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_metric():
"""
Tests, if covariant & contravariant forms of Kerr & Kerr-Newman metrics match, when Q -> 0
"""
r, theta, M, a = 0.1, 4 * np.pi / 5, 1e23, 0.99
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.)
mk_contra = mk.metric_contravariant(x_vec)
mkn_contra = mkn.metric_contravariant(x_vec)
mk_cov = mk.metric_covariant(x_vec)
mkn_cov = mkn.metric_covariant(x_vec)
assert_allclose(mk_contra, mkn_contra, rtol=1e-10)
assert_allclose(mk_cov, mkn_cov, rtol=1e-10)
def test_compare_kerr_kerrnewman_metric(bl):
"""
Tests, if covariant & contravariant forms of Kerr & Kerr-Newman metrics match, when Q -> 0
"""
M = 1e23 * u.kg
a = 0.99 * u.one
Q = 0. * u.C
x_vec = bl.position()
mk = Kerr(coords=bl, M=M, a=a)
mkn = KerrNewman(coords=bl, M=M, a=a, Q=Q)
mk_contra = mk.metric_contravariant(x_vec)
mkn_contra = mkn.metric_contravariant(x_vec)
mk_cov = mk.metric_covariant(x_vec)
mkn_cov = mkn.metric_covariant(x_vec)
assert_allclose(mk_contra, mkn_contra, rtol=1e-10)
assert_allclose(mk_cov, mkn_cov, rtol=1e-10)