Force on an Object according to the General theory of relativity

[KallaNikhil]

What is the force acting on an object according to general theory of relativity? If there is a such a force, can we predict the motion of an object in general relativity just using the modified Newtons laws of mechanics i.e using relativistic mass of an object instead of rest mass ?

 

[phinds]

What is the force acting on an object according to general theory of relativity? If there is a such a force, can we predict the motion of an object in general relativity just using the modified Newtons laws of mechanics i.e using relativistic mass of an object instead of rest mass ?

1) Gravity is not a force in GR
2) "relativistic mass" is a SERIOUSLY deprecated term in modern physics.

 

[Nugatory]

can we predict the motion of an object in general relativity just using the modified Newtons laws of mechanics i.e using relativistic mass of an object instead of rest mass ?

You cannot - in fact, substituting the relativistic mass into the equations of classical mechanics almost never works, which is why the notion of relativistic mass has been largely abandoned in the last few decades. This question comes up often enough that we have an Insights article about it: https://www.physicsforums.com/insights/what-is-relativistic-mass-and-why-it-is-not-used-much/

And as phinds has already pointed out, gravity is not a force in general relativity. The effects that classical physics attributes to a gravitational force proportional to the mass are explained in general relativity as the body moving in a straight line at a constant speed (what you expect when there is no force) through a curved spacetime. Our member @A.T. has posted an excellent short video explaining how this works.

 

[Ibix]

Newtonian gravity is fundamentally incompatible with relativity. It models the influence of gravity as having infinite speed and implicitly assumes a universal definition of "now". Relativity does not allow the former and does not define the latter. Attempts to "fix" Newtonian gravity by adding a propagation speed failed.

You need general relativity, in which gravity is not a force and mass is only one part of the source of gravity, which is the stress-energy tensor.

 

[pervect]

What is the force acting on an object according to general theory of relativity? If there is a such a force, can we predict the motion of an object in general relativity just using the modified Newtons laws of mechanics i.e using relativistic mass of an object instead of rest mass ?

I would tend to assume that the "force on an object" in GR would be the total non-gravitational force on said object. For a particle of small extent (i.e. pointlike), it would be equal to the proper acceleration of the object divided by it's invariant mass.

It's possible an author or a poster with a question might mean something different. But that's what I'd assume what was meant by "force" in GR.

To take an example, a particle orbiting the Earth with only gravity acting on it would have no non-gravitational forces so the "force" on it would be zero. If it was charged and also in an electric field, the force would be non-zero because of the electric field.

The force would appear in the geodesic equations on the right hand side. One might say that in Newtonian mechaincs, force is mass times the ordinary derivative of the velocity, F=m dv/dt. The GR equations are similar but one takes the product of mass with the covariant derivative of the four-velocity rather than the ordinary derivative of the three-velocity.

Explaining this in proper detail takes a lot of background knoowledge, though.