I Explaining Spacetime Dragging: Gravity, EM & Smooth Objects

[bland]

I'm looking for a simple explanation or decent analogy whereby something that is symmetrical and smooth like a black hole or even a spinning neutron star can drag spacetime as if spacetime was a viscous liquid. It guess it might make sense to me if gravity was unified with EM.

I can see how two massive objects orbiting each other could cause ripples, but I don't understand how something that is completely smooth and rotating can drag space around it. Maybe the Earth because it's lumpy. Obviously smooth things do drag spacetime and probably the Earth dragging has nothing to do with the lumpiness.

So how does spacetime "know" that there is a smooth rotating object nearby? What is happening at the boundary of the object, if indeed the boundary has anything to do with it.

 

[PeterDonis]

I'm looking for a simple explanation or decent analogy whereby something that is symmetrical and smooth like a black hole or even a spinning neutron star can drag spacetime as if spacetime was a viscous liquid.

You just gave the analogy: a viscous liquid. It's a limited analogy, but it works within its limitations.

Obviously smooth things do drag spacetime and probably the Earth dragging has nothing to do with the lumpiness.

Correct.

how does spacetime "know" that there is a smooth rotating object nearby?

Because spacetime geometry propagates. The object itself is rotating, which affects the spacetime geometry inside the object, which in turn affects the spacetime geometry outside the object.

 

[bland]

Because spacetime geometry propagates. The object itself is rotating, which affects the spacetime geometry inside the object, which in turn affects the spacetime geometry outside the object.

So does that mean that it's the gradient of the gravity that by rotating about an axis creates the unevenness that affects the geometry?

 

[PeterDonis]

does that mean that it's the gradient of the gravity that by rotating about an axis creates the unevenness that affects the geometry?

No. "Gravity" is another way of saying "spacetime geometry". It isn't what causes the spacetime geometry. What causes the spacetime geometry is the stress-energy tensor (via the Einstein Field Equation), plus how spacetime geometry propagates.

 

[Dale]

So how does spacetime "know" that there is a smooth rotating object nearby?

In GR the source of gravity is not just mass, it is the stress energy tensor. This tensor includes energy density (mostly mass), but it also includes momentum density, pressure, and stress.

A rotating and a non rotating spherical object may have the same energy density, but they will have different momentum densities. They are fundamentally different sources, and the spacetime geometry responds differently to the different momentum densities.

 

[bland]

OK thanks Dale and PD for that answer, I will do some research into the 'stress energy tensor'.

 

[Nugatory]

OK thanks Dale and PD for that answer, I will do some research into the 'stress energy tensor'.

"Einstein field equations" and "Kerr-Newman solution" as search terms will get you started. But fasten your sear belt - it will be a bumpy ride.