Important: The tensor package has been deprecated. Use the superseding packages DifferentialGeometry and Physics instead.
Determine the frame which reduces the Schwarzschild metric to a constant metric:
The metric involves trig functions, modify `tensor/lin_com/simp`:
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`tensor/lin_com/simp`:= proc (x)
local y;
y:=simplify(x);
eval(subs( cos(theta)^2 = 1 - sin(theta)^2, y));
end proc;
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Also, use the frame to carry out a change of basis, make sure that tensor[change_basis] returns things in a simplest form possible. Note that tensor[change_basis] uses `tensor/raise/simp` for simplification (see the help page tensor[simp] for a full list of simplifier routine names).
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`tensor/raise/simp` := proc(a) simplify(a) end proc;
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Now find a frame (note that you are making any required evaluations at the point [t,r,theta,phi] = [3,3,3,3] with a value of 1 for `m' (that is, outside the Schwarzschild radius):
Note that you can replace the [3,3] and [4,4] components of the computed hinv with something a little simpler:
Does this hinv still transform g to const_g?
Now suppose a change to the more general spherically-symmetric geometry
Even though you gave values for all of the variables, there is no way to determine the signs of the entries since the functions f1 and f2 are not known:
This is the best you can do without knowing more about f1 and f2. However, the computed result does give us an indication of a simpler form to use: