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Curvature of space time


Arjun Artro
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I've been thinking about gravity and its curving effect on spacetime. It seems very strange to me that a massive object can warp space and time around it. I have a few questions:

1. Would a magnetic field as strong as the gravity around a black hole bend the spacetime around it? If so, it's the bending effect same as that of gravity?

2. If gravity is a curvature in spacetime, and not a force, why doesn't the centre of an object experience the same curvature? (for eg, Fg=0 at the centre of the earth)as I thought it is because the forces cancel out each other at the centre.

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It is not gravity which 'bends' space-time, rather, it is mass and various forms of energy which 'do the bending'.

It is this ''bending' which we then label, gravity. In effect, in GR, gravity is modeled geometrically.

 

The electromagnetic field has also been modeled geometrically, by adding an additional dimension, in the 1920s, by T. Kaluza and O. Klein. But that isn't what you're asking, is it ?

An EM field has the property of energy, so, yes, a concentrated EM field ( extremely high energy density ) will also 'bend' space-time.

 

As to your second question, the simplest visualization ( and often wrong/confusing ) is by reduction to two dimensions; the mass in the middle of a rubber sheet. This has the added advantage that it also models the gravitational potential. Test masses follow the geodesics, or curved sides of this depression in the rubber sheet, from all sides, and by necessity there cannot be any curvature at the lowest point. This lowest point coincides with where the gravitational potential is at a minimum, i.e. zero and no net force.

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..2. If gravity is a curvature in spacetime, and not a force, why doesn't the centre of an object experience the same curvature? (for eg, Fg=0 at the centre of the earth)as I thought it is because the forces cancel out each other at the centre.

If you imagine a sphere with layers like an onion, the mass - and hence local gravity - of each layer, starting from the outer layer, diminishes to nothing in the middle.

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It seems very strange to me that a massive object can warp space and time around it.

It seems strange to everyone, but that is what the theory tells us and the theory matches observations very well.

 

1. Would a magnetic field as strong as the gravity around a black hole bend the spacetime around it? If so, it's the bending effect same as that of gravity?

When an electromagnetic field is present, you can either consider the field to be on a background space-time (okay for not very strong fields) or you need to find solutions to Einstein-Maxwell theory. Here you take the electromagnetic field to be a source of gravity. So in this sense electromagnetic fields course space-time curvature.

 

2. If gravity is a curvature in spacetime, and not a force, why doesn't the centre of an object experience the same curvature? (for eg, Fg=0 at the centre of the earth)as I thought it is because the forces cancel out each other at the centre.

In short, the curvature depends on the location in space-time in general.

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2. If gravity is a curvature in spacetime, and not a force, why doesn't the centre of an object experience the same curvature? (for eg, Fg=0 at the centre of the earth)as I thought it is because the forces cancel out each other at the centre.

 

Curvature is (I think) maximum at the centre of the Earth but, as you say, the forces due to that curvature cancel.

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