def test_christoffels(bl):
"""
Compares output produced by optimized function, with that, produced via general method (formula)
"""
r, theta = 100.0 * u.m, np.pi / 5 * u.rad
M, a = 6.73317655e26 * u.kg, 0.2 * u.one
x_vec = bl.position()
# Output produced by the optimized function
mk = Kerr(coords=bl, M=M, a=a)
chl1 = mk.christoffels(x_vec)
# Calculated using formula
g_contra = mk.metric_contravariant(x_vec)
dgdx = mk._dg_dx_bl(x_vec)
chl2 = np.zeros(shape=(4, 4, 4), dtype=float)
tmp = np.array([i for i in range(4**3)])
for t in tmp:
i = int(t / (4**2)) % 4
k = int(t / 4) % 4
index = t % 4
for m in range(4):
chl2[i, k, index] += g_contra[i, m] * (
dgdx[index, m, k] + dgdx[k, m, index] - dgdx[m, k, index])
chl2 = np.multiply(chl2, 0.5)
assert_allclose(chl2, chl1, rtol=1e-8)
def test_compare_kerr_kerrnewman_dmetric_dx(test_input):
"""
Tests, if the metric derivatives for Kerr & Kerr-Newman metrics match, when Q -> 0
"""
bl, M, a = test_input
x_vec = bl.position()
mk = Kerr(coords=bl, M=M, a=a)
mkn = KerrNewman(coords=bl, M=M, a=a, Q=0. * u.C)
mkdx = mk._dg_dx_bl(x_vec)
mkndx = mkn._dg_dx_bl(x_vec)
assert_allclose(mkdx, mkndx, rtol=1e-8)
def test_compare_kerr_kerrnewman_dmetric_dx(test_input):
"""
Tests, if the metric derivatives for Kerr & Kerr-Newman metrics match, when Q -> 0
"""
r, theta, M, a = test_input
x_vec = np.array([0., r, theta, 0.])
mk = Kerr(coords="BL", M=M, a=a)
mkn = KerrNewman(coords="BL", M=M, a=a, Q=0.)
mkdx = mk._dg_dx_bl(x_vec)
mkndx = mkn._dg_dx_bl(x_vec)
assert_allclose(mkdx, mkndx, rtol=1e-10)
