(and thus leaves the PNDs intact). The tetrad is given by:
T2 2
T2 + 2
if=~ \ ?P 0, (6-13)
2/(r + is cos 8) i n 0 sin 8
With this tetrad choice, the radial jump conditions are:
8f2h,war = 1 (6-14)
8f2h,war = 16 ,(6-15)
8?2(hit + h,z~ + 2hl,z 2h,>uz) = 1 n (6-16)
8?2(hira + h,and = 16x 5,,2, (6-17)
where the omitted equations follow by taking the prime and/or complex conjugate of those
listed (the factors of a and P"2 remain unchanged; a feature of the symmetric tetrad),
and it is understood that equality only holds in the sense of Equation 6-6. At a glance
Equations 6-14-618 may appear inconsistent, with the same left-hand-side being equated
to different right-hand-sides. In fact, the circular geodesic nature of u" ensures that this is
not the case.
What we have not yet addressed is the question of what, precisely, we mean by mass
and angular momentum. Suitable definitions arise from the Hamiltonian treatment of
General Relativity initiated by Arnowitt, Deser and Misner [71]. The general idea is
that because Minkowski space provides an unambiguous notion of energy and angular
momentum through time translations and rotations, respectively, we can adapt these
notions to curved spaces if the metric becomes Minkowskian at spacelike infinity. Thus
the ADM definitions require us to restrict our attention to .-i-mptotically flat spacetimes,