- #1

- 200

- 1

## Main Question or Discussion Point

Hi!

Given the schwarzschild metric

[tex]ds^2=-e^{2\phi}dt^2+\frac{dr^2}{1-\frac{b}{r}}[/tex]

I can make this coordinate transformation

[tex]

\hat e_t'=e^{-\phi}\hat e_t \\

\hat e_r'=(1-b/r)^{1/2}\hat e_r

[/tex]

and I will get a flat metric. Is this correct?

Another thing I'm a lot confused about: if I am at constant r, than my 4-velocity is

[tex]u^a=(e^{-\phi}, 0)[/tex]

Then I experience an acceleration

[tex] a^a=u^b\nabla_bu^a[/tex]

and this acceleration has a non-null r-component. So, does this mean I'm accelerating in the r-direction? But I supposed I'm at constant r!

Given the schwarzschild metric

[tex]ds^2=-e^{2\phi}dt^2+\frac{dr^2}{1-\frac{b}{r}}[/tex]

I can make this coordinate transformation

[tex]

\hat e_t'=e^{-\phi}\hat e_t \\

\hat e_r'=(1-b/r)^{1/2}\hat e_r

[/tex]

and I will get a flat metric. Is this correct?

Another thing I'm a lot confused about: if I am at constant r, than my 4-velocity is

[tex]u^a=(e^{-\phi}, 0)[/tex]

Then I experience an acceleration

[tex] a^a=u^b\nabla_bu^a[/tex]

and this acceleration has a non-null r-component. So, does this mean I'm accelerating in the r-direction? But I supposed I'm at constant r!