# Understanding Tolman Solution & f(R) Corrections

• A
• inertiagrav
In summary, Tolman solution and the solution with f(R) corrections are two different solutions to the Einstein equations with the same assumptions, but with different mathematical formulations.
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

Last edited:
inertiagrav said:
Tolman solution

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

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

inertiagrav said:
For the closed solution.

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

Hello Peter,

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

inertiagrav said:
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.

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.

Yes

inertiagrav said:
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 . . . ;)

## 1. What is Tolman solution and how does it relate to f(R) corrections?

Tolman solution is a mathematical model that describes the behavior of a spherically symmetric, static and vacuum solution in general relativity. It is often used in cosmology to study the evolution of the universe. f(R) corrections, on the other hand, are modifications to the Einstein field equations that take into account higher-order curvature terms. These corrections are used to better understand the effects of gravity on large scales.

## 2. Why is it important to understand Tolman solution and f(R) corrections?

Understanding Tolman solution and f(R) corrections is important because they provide a more accurate description of the universe and can help us better explain observed phenomena. These concepts are also essential in developing new theories of gravity and improving our understanding of the fundamental laws of physics.

## 3. How does Tolman solution and f(R) corrections impact our understanding of dark energy and dark matter?

Tolman solution and f(R) corrections have been used to study the effects of dark energy and dark matter on the expansion of the universe. These corrections can help us better understand the nature of these mysterious components and their role in shaping the structure of the universe.

## 4. Can Tolman solution and f(R) corrections be tested through experiments?

Yes, Tolman solution and f(R) corrections can be tested through various experiments and observations. For example, the accelerated expansion of the universe, which is attributed to dark energy, can be studied using f(R) corrections. Other experiments, such as those looking at the gravitational lensing of light, can also provide evidence for these concepts.

## 5. Are there any limitations or controversies surrounding Tolman solution and f(R) corrections?

While Tolman solution and f(R) corrections have been successful in explaining many phenomena, there are still limitations and controversies surrounding these concepts. For example, some scientists argue that f(R) corrections may not be the best approach for understanding dark energy and dark matter. Others question the validity of Tolman solution and suggest alternative models. Further research and experimentation are needed to fully understand these concepts and their implications.

Replies
1
Views
2K
Replies
7
Views
1K
Replies
11
Views
1K
Replies
4
Views
1K
Replies
3
Views
2K
Replies
3
Views
2K
Replies
3
Views
1K
Replies
2
Views
3K
Replies
10
Views
8K
Replies
15
Views
3K