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.

DaleSpam

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.

DaleSpam

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

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

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.

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.

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

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.