General spherically symmetric metric:
d
s
2
=
-
d
t
2
a
2
+
1
g
2
æ
ç
è
d
r
-
b
d
t
a
ö
÷
ø
2
+
r
2
d
o
2
a
=
¶
t
t
= reciprocal lapse
(
b
,
g
) = (
¶
t
r
,
¶
r
r
)
= proper radial 4-gradient
General spherically symmetric Einstein equations:
Mass:
¶
M
¶
r
=
4
p
r
2
r
where
1
-
2
M
r
º
g
2
-
b
2
Energy:
¶
t
g
=
b
g
Acceleration:
¶
t
b
=
g
g
-
M
r
2
-
4
p
r
p
r
Euler:
¶
r
p
r
=
2
g
r
(
p
^
-
p
r
)
-
(
r
+
p
r
)
g
Self-similarly accreting Black Hole
Self-similarly accreting Black Hole