- #1

binbagsss

- 1,281

- 11

## Homework Statement

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To take the ##lim J \to \infty ##, what are the two roots of ##r_c## in this case...

So I believe it says' ##J## big enough it had 2 solutions' is basically saying just avoiding the imaginary solutions i.e. ## J^4 \geq 12G^2M^2J^2 ## (equality for one route obvs).

## Homework Equations

see attachment

## The Attempt at a Solution

So I believe it says' ##J## big enough it had 2 solutions' is basically saying just avoiding the imaginary solutions i.e. ## J^4 \geq 12G^2M^2J^2 ## (equality for one route obvs).

If I write it as

##r_c= \frac{J^2 \pm \sqrt{J^4}\sqrt{1-\frac{12G^2M^2}{J^2}}}{2GM}##

then as ##J \to \infty ## the last term vanishes and for the + root clearly get ## \frac{J^2}{GM} ## , the first given in 3.48.

However for the - root I would get ##0##. I have no idea how to get ##3GM## , do I need to do some sort of expansion?

Many thanks