Mathematical prerequisites for General Relativity

[arunmk]

I am a working professional trying to get back to some physics that I used to enjoy a couple of decades ago. I still do remember the basic calculus (integrals, partial derivatives, basic ODE) and am interested in studying General Relativity. I have a decent understanding and memory of Special Relativity but will refresh myself on it.

What is the best method (courses, set of books etc) to learn the prerequisite Mathematics needed? I think I will need a refresher of Linear Algebra and Vector Calculus. I do want to eventually be able to solve problems in GR, but do not want to get bogged down too much by proof-oriented mathematics books. I would also eventually like to plod my way through MTW.

Also, what would be a good GR book for someone of this background?

Thanks in advance!

 

[PeroK]

I am a working professional trying to get back to some physics that I used to enjoy a couple of decades ago. I still do remember the basic calculus (integrals, partial derivatives, basic ODE) and am interested in studying General Relativity. I have a decent understanding and memory of Special Relativity but will refresh myself on it.

What is the best method (courses, set of books etc) to learn the prerequisite Mathematics needed? I think I will need a refresher of Linear Algebra and Vector Calculus. I do want to eventually be able to solve problems in GR, but do not want to get bogged down too much by proof-oriented mathematics books. I would also eventually like to plod my way through MTW.

Also, what would be a good GR book for someone of this background?

Thanks in advance!

Take a look at Hartle's Gravity - An Introduction to GR.

You'll need a solid grasp of vector calculus but you don't need an extensive course in differential geometry.

Hartle gives a brief review of SR, but I suggest you revise SR thoroughly beforehand.

 

[arunmk]

Take a look at Hartle's Gravity - An Introduction to GR.

You'll need a solid grasp of vector calculus but you don't need an extensive course in differential geometry.

Hartle gives a brief review of SR, but I suggest you revise SR thoroughly beforehand.

Thanks.

For Vector Calculus (which is a gap for me), how much knowledge is enough? I remember the basic operations and get the required skills soon. Do we need Stokes’ theorem etc?

For SR, I plan to go through Taylor and Wheeler. Would that need Maxwell’s equations?

Thanks again!

 

[PeroK]

Thanks.

For Vector Calculus (which is a gap for me), how much knowledge is enough? I remember the basic operations and get the required skills soon. Do we need Stokes’ theorem etc?

For SR, I plan to go through Taylor and Wheeler. Would that need Maxwell’s equations?

Thanks again!

Re calculus generally, if you search for "paul's online notes calculus" you'll find university course notes that are useful for revision and reference.

Even though Hartle goes as easy as possible on the student, you need to be familiar with multivariable calculus. I remember someone a year or two ago came to something early in Hartle that threw him. As far as he was concerned it was complex maths pulled out of thin air, but it was just fairly standard calculus.

Maxwell's equations don't feature in Hartle's book.

 

[arunmk]

Take a look at Hartle's Gravity - An Introduction to GR.

You'll need a solid grasp of vector calculus but you don't need an extensive course in differential geometry.

Hartle gives a brief review of SR, but I suggest you revise SR thoroughly beforehand.

Thanks. Could you tell me what would mean by a thorough review of SR?

Re calculus generally, if you search for "paul's online notes calculus" you'll find university course notes that are useful for revision and reference.

Even though Hartle goes as easy as possible on the student, you need to be familiar with multivariable calculus. I remember someone a year or two ago came to something early in Hartle that threw him. As far as he was concerned it was complex maths pulled out of thin air, but it was just fairly standard calculus.

Maxwell's equations don't feature in Hartle's book.

Thanks for the clarifications, this is awesome.

 

[PeroK]

Thanks. Could you tell me what would mean by a thorough review of SR?

You need to have the core concepts of SR understood completely. Especially spacetime and four-vectors.

Also, if you haven't studied physics for a while, it may be a useful, even essential, step to relearn SR completely before tackling GR.

 

[arunmk]

You need to have the core concepts of SR understood completely. Especially spacetime and four-vectors.

Also, if you haven't studied physics for a while, it may be a useful, even essential, step to relearn SR completely before tackling GR.

Thanks a lot. I’ll follow your advise and reread SR before tackling GR.

 

[Daverz]

Thanks.

For Vector Calculus (which is a gap for me), how much knowledge is enough? I remember the basic operations and get the required skills soon. Do we need Stokes’ theorem etc?

For SR, I plan to go through Taylor and Wheeler. Would that need Maxwell’s equations?

Thanks again!

Basic concepts of mechanics (e.g. momentum conservation) and trig should be enough for Taylor & Wheeler.

For GR, I don't think a lot of vector calculus manipulation of the sort used in EM is needed. You should know basics like the gradient, divergence, curl and Laplacian.

You should be familiar with some classical physics concepts for GR: Gauss's Law, Poisson's equation, Newtonian orbits, effective potential, plain waves.

You may want to get a good reference on Newtonian mechanics (e.g. Symon) for background reading.

 

[arunmk]

Basic concepts of mechanics (e.g. momentum conservation) and trig should be enough for Taylor & Wheeler.

For GR, I don't think a lot of vector calculus manipulation of the sort used in EM is needed. You should know basics like the gradient, divergence, curl and Laplacian.

You should be familiar with some classical physics concepts for GR: Gauss's Law, Poisson's equation, Newtonian orbits, effective potential, plain waves.

You may want to get a good reference on Newtonian mechanics (e.g. Symon) for background reading.

Thanks for this info!