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In the derivation of the spin–orbit interaction, we transform to a frame that is fixed on the electron. I have several questions about this:

  1. Will I see any radiation if I orbit around a static charge?
  2. Will I see a Kerr black hole if I orbit around a Schwarzchild black hole?
  3. If I orbit around a Kerr black hole with the opposite direction of its angular momentum, will I see the black hole revolves around me without rotation? Is this a Schwarzchild black hole?

This is the Kerr metric Kerr metric

By the coordinate transformation $\phi^{'}=\phi+\Omega t$ enter image description here

I'll get enter image description here This isn't Schwarzchild metric

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    $\begingroup$ no if you orbit a Schwarzschild black hole you don't get a Kerr black hole, and also not a Schwarzschild black hole if you retrogradely orbit Kerr. Rotation and acceleration is not relative, in contrast to translatory motions. $\endgroup$ – Yukterez Apr 15 at 9:17
  • $\begingroup$ So if I orbit around a Schwarzchild black hole, I still see a Schwarzchild black hole, it just changes another metric under my rotating reference frame. And for I retrograde orbit Kerr, I will see a black hole which is not rotating, but it’s still Kerr. $\endgroup$ – Brian Chang Apr 16 at 4:14
  • $\begingroup$ why would it not be rotating if you orbit retrogradely? then the relative velocity of the surface would be even higher than if you orbit progradely. if you want to know what an unfed Kerr black hole (without an accretion disk) looks if you orbit retrogradely see here: notizblock.yukterez.net/viewtopic.php?p=533#aberration . also if you want to orbit the black hole with the same angular velocity as the black hole itself that might easily exceed the speed of light, since same angular velocity times a higher radius is an even higher local velocity. $\endgroup$ – Yukterez Apr 16 at 4:40
  • $\begingroup$ Oh yes, I mean prograde. My question is that is it possible for me to see a Kerr black hole which doesn’t rotate? Suppose I throw an object with a very small angular momentum into a Schwarzchild black hole, it will become a Kerr black hole with a very small angular momentum, is it possible for me to catch up? $\endgroup$ – Brian Chang Apr 16 at 7:02
  • $\begingroup$ Is this picture correct? A spacecraft outside the ergosphere can accelerate to reach a tie with the frame-dragging effect, and an infinite far observer will see the spacecraft as if it seems to stop by the Kerr BH, but the people inside the spacecraft will feel a great acceleration. Another question is that does frame-dragging effect breaks Mach’s principle? $\endgroup$ – Brian Chang Apr 16 at 15:06

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