- #1

- 1

- 0

## Main Question or Discussion Point

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):