Resource Request for Relativistic Mechanics

[Al-Layth]

I am aware of the Newtonian model of Gravitation and I am interested in Relativistic Mechanics.
I do not know anything about relativistic mechanics other than its more "accurate" at modelling gravitation and that it "reduces" to the classical formulation in some cases.

I only want to be able to use relativistic mechanics to be able to write and solve equations of motions under the influence of gravity, I am not very interested in the other parts of the theory itself.

Can someone recommend a resource so that I can learn to do this? thank you(my mathematical background is only up to vector calculus and PDEs. I am prepared to learn tensor calculus and differential geometry and anything else, though so don't constrain your recommendations out of concern for my lack of math knowledge as then I may not be able to do what I want, that is to use relativistic mechanics to mathematically model gravitation)

 

[PeterDonis]

I only want to be able to use relativistic mechanics to be able to write and solve equations of motions under the influence of gravity, I am not very interested in the other parts of the theory itself.

Unfortunately, the equations of motion under the influence of gravity unavoidably involve "the other parts of the theory" in General Relativity, which is the relativistic theory of gravity. The reason is that in order to even have equations of motion, you have to know which solution of the Einstein Field Equation you are using, and that will depend on the distribution of matter and energy that you want to model.

Can someone recommend a resource so that I can learn to do this?

I would start with an introductory textbook on General Relativity. Sean Carroll's online lecture notes are available for free:

https://www.preposterousuniverse.com/grnotes/

 

[anorlunda]

I only want to be able to use relativistic mechanics to be able to write and solve equations of motions under the influence of gravity, I am not very interested in the other parts of the theory itself.

Are you sure you need relativistic mechanics? What maximum speed are you interested in?

 

[malawi_glenn]

Are you sure you need relativistic mechanics? What maximum speed are you interested in?

Mercury is heavily affected by effects due to general relativity despite having low speed

 

[PeterDonis]

Mercury is heavily affected by effects due to general relativity

I'm not sure what you mean by "heavily affected". AFAIK the only GR correction to Newtonian behavior that is observable for Mercury is the extra perihelion precession, which is only 43 arc seconds per century. That's very small.

 

[malawi_glenn]

43 arc seconds per century

well I meant that it is measurable :)

 

[Mondayman]

Mercury is heavily affected by effects due to general relativity despite having low speed

I read this half asleep and had a real space cadet moment. I thought you meant elemental Mercury.

 

[Vanadium 50]

elemental Mercury

Which is pretty heavy. Ever hold a jar of it?

extra perihelion precession

A lot of people don't know that the GR effect is only about 8% of the total perihelion advance.

 

[anorlunda]

The OP seems to have left the room.

 

[PeterDonis]

I meant that it is measurable :)

Ok, but "measurable" is a much weaker claim than "heavily affected". Please be careful in choosing your words.