- #1
zerop
- 1
- 0
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
t
r
theta
phi
with(tensor):
coord := [t, r, theta, Phi]:
g_compts:=array(sparse,1..4,1..4):
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:
g_compts[1,4]:= 4*G*M*a*r*(sin(theta))^2/(c*p2):
g_compts[2,2]:= -p2/triangle:
g_compts[3,3]:= -p2:
g_compts[4,4]:= -A*(sin(theta)^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):
displayGR(Christoffel2,Cf2_1):
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
t
r
theta
phi
with(tensor):
coord := [t, r, theta, Phi]:
g_compts:=array(sparse,1..4,1..4):
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:
g_compts[1,4]:= 4*G*M*a*r*(sin(theta))^2/(c*p2):
g_compts[2,2]:= -p2/triangle:
g_compts[3,3]:= -p2:
g_compts[4,4]:= -A*(sin(theta)^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):
displayGR(Christoffel2,Cf2_1):