frame around the origin, where the rotation is confined to the two-dimensional
submanifold E : {t = const, r = const, 0, 0}. They are separated into the three
groups:
(i) Scalars pem
{jh, hm, h7}, which have the form
'em = constY'em(0, ), (5-40)
(ii) Vectors qm
{hto, h4, hto, hm }, which have two distinct types with opposite parity
Teven) constYtm;a, parity (-), (5-41)
todd) constcaby parity (-)+1, (5-42)
(iii) Tensors mab
{h, h, h}, which consist of three fundamental types of tensor
(scalar) consta OY m, (5-43)
(even) constYsm;ai,, parity (- (5-44)
(i0dd) COconst (EcYam. Y 1) parity (-+,1 (5-45)
where the labels a and b run over 0 and Q, and the semicolon denotes covariant
differentiation, and ara represents the metric tensor on the two-dimensional sphere
E, defined by
Jab 9/r2, (5-46)
and ea is the alternating tensor on E, defined by
J ab 6ba = Vdet(), if a(b7
(5-47)
eb = O, if a = b