Asdasda
Asfa
Shawsn sda
Asda
Asda
Qweq
2
12
(1 2m/r)dt2 [A(p)]2[dp2
+ p2{d92 + sin20d<£2)].
(14.52)
We could consider how
(14.47) transforms under
fi
the transformation
(14.51),
but it is easier to proceed
as follows. Comparing
(14.52) with (14.47),
coef cients of d82 +
sin20d</>2 must be
equal, which requires
r2 = k2p2.
Equating the two radial
elements produces
(l-2m/r)-1dr2 = /l2dp2.
fi
Eliminating A and taking
square roots, we nd
dr
(r2 - 2mr)
*-±
dp
(14.53)
(14.54)
(14.55)
This is an ordinary
differential equation in
fi
fi
which the variables are
separated.
Since we require p ->■
oo as r ->■ oo, we take
the positive sign, and by
integration we nd
(exercise)
r = p(l+im/p)2 (1456)
and so, from (14.53),
A2 = (1 + WP)4 (14.57)
Using (14.56) to
eliminate r, we nd that
the Schwarzschild
solution can
written in the following
isotropic form: