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## Main Question or Discussion Point

Hi all,

I have just started learning about general relativity. Unfortunately my book is very math-oriented which makes it a bit challenging to understand the content from a physical point of view. I hope you can help.

I am familiar with special relativity theory and Minkowsky Space. As I understand it the most simple version of the metric tensor, g, is used to describe this flat space.

If a pick a point in a gravitational field the space around it curves. Unlike flat space we can only consider a very small section around this point, in order to make the space around it seem flat, right? But if the small section is very-nearly-flat why not use the equation from Minkowsky Space to describe it?

I am referring to this equation:

[tex](d\tau)^2 = c^2(dt)^2 + r^2[/tex]

I mean, what is the point of zooming in to make it look flat if it is not treated as flat space anyway?

If space is curved the metric tensor becomes a lot more complex and the equation becomes:

[tex](d\tau)^2 = -g_{\mu\nu}dx^{\mu}dx^{\nu}[/tex]

Am I right when I say that the equation describes processes in a very small, free-falling nearly-flat-but-still-curving section around a point in a big(ger) gravitational field? That g is not simple anymore due to the curvature in this small section? And that the point of view is that of a free-falling observer in that exact point?

And here is a bonus question: if a free falling observer (or the very small section) does not feel gravity why does he still percieve the space as curved?

Thank you in advance,

Diana

I have just started learning about general relativity. Unfortunately my book is very math-oriented which makes it a bit challenging to understand the content from a physical point of view. I hope you can help.

I am familiar with special relativity theory and Minkowsky Space. As I understand it the most simple version of the metric tensor, g, is used to describe this flat space.

If a pick a point in a gravitational field the space around it curves. Unlike flat space we can only consider a very small section around this point, in order to make the space around it seem flat, right? But if the small section is very-nearly-flat why not use the equation from Minkowsky Space to describe it?

I am referring to this equation:

[tex](d\tau)^2 = c^2(dt)^2 + r^2[/tex]

I mean, what is the point of zooming in to make it look flat if it is not treated as flat space anyway?

If space is curved the metric tensor becomes a lot more complex and the equation becomes:

[tex](d\tau)^2 = -g_{\mu\nu}dx^{\mu}dx^{\nu}[/tex]

Am I right when I say that the equation describes processes in a very small, free-falling nearly-flat-but-still-curving section around a point in a big(ger) gravitational field? That g is not simple anymore due to the curvature in this small section? And that the point of view is that of a free-falling observer in that exact point?

And here is a bonus question: if a free falling observer (or the very small section) does not feel gravity why does he still percieve the space as curved?

Thank you in advance,

Diana