def test_compare_metrics_under_limits(sph, bl):
"""
Tests if KerrNewman Metric reduces to Kerr Metric, in the limit Q -> 0 and to Schwarzschild \
Metric, in the limits, a -> 0 & Q -> 0
"""
M = 6.73317655e26 * u.kg
a1, a2 = 0.5 * u.one, 0. * u.one
Q = 0. * u.C
ms = Schwarzschild(coords=sph, M=M)
mk = Kerr(coords=bl, M=M, a=a1)
mk0 = Kerr(coords=bl, M=M, a=a2)
mkn = KerrNewman(coords=bl, M=M, a=a1, Q=Q)
mkn0 = KerrNewman(coords=bl, M=M, a=a2, Q=Q)
x_vec_sph = sph.position()
x_vec_bl = bl.position()
ms_mat = ms.metric_covariant(x_vec_sph)
mk_mat = mk.metric_covariant(x_vec_bl)
mk0_mat = mk0.metric_covariant(x_vec_bl)
mkn_mat = mkn.metric_covariant(x_vec_bl)
mkn0_mat = mkn0.metric_covariant(x_vec_bl)
assert_allclose(ms_mat, mk0_mat, rtol=1e-8)
assert_allclose(mk_mat, mkn_mat, rtol=1e-8)
assert_allclose(mkn0_mat, ms_mat, rtol=1e-8)
def test_calculate_trajectory_kerr(x_vec, v_vec, t, M, a, end_lambda,
step_size):
mk_cov = Kerr(coords="BL", M=M, a=a)
x_4vec = four_position(t, x_vec)
mk_cov_mat = mk_cov.metric_covariant(x_4vec)
init_vec = stacked_vec(mk_cov_mat, t, x_vec, v_vec, time_like=True)
geod = Geodesic(metric=mk_cov,
init_vec=init_vec,
end_lambda=end_lambda,
step_size=step_size,
return_cartesian=False)
ans = geod.trajectory
testarray = list()
for i in ans:
x = i[:4]
g = mk_cov.metric_covariant(x)
testarray.append(g[0][0] * (i[4]**2) + g[1][1] * (i[5]**2) + g[2][2] *
(i[6]**2) + g[3][3] * (i[7]**2) +
2 * g[0][3] * i[4] * i[7])
testarray = np.array(testarray, dtype=float)
assert_allclose(testarray, 1., 1e-4)
def test_compare_metrics_under_limits():
"""
Tests if KerrNewman Metric reduces to Kerr Metric, in the limit Q -> 0 and to Schwarzschild \
Metric, in the limits, a -> 0 & Q -> 0
"""
r, theta = 99.9, 5 * np.pi / 6
M = 6.73317655e26
x_vec = np.array([0., r, theta, 0.])
ms = Schwarzschild(M=M)
mk = Kerr(coords="BL", M=M, a=0.5)
mk0 = Kerr(coords="BL", M=M, a=0.)
mkn = KerrNewman(coords="BL", M=M, a=0.5, Q=0.)
mkn0 = KerrNewman(coords="BL", M=M, a=0., Q=0.)
ms_mat = ms.metric_covariant(x_vec)
mk_mat = mk.metric_covariant(x_vec)
mk0_mat = mk0.metric_covariant(x_vec)
mkn_mat = mkn.metric_covariant(x_vec)
mkn0_mat = mkn0.metric_covariant(x_vec)
assert_allclose(ms_mat, mk0_mat, rtol=1e-8)
assert_allclose(mk_mat, mkn_mat, rtol=1e-8)
assert_allclose(mkn0_mat, ms_mat, rtol=1e-8)
def test_four_velocity(v_vec, time_like):
"""
Tests, if the 4-Velocity in KerrNewman Metric is the same as that in Kerr Metric, \
in the limit Q -> 0 and if it becomes the same as that in Schwarzschild \
Metric, in the limits, a -> 0 & Q -> 0
"""
M = 1e24
x_vec = np.array([1.0, np.pi / 2, 0.1])
x_vec = np.array([1.0, np.pi / 2, 0.1])
ms = Schwarzschild(M=M)
mk = Kerr(coords="BL", M=M, a=0.5)
mk0 = Kerr(coords="BL", M=M, a=0.)
mkn = KerrNewman(coords="BL", M=M, a=0.5, Q=0.)
mkn0 = KerrNewman(coords="BL", M=M, a=0., Q=0.)
ms_mat = ms.metric_covariant(x_vec)
mk_mat = mk.metric_covariant(x_vec)
mk0_mat = mk0.metric_covariant(x_vec)
mkn_mat = mkn.metric_covariant(x_vec)
mkn0_mat = mkn0.metric_covariant(x_vec)
v4vec_s = four_velocity(ms_mat, v_vec, time_like)
v4vec_k = four_velocity(mk_mat, v_vec, time_like)
v4vec_k0 = four_velocity(mk0_mat, v_vec, time_like)
v4vec_kn = four_velocity(mkn_mat, v_vec, time_like)
v4vec_kn0 = four_velocity(mkn0_mat, v_vec, time_like)
assert_allclose(v4vec_s, v4vec_k0, rtol=1e-8)
assert_allclose(v4vec_k, v4vec_kn, rtol=1e-8)
assert_allclose(v4vec_kn0, v4vec_s, rtol=1e-8)
def test_compare_vt_schwarzschild_kerr_kerrnewman():
"""
Tests, whether the timelike component of 4-Velocity in KerrNewman Metric is the same as that \
in Kerr Metric, in the limit Q -> 0 and if it becomes the same as that in Schwarzschild \
Metric, in the limits, a -> 0 & Q -> 0
"""
M = 1e24
x_vec = np.array([1.0, np.pi / 2, 0.1])
v_vec = np.array([-0.1, -0.01, 0.05])
ms = Schwarzschild(M=M)
mk = Kerr(coords="BL", M=M, a=0.5)
mk0 = Kerr(coords="BL", M=M, a=0.)
mkn = KerrNewman(coords="BL", M=M, a=0.5, Q=0.)
mkn0 = KerrNewman(coords="BL", M=M, a=0., Q=0.)
ms_mat = ms.metric_covariant(x_vec)
mk_mat = mk.metric_covariant(x_vec)
mk0_mat = mk0.metric_covariant(x_vec)
mkn_mat = mkn.metric_covariant(x_vec)
mkn0_mat = mkn0.metric_covariant(x_vec)
vt_s = v_t(ms_mat, v_vec)
vt_k = v_t(mk_mat, v_vec)
vt_k0 = v_t(mk0_mat, v_vec)
vt_kn = v_t(mkn_mat, v_vec)
vt_kn0 = v_t(mkn0_mat, v_vec)
assert_allclose(vt_s, vt_k0, rtol=1e-8)
assert_allclose(vt_k, vt_kn, rtol=1e-8)
assert_allclose(vt_kn0, vt_s, rtol=1e-8)
def test_calculate_trajectory_iterator_RuntimeWarning_kerr():
t = 0.
M = 1e25
a = 0.
x_vec = np.array([306., np.pi / 2, np.pi / 2])
v_vec = np.array([0., 0.01, 10.])
mk_cov = Kerr(coords="BL", M=M, a=a)
x_4vec = four_position(t, x_vec)
mk_cov_mat = mk_cov.metric_covariant(x_4vec)
init_vec = stacked_vec(mk_cov_mat, t, x_vec, v_vec, time_like=True)
end_lambda = 1.
stepsize = 0.4e-6
OdeMethodKwargs = {"stepsize": stepsize}
geod = Geodesic(metric=mk_cov,
init_vec=init_vec,
end_lambda=end_lambda,
step_size=stepsize,
return_cartesian=False)
with warnings.catch_warnings(record=True) as w:
it = geod.calculate_trajectory_iterator(
OdeMethodKwargs=OdeMethodKwargs, )
for _, _ in zip(range(1000), it):
pass
assert len(w) >= 1
def test_calculate_trajectory_iterator_kerr(x_vec, v_vec, t, M, a, end_lambda,
step_size, OdeMethodKwargs,
return_cartesian):
mk_cov = Kerr(coords="BL", M=M, a=a)
x_4vec = four_position(t, x_vec)
mk_cov_mat = mk_cov.metric_covariant(x_4vec)
init_vec = stacked_vec(mk_cov_mat, t, x_vec, v_vec, time_like=True)
geod = Geodesic(metric=mk_cov,
init_vec=init_vec,
end_lambda=end_lambda,
step_size=step_size,
return_cartesian=return_cartesian)
traj = geod.trajectory
traj_iter = geod.calculate_trajectory_iterator(
OdeMethodKwargs=OdeMethodKwargs, return_cartesian=return_cartesian)
traj_iter_list = list()
for _, val in zip(range(50), traj_iter):
traj_iter_list.append(val[1])
traj_iter_arr = np.array(traj_iter_list)
assert_allclose(traj[:50, :], traj_iter_arr, rtol=1e-10)
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_calculate_trajectory3_kerr():
# Based on the revolution of earth around sun
# Data from https://en.wikipedia.org/wiki/Earth%27s_orbit
# Initialized with cartesian coordinates
# Function returning cartesian coordinates
t = 0.
M = 1.989e30
a = 0.
distance_at_perihelion = 147.10e9
speed_at_perihelion = 30290
x_sph = CartesianConversion(distance_at_perihelion / np.sqrt(2),
distance_at_perihelion / np.sqrt(2), 0.,
-speed_at_perihelion / np.sqrt(2),
speed_at_perihelion / np.sqrt(2),
0.).convert_spherical()
x_vec = x_sph[:3]
v_vec = x_sph[3:]
mk_cov = Kerr(coords="BL", M=M, a=a)
x_4vec = four_position(t, x_vec)
mk_cov_mat = mk_cov.metric_covariant(x_4vec)
init_vec = stacked_vec(mk_cov_mat, t, x_vec, v_vec, time_like=True)
end_lambda = 3.154e7
geod = Geodesic(
metric=mk_cov,
init_vec=init_vec,
end_lambda=end_lambda,
step_size=end_lambda / 2e3,
)
ans = geod.trajectory
# velocity should be 29.29 km/s at aphelion(where r is max)
R = np.sqrt(ans[:, 1]**2 + ans[:, 2]**2 + ans[:, 3]**2)
i = np.argmax(R) # index where radial distance is max
v_aphelion = ((np.sqrt(ans[i, 5]**2 + ans[i, 6]**2 + ans[i, 7]**2) *
(u.m / u.s)).to(u.km / u.s)).value
assert_allclose(v_aphelion, 29.29, rtol=0.01)
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)
def test_calculate_trajectory_kerr(bl, M, a, end_lambda, step_size):
mk = Kerr(coords=bl, M=M, a=a)
geod = Timelike(metric=mk,
coords=bl,
end_lambda=end_lambda,
step_size=step_size,
return_cartesian=False)
ans = geod.trajectory
testarray = list()
for i in ans:
x = i[:4]
g = mk.metric_covariant(x)
testarray.append(g[0][0] * (i[4]**2) + g[1][1] * (i[5]**2) + g[2][2] *
(i[6]**2) + g[3][3] * (i[7]**2) +
2 * g[0][3] * i[4] * i[7])
testarray = np.array(testarray)
assert_allclose(testarray, _c**2, 1e-8)