describe the main features of bs for the next Section
2EF
P2 (E2 f)(t t) 2 (t to)(r- o)- 2EJ(t-
f
+(+ ) (r ro)2+ 2 ( 7)2 2(
f f 2 f
+(r2 + J2)( 2 (t-to)3
00
To
M ( 2E2 r 2 MJr
+ + 2 + t- o)2(r o + -o (t
MEi 2(ro M)E
f2 2 (t to r _r0)2 fr (t t)(r
J '0 J'0
+roE(t to) (0- 2) + roE (t to)( o)2
M ( 2 (2ro-2)r 5M)Jr
22o 3 +12 2 r0
(r 2 0f2 2 ( 2
f 2f r
7+ r2 (+-r ( t r2 + 2J
-roJ ( ) ( o)- oJr ( o )3
+P1v(t, 0, 0) + Pv(t, r, 0, 0) + O[(x Xo)6,
o)(0 o)
to)2( o)
ro)( (- o)
2
r(r
2 /
0
0o)
ro)(0 o )2
(4-144)
where Piv(t, r, 0, 0) and Pv(t, r, 0, 0) represent the quartic and quintic order terms,
respectively. All these terms can be specified using MAPLE and GRTENSOR.
It is important to note that only the minimum information about the back-
ground spacetime is required for constructing XA in order to determine p2 to any
high order we desire. In other words, we specify XA only to the quadratic order
as in Eq. (4-131) for its use in Eq. (4-143), and the specification of XA to cubic or
higher order would not make any difference in p2
4.4 Determination of Regularization Parameters
In Section 4.3, we saw that an approximation of bs is particularly simple in
THZ normal coordinates,
s q/p + O(p3/R),
(4-145)