I am trying to solve geodesic equations in some 3D black hole spacetime. It is a coupled ODE system with boundary conditions. Due to the symmetry of the spacetime, I expect the solutions to be even functions, with r'[0] == 0
and v'[0] == 0
.
Here's my code:
f[r_, v_] := r^2 - 1/2 Tanh[v] - 1/2
NDSolve[
{0 == D[(r[x]^2 + 2 r'[x] v'[x] - f[r[x], v[x]] v'[x]^2)/r[x]^4, x],
r[x]^2 - r[x]^2 v'[x]^2 - r[x] v''[x] + 2 v'[x] r'[x] == 0,
r[-1.5] == 100, r[1.5] == 100, v[-1.5] == 10, v[1.5] == 10},
{r, v}, {x, -1.5, 1.5}]
But I don't get results, but only the following messages:
Power::infy: Infinite expression 1/0. encountered.
Power::infy: Infinite expression 1/0. encountered.
Infinity::indet: Indeterminate expression 0. ComplexInfinity ComplexInfinity encountered.
Power::infy: Infinite expression 1/0. encountered.
Can someone point out what is wrong with my code?
r == 0
asNDSolve
attempts to match the boundary conditions. Qualitatively, what do you expect the solutions to look like? $\endgroup$