Why do standing waves fit inside black holes with a node at the event horizon?

[ColdFusion85]

I am reading an article on black holes and they state, "Now what kinds of waves are possible inside a black hole? The answer is standing waves, waves that "fit" inside the black hole with a node at the event horizon."

Can anyone explain to me why they know the answer is standing waves, and what do they mean when they say they "fit" inside the black hole??

 

[Werg22]

Hummm I think they mean electromagnetic waves particles such as photons are not able to leave the black hole since even at the speed of light it cannot escape the tremendous gravity. For the fitting, I have at the moment no idea.

 

[Claude Bile]

Any specific solution to a DE (in this case the wave equation) depends on the boundary conditions.

Since information cannot escape from a black hole, waves themselves may not escape from a black hole. The event horizon (i.e. the boundary of the black hole) must therefore be fixed at zero for all time.

The solution to such problems is a standing wave, as any 'non' standing wave violates this boundary condition.

Claude.

 

[ColdFusion85]

That makes things much clearer. Thanks Calude Bile.

 

[James Jackson]

But surely the geometry inside a black hole is so messed up we can't even think about standing waves within them? The geometry of a singular point with infinite density. Hmmm, nice.

 

[Claude Bile]

The Black Hole is not just a singularity, it is has a finite volume that is the region of space where light cannot escape from its embrace. I see no reason why laws of physics cannot be applied to this space.

The singularity itself is a different matter.

Claude.