the Einsteinian world is that in a supernova explosion some mass is lost, most is hyper compressed and the "shape" of space time around the remaining mass would change.

That sudden change in shape (i.e. gradient) would cause a gravitational wave. How would light passing through this wave behave?

 

[pervect]

Spherically symmetric explosions don't generate any gravity waves. What you'd find is that light would be deflected by the enclosed mass. As the explosion caries mass away, the deflection would go down if the light passes through the region after the debris have left, assuming that the explosion debris don't block or distort the signal.

See http://en.wikipedia.org/w/index.php?title=Birkhoff's_theorem_(relativity)&oldid=417061895" for why - any spherically symmetric solution must be Schwarzschild. That means - no gravity waves.

There is a good chance that there would be non-gravitational effects on the light from the debris, but I don't think you are asking about those.