So, I've been reading through "Exploring Black Holes: Introduction to General Relativity" by Wheeler and Taylor, and I've had some ideas I wanted to pursue and do some research in regarding trajectories within the event horizon.(adsbygoogle = window.adsbygoogle || []).push({});

In this, I'd like to have the mathematical tools to investigate the validity of various claims. I know PF isn't a place to do research - these aren't those questions I aim to address with my work, these are different questions which I know others already know the answer to better than I do:

The book brings up the Kerr Metric but doesn't go too deeply into it, and also raises the point of the Cauchy Horizon, which, due to the fact that real black holes are probably best described by the extreme case of a maximally spinning black hole, and that the Kerr Metric is no longer valid at (or within, I assume?) the Cauchy Horizon, and that in such a maximally spinning black hole, the Cauchy horizon is at the same radius as the usual Event Horizon, the Kerr Metric would then seem invalid for describing anywhere within the event horizon of a real black hole (as approximated by the maximally spinning case).

The problem is, the questions I'd like to answer require mathematical analysis that will reveal some properties of a trajectory inside arealblack hole.

So, if the Kerr is explicitly stated to be invalid in this region,

1) am I better off asking these questions and analyzing them with the Schwarzschild solution? Even though the Schwarzchild describes a non-spinning black hole, perhaps at least some of the qualitative features I'm after will carry over, and remain true in the case of a spinning black hole? Or would I be better off using the Kerr solution, as it retainsmorevalidity, even if not an accurate description of the Cauchy Horizon?

I'm limited in my mathematical knowledge at the moment to single variable calculus and linear algebra (matrices and the sort), otherwise I could, of course, just use more general equations instead of relying on specific solutions/metrics, such as the Kerr and Schwarzschild.

And two other big questions;

2) Is the Cauchy Horizon a regionnearwhich the Kerr solution is invalid, or is it a regionwithinwhich the Kerr solution is invalid? In other words, could I still use the Kerr solution to answer my questions as long as I'm not near the Horizon or the Singularity (or is the singularity the Cauchy Horizon)?

3) Is there a metric I could use, knowing only single variable calculus, thatisvalid everywhere inside a spinning black hole?

Thanks very much!

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# The Validity of the Schwarzschild Metric Inside of a Real BH

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