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Jan10-11, 07:45 AM
1. What are the value of physics constant in Kerr metric, including G, M, c, a, r, or others?
I expect to simplify Gamma
2. why g_compts[1,4] has element and not [4,1]?
3. Some book assume G = c = 1, what is the meaning of this setting?
4. Different material have different metric, are there a metric table for element table?
5. What is theta in Kerr metric?
************** Kerr metric *****************
t r theta phi
coord := [t, r, theta, Phi]:
G := 6.67*10^(-11)
triangle := r^2 - 2*G*M*r/c^2 + a^2:
p2 := r^2 + ((cos(theta))^2)*a^2:
A := (r^2+a^2)^2 - (a^2)*triangle*(sin(theta))^2:
g_compts[1,1]:= (triangle - (a^2)*(sin(theta))^2)*(c^2)/p2:
g1 := create([-1,-1], eval(g_compts)):
g1_inv := invert( g1, 'detg' ):
D1g := d1metric( g1, coord ):
Cf1_1 := Christoffel1(D1g):
Cf2_1 := Christoffel2(g1_inv, Cf1_1):
Jan19-11, 06:28 AM
G is the gravitational constant in units m^3/(kg s^2) (1 in geometric units)
m is mass in kg where M is the geometric unit for mass (M=Gm/c^2) in metres
c is the speed of light in m/s (or 1 in geometric units)
a is the geometric units for angular momentum in metres (a=J/mc where J is angular momentum in SI units)
r is radius in metres
Delta (or triangle as you call it) is the radial parameter in m^2.
when writing delta, you have written delta=r^2-2*G*m*r/c^2+a^2. If geometric units are used, you can simply write delta=r^2-2M+a^2 where M=*G*m*r/c^2, the answers are the same.
g_compts[1,4] does include for [4,1], they've just substituted the 2*(2*.. with a 4*.., it can be rewritten-
g_compts[1,4]=2*(2*M*a*r*(sin(theta))^2/(p2)), [1,4] & [4,1] being the same, another way of writing it is 2*g_compts[1,4].
theta is the latitude approach, 90 degrees (or pi/2) at the equator and 0 at the poles.
You may also find this web page useful-
Jan20-11, 02:01 AM
The text above relating to delta should read-
'when writing delta, you have written delta=r^2-2*G*m*r/c^2+a^2. If geometric units are used, you can simply write delta=r^2-2Mr+a^2 where M=G*m/c^2, the answers are the same.'
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