Cauchy horizon in a Kerr rotating black hole

[stevebd1]

I'm currently in the process of understanding the properties of the Cauchy (or inner event) horizon in a rotating Kerr black hole. Initially, I thought the horizon was a result of centrifugal forces from the rotating ring singularity and extreme frame dragging that forced matter outwards, re-creating extremely curved time-like space within the confines of the black hole. I've since read that the Cauchy horizon is a result of matter hitting the ring singularity at (supposedly) superluminal speeds, recoiling and colliding with other matter falling inwards which causes a slow down and the re-creation of time-like space.

I was also initially under the impression that within the Cauchy horizon there would be a virtually pure vacuum with matter/light that had passed through the outer event horizon crashing into the Cauchy horizon as it was forced to slow down. I've recently read that within the Cauchy horizon of charged black holes, the volume consists of dense relativistic plasma and this might also apply to rotating black holes. I have slight issue with this as I've also read that within the confines of the ring singularity is negative space that exerts negative (or repellent) gravity. Wouldn't this repel the dense plasma away from the ring singularity towards the outer edge of the Cauchy horizon, leaving the ring singularity spinning in a disk of dense relativistic plasma that also reached out to the Cauchy horizon?

Another thing I've noticed is that the Cauchy horizon within a Kerr black hole seems to be frowned upon altogether (particularly within the discussion section of wiki for black holes where a suggestion to remove the section regarding the inner event horizon was carried through). The Cauchy horizon appears to be a part of Kerr metric, was it proposed by Roy Kerr or did he propose the metric for just the ergosphere and reduced outer event horizon, the inner event horizon suggested later? I'm also aware that some astrophysicists state that the Cauchy horizon wouldn't be stable due to the constant bombardment of extremely blue shifted light (gamma rays, etc.).

I'd be interested to hear peoples thoughts and opinions.

regards
Steve

 

[stevebd1]

The Cauchy horizon seems to be created when in falling matter hits the ring singularity and is tossed back temporarily into the path of other incoming matter which is slowed down; a more correct description being relativistic streaming which occurs between ingoing and back scattered outgoing radiation (sometimes referred to as mass-inflation), re-creating spacetime inside a rotating black hole. I imagine that as matter hits the ring singularity, it wouldn't be tossed back directly into the path it came but tangentially off into the direction of the spin, the distance reached by the back scatter dependent on the properties of the ring (when considering the ring as Planck matter, the radius is dependent on the spin factor 'a', the higher 'a', the larger the radius of the ring and therefore radiation is thrown out at more of a tangent, creating a larger radius for the Cauchy horizon; the higher 'a' is, the larger the ring singularity, the further the back scatter radiation reaches and the larger the Cauchy horizon).

When regular matter is falling into the rotating black hole, a dense ultra-relativistic plasma is formed within the Cauchy horizon but what would happen when no regular matter was falling into the black hole, if there was just dark matter and photons falling in? It's not unusual that black holes go through relatively quiet phases where the accretion disk has been exhausted and other matter orbits at a safe distance. Is there any theoretical evidence to suggest that relativistic streaming still occurs between incoming and back scattered dark matter and photons?

Also, while it's accepted that the photon is massless, it's accepted that it carries energy as E = pc. The light coming into the black hole would be highly blue shifted, and as it hits the ring singularity, it would be reasonable to assume that the energy would be transferred to the ring and as the radiation back scatters, it would be highly redshifted as it fought the immense gravity and curved space. As energy is mass, would it be fair to assume that even during quiet periods, the black hole would slightly increase in mass as high energy EM radiation fell into it?

 

[Oberst Villa]

Also, while it's accepted that the photon is massless, it's accepted that it carries energy as E = pc. The light coming into the black hole would be highly blue shifted, and as it hits the ring singularity, it would be reasonable to assume that the energy would be transferred to the ring and as the radiation back scatters, it would be highly redshifted as it fought the immense gravity and curved space. As energy is mass, would it be fair to assume that even during quiet periods, the black hole would slightly increase in mass as high energy EM radiation fell into it?

I don't completely understand your line of thought here, but that's not your fault but mine - I only understand non-rotating black holes on a qualitative level (maybe), and rotating ones not at all.

but I am pretty sure that your conclusion is right - photons that fall into a black hole will add their energy to the total energy of the black hole and thereby increase its mass. (whether the black hole is rotating or not should not matter)

 

[stevebd1]

Thanks for the response Oberst, it would be interesting to know if there has been any work done regarding the possibility of a black hole increasing slightly in mass from the influx of high energy photons, would it not also be a reasonable suggestion that it may balance out the mass lost through Hawking radiation?

 

[jimgraber]

Thanks for the response Oberst, it would be interesting to know if there has been any work done regarding the possibility of a black hole increasing slightly in mass from the influx of high energy photons, would it not also be a reasonable suggestion that it may balance out the mass lost through Hawking radiation?

Steve, I think it is widely accepted that the mass of astronomical sized black holes increases due to absorption of the CMBR and even starlight much faster than it decreases due to Hawking radiation. All this is based on theory and calculation, not observation of course. The ones we can "see" are accreting matter at an even higher rate.

Jim Graber

 

[Erich Schoedl]

I guess I'll admit to having a problem with an inner event horizon to any kind of black hole. On the qualitative level, I think that if a point on the outer horizon surface does not age relative to a given outside reference frame, then anything inside of this surface is technically beyond observation.

Yes I know how there is a mathematical trick employed to allow the reference frame of an in-falling observer to observe locally continuous space-time inside of the radius of an event horizon - but there is a huge flaw in this mathematicaly trick. It assumes the scale of this falling reference frame doesn't change. So to an in-falling observer - when "passing" the event horizon radius in his own reference frame - his measuring stick would just be increasing in size as his frame changes to make the radius of the event horizon appear relatively smaller. Assuming this change in scale for the falling observer, the horizon is still not ever passed relative to any observer - it's an impassible boundary as it should be. Assuming no change in scale relative to the outside observer to me seems to be more of an obsurd assumption, but both are assumptions.