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_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_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_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_calculate_trajectory_iterator(
pos_vec,
vel_vec,
time,
M,
a,
start_lambda,
end_lambda,
OdeMethodKwargs,
return_cartesian,
):
cl1 = Kerr.from_BL(pos_vec, vel_vec, time, M, a)
arr1 = cl1.calculate_trajectory(
start_lambda=start_lambda,
end_lambda=end_lambda,
OdeMethodKwargs=OdeMethodKwargs,
return_cartesian=return_cartesian,
)[1]
cl2 = Kerr.from_BL(pos_vec, vel_vec, time, M, a)
it = cl2.calculate_trajectory_iterator(
start_lambda=start_lambda,
OdeMethodKwargs=OdeMethodKwargs,
return_cartesian=return_cartesian,
)
arr2_list = list()
for _, val in zip(range(100), it):
arr2_list.append(val[1])
arr2 = np.array(arr2_list)
assert_allclose(arr1[:100, :], arr2, rtol=1e-10)
def test_nonzero_christoffels():
"""
Compares count of non-zero Christoffel Symbols List in BL coordinates \
with that generated algorithmically
"""
mk = Kerr(coords="BL", M=1. * u.kg, a=0.5 * u.one)
l1 = mk.nonzero_christoffels()
l2 = mk._nonzero_christoffels_list_bl
assert collections.Counter(l1) == collections.Counter(l2)
def test_compare_kerr_kerrnewman_christoffels(test_input):
"""
Compares KerrNewman Christoffel Symbols, with that of Kerr metric, 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)
mk_chl = mk.christoffels(x_vec)
mkn_chl = mkn.christoffels(x_vec)
assert_allclose(mk_chl, mkn_chl, 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_singularities_ks_raises_NotImplementedError():
"""
Tests, if a NotImplementedError is raised, when KerrSchild coordinates \
are used with ``singularities()``
"""
mk = Kerr(coords="KS", M=1e22, a=0.5)
try:
mk_sing = mk.singularities()
assert False
except NotImplementedError:
assert True
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)
def test_compare_kerr_kerrnewman_christoffels(test_input):
"""
Compares KerrNewman Christoffel Symbols, with that of Kerr metric, 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.)
mk_chl = mk.christoffels(x_vec)
mkn_chl = mkn.christoffels(x_vec)
assert_allclose(mk_chl, mkn_chl, rtol=1e-8)
def test_calculate_trajectory_iterator_RuntimeWarning_kerr():
M = 1e25 * u.kg
a = 0. * u.one
bl = BoyerLindquistDifferential(
t=0.0 * u.s,
r=306.0 * u.m,
theta=np.pi / 2 * u.rad,
phi=np.pi / 2 * u.rad,
v_r=0.0 * u.m / u.s,
v_th=0.01 * u.rad / u.s,
v_p=10.0 * u.rad / u.s,
)
mk = Kerr(coords=bl, M=M, a=a)
end_lambda = 1.
stepsize = 0.4e-6
OdeMethodKwargs = {"stepsize": stepsize}
geod = Timelike(metric=mk,
coords=bl,
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(
pos_vec, vel_vec, time, M, a, start_lambda, end_lambda, OdeMethodKwargs
):
_scr = schwarzschild_radius(M).value
obj = Kerr.from_BL(pos_vec, vel_vec, time, M, a)
ans = obj.calculate_trajectory(
start_lambda=start_lambda,
end_lambda=end_lambda,
OdeMethodKwargs=OdeMethodKwargs,
)
ans = ans[1]
testarray = list()
for ansi in ans:
g = kerr_utils.metric(_c, ansi[1], ansi[2], _scr, a)
tmp = (
g[0][0] * (ansi[4] ** 2)
+ g[1][1] * (ansi[5] ** 2)
+ g[2][2] * (ansi[6] ** 2)
+ g[3][3] * (ansi[7] ** 2)
+ 2 * g[0][3] * ansi[4] * ansi[7]
)
testarray.append(tmp)
testarray = np.array(testarray, dtype=float)
comparearray = np.ones(shape=ans[:, 4].shape, dtype=float)
assert_allclose(testarray, comparearray, 1e-4)
def test_calculate_trajectory3():
# Based on the revolution of earth around sun
# Data from https://en.wikipedia.org/wiki/Earth%27s_orbit
# Initialialized with cartesian coordinates
# Function returning cartesian coordinates
M = 1.989e30 * u.kg
distance_at_perihelion = 147.10e6 * u.km
speed_at_perihelion = 30.29 * u.km / u.s
cart_obj = CartesianDifferential(
distance_at_perihelion / np.sqrt(2),
distance_at_perihelion / np.sqrt(2),
0 * u.km,
-1 * speed_at_perihelion / np.sqrt(2),
speed_at_perihelion / np.sqrt(2),
0 * u.km / u.h,
)
end_lambda = ((1 * u.year).to(u.s)).value
a = 0 * u.km
cl = Kerr.from_cartesian(cart_obj, M, a)
ans = cl.calculate_trajectory(
start_lambda=0.0,
end_lambda=end_lambda,
return_cartesian=True,
OdeMethodKwargs={"stepsize": end_lambda / 2e3},
)[1]
# velocity should be 29.29 km/s at apehelion(where r is max)
R = np.sqrt(ans[:, 1]**2 + ans[:, 2]**2 + ans[:, 3]**2)
i = np.argmax(R) # index whre radial distance is max
v_apehelion = ((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_apehelion, 29.29, rtol=0.01)
def test_wrong_or_no_units_in_init(M, a, Q, q):
"""
Tests, if wrong or no units are flagged as error, while instantiation
"""
sph = SphericalDifferential(
t=10000.0 * u.s,
r=130.0 * u.m,
theta=np.pi / 2 * u.rad,
phi=-np.pi / 8 * u.rad,
v_r=0.0 * u.m / u.s,
v_th=0.0 * u.rad / u.s,
v_p=0.0 * u.rad / u.s,
)
bl = BoyerLindquistDifferential(
t=10000.0 * u.s,
r=130.0 * u.m,
theta=np.pi / 2 * u.rad,
phi=-np.pi / 8 * u.rad,
v_r=0.0 * u.m / u.s,
v_th=0.0 * u.rad / u.s,
v_p=0.0 * u.rad / u.s,
)
try:
bm = BaseMetric(coords=sph, M=M, a=a, Q=Q)
ms = Schwarzschild(coords=sph, M=M)
mk = Kerr(coords=bl, M=M, a=a)
mkn = KerrNewman(coords=bl, M=M, a=a, Q=Q, q=q)
assert False
except (u.UnitsError, TypeError):
assert True
def test_singularities_raises_NotImplementedError(sph, bl):
"""
Tests, if ``singularities()`` raises a NotImplementedError, \
when there is a coordinate mismatch between supplied coordinate \
object and the coordinate object, metric was instantiated with
"""
M = 5e27 * u.kg
a = 0. * u.one
Q = 0. * u.C
theta = np.pi / 4
ms = Schwarzschild(coords=bl, M=M)
mk = Kerr(coords=sph, M=M, a=a)
mkn = KerrNewman(coords=sph, M=M, a=a, Q=Q)
def mssing(ms):
mssing = ms.singularities()
def mksing(mk):
mksing = mk.singularities()
def mknsing(mkn):
mknsing = mkn.singularities()
with pytest.raises(NotImplementedError):
mssing(ms)
with pytest.raises(NotImplementedError):
mksing(mk)
with pytest.raises(NotImplementedError):
mknsing(mkn)
def test_v_t_getter_setter0(cartesian_differential, spherical_differential,
bl_differential):
M = 1e24 * u.kg
a = 0. * u.one
ms = Schwarzschild(coords=spherical_differential, M=M)
mk = Kerr(coords=bl_differential, M=M, a=a)
def cd_vt(cartesian_differential, ms):
cartesian_differential.v_t = (ms, )
def sd_vt(spherical_differential, mk):
spherical_differential.v_t = (mk, )
# This should not raise CoordinateError
try:
spherical_differential.v_t = (ms, )
except CoordinateError:
pytest.fail("Unexpected TypeError!")
# These 2 should raise CoordinateError
with pytest.raises(CoordinateError):
cd_vt(cartesian_differential, ms)
with pytest.raises(CoordinateError):
sd_vt(spherical_differential, mk)
def test_v_t_raises_CoordinateError(cartesian_differential,
spherical_differential, bl_differential):
M = 1e24 * u.kg
a = 0. * u.one
ms = Schwarzschild(coords=spherical_differential, M=M)
mk = Kerr(coords=bl_differential, M=M, a=a)
cd, sd, bd = cartesian_differential, spherical_differential, bl_differential
def cd_s(cd, ms):
return cd.velocity(metric=ms)
def bd_s(bd, ms):
return bd.velocity(metric=ms)
def cd_k(cd, mk):
return cd.velocity(metric=mk)
def sd_k(sd, mk):
return sd.velocity(metric=mk)
with pytest.raises(CoordinateError):
cd_s(cd, ms)
with pytest.raises(CoordinateError):
bd_s(bd, ms)
with pytest.raises(CoordinateError):
cd_k(cd, mk)
with pytest.raises(CoordinateError):
sd_k(sd, mk)
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_velocity2(spherical_differential, bl_differential):
M = 1e24 * u.kg
a = 0. * u.one
ms = Schwarzschild(coords=spherical_differential, M=M)
mk = Kerr(coords=bl_differential, M=M, a=a)
sd, bd = spherical_differential, bl_differential
assert_allclose(sd.velocity(metric=ms)[1:], [sd.v_r.value, sd.v_th.value, sd.v_p.value])
assert_allclose(bd.velocity(metric=mk)[1:], [bd.v_r.value, bd.v_th.value, bd.v_p.value])
def test_deprecation_warning_for_calculate_trajectory():
"""
Tests, if a Deprecation Warning is shown, when accessing calculate_trajectory \
for all metric classes
"""
M, a, Q = 5e27, 0., 0.
ms = Schwarzschild(M=M)
mk = Kerr(coords="BL", M=M, a=a)
mkn = KerrNewman(coords="BL", M=M, a=a, Q=Q)
with warnings.catch_warnings(record=True) as w:
warnings.simplefilter("always")
ms.calculate_trajectory()
mk.calculate_trajectory()
mkn.calculate_trajectory()
assert len(w) == 3 # 3 warnings to be shown
assert issubclass(w[-1].category, DeprecationWarning)
def test_singularities_for_uncharged_nonrotating_case():
"""
Tests, if all metric singularities match up across Schwarzschild, Kerr & Kerr-Newman \
spacetimes, when a -> 0 & Q -> 0, subject to choice to coordinates (here, Spherical and BL)
"""
theta = np.pi / 4
M, a, Q = 5e27, 0., 0.
ms = Schwarzschild(M=M)
mk = Kerr(coords="BL", M=M, a=a)
mkn = KerrNewman(coords="BL", M=M, a=a, Q=Q)
mssing = ms.singularities()
mksing = mk.singularities()
mknsing = mkn.singularities()
mssinglist = [
mssing["inner_ergosphere"],
mssing["inner_horizon"],
mssing["outer_horizon"],
mssing["outer_ergosphere"]
]
mksinglist = [
mksing["inner_ergosphere"](theta),
mksing["inner_horizon"],
mksing["outer_horizon"],
mksing["outer_ergosphere"](theta)
]
mknsinglist = [
mknsing["inner_ergosphere"](theta),
mknsing["inner_horizon"],
mknsing["outer_horizon"],
mknsing["outer_ergosphere"](theta)
]
scr = ms.schwarzschild_radius(M)
assert_allclose(mssinglist, mksinglist, rtol=1e-4, atol=0.0)
assert_allclose(mksinglist, mknsinglist, rtol=1e-4, atol=0.0)
assert_allclose(mknsinglist, mssinglist, rtol=1e-4, atol=0.0)
assert_allclose(mksinglist[2], scr, rtol=1e-4, atol=0.0)
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_str_repr():
"""
Tests, if the ``__str__`` and ``__repr__`` messages match
"""
ms = Schwarzschild(M=1e22)
mk = Kerr(coords="BL", M=1e22, a=0.5)
mkn = KerrNewman(coords="BL", M=1e22, a=0.5, Q=0.)
assert str(ms) == repr(ms)
assert str(mk) == repr(mk)
assert str(mkn) == repr(mkn)
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)
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)
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_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_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)