def test_em_tensor_contravariant():
"""
Tests skew-symmetric property of EM Tensor
Theoretical background is required to write extensive tests. \
Right now only skew-symmetric property is being checked.
"""
M, a, Q = 1e22 * u.kg, 0.7 * u.one, 45.0 * u.C
bl = BoyerLindquistDifferential(
t=0. * u.s,
r=5.5 * u.m,
theta=2 * np.pi / 5 * u.rad,
phi=0. * u.rad,
v_r=200. * u.m / u.s,
v_th=9. * u.rad / u.s,
v_p=10. * u.rad / u.s
)
x_vec = bl.position()
# Using function from module
mkn = KerrNewman(coords=bl, M=M, a=a, Q=Q)
mkn_em_contra = mkn.em_tensor_contravariant(x_vec)
assert_allclose(0., mkn_em_contra + np.transpose(mkn_em_contra), atol=1e-8)
def test_em_tensor_covariant():
"""
Tests, if the calculated Maxwell Tensor is the same as that from the formula
Formula for testing from https://arxiv.org/abs/gr-qc/0409025
"""
M, a, Q = 2e22 * u.kg, 0.5 * u.one, 10.0 * u.C
bl = BoyerLindquistDifferential(t=0. * u.s,
r=1.5 * u.m,
theta=3 * np.pi / 5 * u.rad,
phi=0. * u.rad,
v_r=0. * u.m / u.s,
v_th=0. * u.rad / u.s,
v_p=0. * u.rad / u.s)
x_vec = bl.position()
r, theta = x_vec[1], x_vec[2]
alpha = BaseMetric.alpha(M, a)
# Using function from module
mkn = KerrNewman(coords=bl, M=M, a=a, Q=Q)
mkn_em_cov = mkn.em_tensor_covariant(x_vec)
# Checking Skew-Symmetry of Covariant Maxwell Tensor
assert_allclose(0., mkn_em_cov + np.transpose(mkn_em_cov), atol=1e-8)
th, r2, alpha2 = theta, r**2, alpha**2
# Unit Scaling factor for Charge
scale_Q = np.sqrt(_G * _Cc) / _c**2
# Electric and Magnetic Fields
D_r = (scale_Q * Q.value *
(r2 - (alpha * np.cos(th))**2)) / ((r2 +
(alpha * np.cos(th))**2)**2)
D_th = ((alpha2) * (-(scale_Q * Q.value)) * np.sin(2 * th)) / (
(r2 + (alpha * np.cos(th))**2)**2)
H_r = (2 * alpha * (scale_Q * Q.value) *
(r2 + alpha2) * np.cos(th)) / (r * ((r2 +
(alpha * np.cos(th))**2)**2))
H_th = ((alpha * (scale_Q * Q.value) * np.sin(th) *
(r2 - (alpha * np.cos(th))**2)) /
(r * ((r2 + (alpha * np.cos(th))**2)**2)))
assert_allclose(D_r, mkn_em_cov[0, 1], rtol=1e-8)
assert_allclose(r * D_th, mkn_em_cov[0, 2], rtol=1e-8)
assert_allclose(-r * np.sin(theta) * H_th, mkn_em_cov[1, 3], rtol=1e-8)
assert_allclose((r**2) * np.sin(theta) * H_r, mkn_em_cov[2, 3], rtol=1e-8)
def test_f_vec_bl_kerr():
M, a = 6.73317655e26 * u.kg, 0.2 * u.one
bl = BoyerLindquistDifferential(t=0. * u.s,
r=1e6 * u.m,
theta=4 * np.pi / 5 * u.rad,
phi=0. * u.rad,
v_r=0. * u.m / u.s,
v_th=0. * u.rad / u.s,
v_p=2e6 * u.rad / u.s)
f_vec_expected = np.array([
3.92128321e+03, 0.00000000e+00, 0.00000000e+00, 2.00000000e+06,
-0.00000000e+00, 1.38196394e+18, -1.90211303e+12, -0.00000000e+00
])
mk = Kerr(coords=bl, M=M, a=a)
state = np.hstack((bl.position(), bl.velocity(mk)))
f_vec = mk._f_vec(0., state)
assert isinstance(f_vec, np.ndarray)
assert_allclose(f_vec_expected, f_vec, rtol=1e-8)
