- #1

timmdeeg

Gold Member

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## Main Question or Discussion Point

In de Sitter-Schwarzschild spacetime things close to the black hole are falling towards it whereas in greater distance they are receding. So there should be a certain (unstable) ##r##-coordinate, where things are static. The de Sitter-Schwarzschild metric has according to Wikipedia

https://en.wikipedia.org/wiki/De_Sitter–Schwarzschild_metric

2 solutions:

##f(r)=1-2M/r##

##f(r)=1-\Lambda*r^2##

Equating yields ##r=(2M/\Lambda)^{1/3}##

Is this the wanted static r-coordinate? Heuristically it seems to make sense, r increases with increasing ##M## and decreases with increasing ##\Lambda##.

But is this correct? Please advise.

https://en.wikipedia.org/wiki/De_Sitter–Schwarzschild_metric

2 solutions:

##f(r)=1-2M/r##

##f(r)=1-\Lambda*r^2##

Equating yields ##r=(2M/\Lambda)^{1/3}##

Is this the wanted static r-coordinate? Heuristically it seems to make sense, r increases with increasing ##M## and decreases with increasing ##\Lambda##.

But is this correct? Please advise.