def test_compare_kerr_kerrnewman_dmetric_dx(c, G, Cc, r, theta, M, a):
# differentiation of metric for kerr and kerr-newman metric should be equal when Q=0
scr = M * G / (c**2)
a_scaled = kerr_utils.scaled_spin_factor(a, M, c, G)
m1 = kerr_utils.dmetric_dx(c, r, theta, scr, a_scaled)
m2 = kerrnewman_utils.dmetric_dx(c, G, Cc, r, theta, scr, a_scaled, 0.0)
assert_allclose(m1, m2, rtol=1e-10)
def test_compare_kerr_kerrnewman_dmetric_dx(test_input):
c, G, Cc, r, theta, M, a = test_input
# differentiation of metric for Kerr and Kerr-Newman metric should be equal when Q=0
scr = 2 * M * G / (c ** 2)
a_scaled = kerr_utils.scaled_spin_factor(a, M)
m1 = kerr_utils.dmetric_dx(r, theta, M, a_scaled)
m2 = kerrnewman_utils.dmetric_dx(r, theta, M, a_scaled, 0.0)
assert_allclose(m1, m2, rtol=1e-10)
def test_christoffels1(c, G, Cc, r, theta, M, a, Q):
# compare christoffel symbols output by optimized function and by brute force
scr = M * G / (c**2)
a_scaled = kerr_utils.scaled_spin_factor(a, M, c, G)
chl1 = kerrnewman_utils.christoffels(c, G, Cc, r, theta, scr, a_scaled, Q)
# calculate by formula
invg = kerrnewman_utils.metric_inv(c, G, Cc, r, theta, scr, a_scaled, Q)
dmdx = kerrnewman_utils.dmetric_dx(c, G, Cc, r, theta, scr, a_scaled, Q)
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
l = t % 4
for m in range(4):
chl2[i, k, l] += invg[i, m] * (dmdx[l, m, k] + dmdx[k, m, l] -
dmdx[m, k, l])
chl2 = np.multiply(chl2, 0.5)
assert_allclose(chl2, chl1, rtol=1e-10)