Graduate Understanding Tolman Solution & f(R) Corrections

[inertiagrav]

Hello,

Can anyone suggest some text(books/papers) for a better understanding of Tolman solution and the solution with f(R) corrections?

I came across Tolman solution while studying exact solutions of Einstein's equations,first in "Lectures on General Relativity by A. Papapetrou" and later in "An introduction to the theory of early universe(vol. 2) by Gorbunov and Rubakov". But still i need more literature on the subject and i wish to study the solution in presence of f(r) corrections.

Thanks

 

[PeterDonis]

Tolman solution

Can you give more information or a reference for which solution this is?

 

[inertiagrav]

For the closed solution.
I am looking for an example of the closed solution and the solution with f(R) corrections.

 

[PeterDonis]

For the closed solution.

Sorry, that doesn't help. Please give a reference.

 

[inertiagrav]

Hello Peter,

I am actually looking for a reference or example myself to study from.

 

[PeterDonis]

I am actually looking for a reference or example myself to study from.

How do you know about "the Tolman solution"? Where did you learn of it? You have to have some source of information.

 

[inertiagrav]

I came across Tolman solution while studying exact solutions of Einstein's equations,first in "Lectures on General Relativity by A. Papapetrou" and later in "An introduction to the theory of early universe(vol. 2) by Gorbunov and Rubakov". But still i need more literature on the subject and i wish to study the solution in presence of f(r) corrections.

As for the latter part i came across this-
http://www.worldscientific.com/doi/abs/10.1142/9789814374552_0384

but i prefer a cheaper alternative.

Sorry, i should have posted the details beforehand.

 

[PeterDonis]

So the Tolman solution itself would be this:

https://en.wikipedia.org/wiki/Lemaître–Tolman_metric

And the f(R) generalization would be the solution with the same assumptions (spherically symmetric dust) in f(R) gravity:;

https://en.wikipedia.org/wiki/F(R)_gravity

Correct?

 

[inertiagrav]

Yes

 

[m4r35n357]

I came across Tolman solution while studying exact solutions of Einstein's equations,first in "Lectures on General Relativity by A. Papapetrou" and later in "An introduction to the theory of early universe(vol. 2) by Gorbunov and Rubakov". But still i need more literature on the subject and i wish to study the solution in presence of f(r) corrections.

As for the latter part i came across this-
http://www.worldscientific.com/doi/abs/10.1142/9789814374552_0384

There is lots of recent stuff related to this topic on arxiv, and it's not paywalled. I've been looking at a few papers on Tolman-Bondi gravitational collapse, but the maths is way over my head unfortunately. I'd appreciate more discussion on the matter . . . ;)