Skip to main content
Physics

Return to Question

Notice removed Authoritative reference needed by CommunityBot
Bounty Ended with Void's answer chosen by CommunityBot
edited title
Link
Qmechanic ♦
Qmechanic ♦
  • 206.6k
  • 48
  • 566
  • 2.3k

why Why domain of Kerr black hole includes negative values for r$r$ coordinate?

added 2 characters in body; edited tags
Source Link
Níckolas Alves
Níckolas Alves
  • 22.1k
  • 3
  • 34
  • 106

I understand the domain of t$t$ is all real numbers but mathematically, how to prove the domain of r$r$ coordinate is also all real numbers except $r=0$ when $\theta = \pi/2$. I know that we get two disks when $\theta <\pi/2$$\theta < \pi/2$ and $\theta > \pi/2$ for $r=0$ but could we use this result and say $r<0$ as well  ? Secondly these two regions are timelike or spacelike  ? And if they are timelike can we go from one disk to other disk easily because there is a ring at the center which is curvature singularity  ?

I understand the domain of t is all real numbers but mathematically, how to prove the domain of r coordinate is also all real numbers except $r=0$ when $\theta = \pi/2$. I know that we get two disks when $\theta <\pi/2$ and $\theta > \pi/2$ for $r=0$ but could we use this result and say $r<0$ as well  ? Secondly these two regions are timelike or spacelike  ? And if they are timelike can we go from one disk to other disk easily because there is a ring at the center which is curvature singularity  ?

I understand the domain of $t$ is all real numbers but mathematically, how to prove the domain of $r$ coordinate is also all real numbers except $r=0$ when $\theta = \pi/2$. I know that we get two disks when $\theta < \pi/2$ and $\theta > \pi/2$ for $r=0$ but could we use this result and say $r<0$ as well? Secondly these two regions are timelike or spacelike? And if they are timelike can we go from one disk to other disk easily because there is a ring at the center which is curvature singularity?

Notice added Authoritative reference needed by Talha Ahmed
Bounty Started worth 50 reputation by Talha Ahmed
Source Link
Talha Ahmed
Talha Ahmed
  • 59
  • 7

why domain of Kerr black hole includes negative values for r coordinate?

I understand the domain of t is all real numbers but mathematically, how to prove the domain of r coordinate is also all real numbers except $r=0$ when $\theta = \pi/2$. I know that we get two disks when $\theta <\pi/2$ and $\theta > \pi/2$ for $r=0$ but could we use this result and say $r<0$ as well ? Secondly these two regions are timelike or spacelike ? And if they are timelike can we go from one disk to other disk easily because there is a ring at the center which is curvature singularity ?