# Mass Inflation Instability in Kerr and Reisnerr black holes.

1. Dec 29, 2014

### Lamdbaenergy

What exactly is this mass inflation instability phenomenon that is said to happen near the inner horizon of black holes?
I got the nutshell of it, but I think I need someone to really explain this.

2. Dec 30, 2014

### Simon Bridge

Please explain your "nutshell" so we know what you need, and what level you need it at.
Do you know what "mass inflation" refers to, for example?

3. Dec 30, 2014

### Lamdbaenergy

Sorry 'bout that; I don't have a good level of mathematics. I got that light tends towards an infinite blue shift at the inner horizon, as said in the link. The confusing part was where it talked about ingoing and outgoing particles "trying to travel back and forth in time and exceeding the speed of light relative to one another" near the inner horizon and causing some kind of instability, vaporizing any person and or object before it got to the singularity.

To be honest I'm not too familiar with the term "mass inflation" and just got aware of it while I was reading that link. I guess my more specific questions are now:

What happens to radial and time directions r and t inside different black holes?

What is a black hole 'firewall?'

And can the singularity repel stuff out rather than suck it in?

Any answer without an extreme amount of much math is fine; I'll attempt my best to understand it.

4. Dec 30, 2014

### Simon Bridge

So you won't have much GR either, then, and you are trying to find out about the space-time geometry inside a black hole?
Have you gone through the basics with non-rotating, neutral charge, black holes? (References below JIC.)

I don't think I can give you a complete explanation in one go. Instead I'll try pointing you in a useful direction.

Loosely. What the article is referring to is a method of doing a calculation called a "perturbation" where you start with the well-known solutions and then tweak the situation a little - i.e. you start modelling the Earth as a sphere, then gradually account for how the Earth diverges from perfectly spherical after working out the results for the simpler shape. The calculation usually involves a lot of steps - think of an infinite sum. This is not a problem when the terms get smaller and smaller in a nice way so the overall sum converges, and this is what normally happens like when you want to figure the gravity of the Earth. However, if you try to use this method for specific types of black hole, the perturbation calculation no longer converges everywhere. You can think of the incoming and outgoing "streams" as an artifact of the calculation method. The "instability" just means that the calculation method fails.

Bottom line is that this is one of those things where you need the maths.

Time and space swap roles across the event horizons
http://www.einstein-online.info/spotlights/changing_places
http://www.jimhaldenwang.com/black_hole.htm
... because of the symmetry, it is useful to define a radial direction and a couple of angular ones for space.
Firewall: have you seen: http://en.wikipedia.org/wiki/Firewall_(physics)
I suspect you are being glib here, but the key to figuring out relativity is to be careful with how you say things.

The "singularity" is just the name given to the situation where our maths fail - it has no physical meaning. It's just a mathy way of saying "we dunno what's going on here". You can see this with just normal gravity ... the force is given by $F=GMm/r^2$, and you can see that the force blows up at $r=0$. It just means that the equation does not work when the small mass m is very close to the center of the big one M. Same with the singularity of a black hole.

"Repel" and "attract" are terms that make no sense in space-time ... these are concepts that require a well-defined time axis. Inside the black hole you don't have one, so the articles are playing a bit loose with the terminology. If you've followed the basic stuff above, you may have a better shot at figuring what the authors you are trying to understand are trying to talk about.

5. Jan 4, 2015

### stevebd1

Here's the old library entry for mass inflation-

What is mass inflation