Study After Schwarzschild Spacetime: What's Next?

[kent davidge]

For someone who have just finished the study of the (fundamentals) of Schwarzschild spacetime, what would be the next natural topic to study?

 

[Nugatory]

Depends... what is your goal here?

 

[kent davidge]

Depends... what is your goal here?

To be able to tell friends that I know all of the fundamentals of General Relativity :)

 

[PAllen]

Study Hartle’s textbook. I actually don’t have it, but many sources say it is by far the most accessible text, suitable for second or third year undergrads, focusing on the physics first.

 

[PeterDonis]

If you're interested in understanding particular solutions of interest, the obvious next ones after Schwarzschild would be Kerr spacetime and FRW spacetime.

 

[kent davidge]

Kerr spacetime and FRW spacetime

In this order?

 

[George Jones]

To be able to tell friends that I know all of the fundamentals of General Relativity :)

Study Hartle’s textbook.

Yes, systematically study a textbook like Hartle or Moore, and work half the problems.

 

[PAllen]

Yes, systematically study a textbook like Hartle or Moore, and work half the problems.

Seconding this, I’ll add @ZapperZ ’s recommendation to keep a notebook of your problem solution efforts. I still have mine from Bergmann’s 1942 textbook, which was the first GR text I studied.

 

[kent davidge]

I’ll add @ZapperZ ’s recommendation to keep a notebook of your problem solution efforts

The problem is that most textbooks don't give the solutions. So we have no way of checking our attempts.

I once emailed a famous author asking him why they don't give the answers so that we can verify if our solutions are correct, and surprisingly he answered my email. He told me that they want students to learn by attempting to solve the problems, and if they would publish the answers, people tend to read them before they have tried really hard.

 

[PeterDonis]

In this order?

I don't know that it matters that much, but Kerr spacetime is more closely related to Schwarzschild than FRW is, so probably yes.

 

[PeterDonis]

The problem is that most textbooks don't give the solutions. So we have no way of checking our attempts.

Another answer your famous author might have given (which one professor of mine once gave me) is that once you really understand the material, you won't have to ask if your solution is correct or not; you'll know.

 

[PAllen]

The problem is that most textbooks don't give the solutions. So we have no way of checking our attempts.

I once emailed a famous author asking him why they don't give the answers so that we can verify if our solutions are correct, and surprisingly he answered my email. He told me that they want students to learn by attempting to solve the problems, and if they would publish the answers, people tend to read them before they have tried really hard.

In the past that was a real issue. However, now you could post your solutions efforts you have any doubts about here, and people would help you confirm or correct them.

 

[martinbn]

To be able to tell friends that I know all of the fundamentals of General Relativity :)

You can do that anyway.

 

[weirdoguy]

once you really understand the material, you won't have to ask if your solution is correct or not;

And what does "really understand" mean? The problem is that sometimes you think you understand, when actually you don't and there is no one there to tell you that. I guess it depends on how hard the exercises are. I have some old russian books on electrodynamics with exercises that some of my faculty proffessors had problems with.

 

[PeterDonis]

The problem is that sometimes you think you understand, when actually you don't and there is no one there to tell you that.

Yes, but if you keep working other problems related to the same physics, you'll soon find that what you thought you understood, you don't, because you'll get stuck.

The disadvantage of being told the answer, when you weren't able to find it yourself, is that being told does not help your understanding; you'll still be just as stuck on the next problem. That's one reason why we don't give answers in our homework forum (the other is that we don't want to become the Internet's lookup table for homework answers); we only give hints.