Do Gravitational Field Lines Change Instantly for an Accelerating Mass?

[FallenApple]

I was looking for a qualitative explanation on how radiation occurs classically and came across this diagram.

Which is for an accelerating charge.

Then I started thinking if this break can occur for the gravitational field.

Does the same thing happen for the gravitational field lines for a accelerating mass? I mean, once the mass displaces, wouldn't that cause the field lines in the vicinity to differ than those of the field lines afar? Is this possible classically?

 

[Nugatory]

Not with classical gravitation. To make Newton's law of gravity work, you have to require that the gravitational force between two objects at any given moment is based on where they are at that moment. If you displace an object, its gravitational field lines everywhere instantaneously change to point to the new position; there's no speed of light propagation delay as with electromagnetism which is governed by Maxwell's equations.

Newton himself found this action at a distance problematic, and of course it's hopelessly incompatible with special relativity. That incompatibility was Einstein's primary motivation for developing General Relativity.

 

[FallenApple]

Not with classical gravitation. To make Newton's law of gravity work, you have to require that the gravitational force between two objects at any given moment is based on where they are at that moment. If you displace an object, its gravitational field lines everywhere instantaneously change to point to the new position; there's no speed of light propagation delay as with electromagnetism which is governed by Maxwell's equations.

Newton himself found this action at a distance problematic, and of course it's hopelessly incompatible with special relativity. That incompatibility was Einstein's primary motivation for developing General Relativity.

Oh right that makes sense. The idea of a field came after Newton. I guess it dealt with the mysterious action at a distance problem for electric force.