def test_f_vec_bl_schwarzschild():
M = 6.73317655e26 * u.kg
sph = SphericalDifferential(
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
]
)
ms = Schwarzschild(coords=sph, M=M)
state = np.hstack((sph.position(), sph.velocity(ms)))
f_vec = ms._f_vec(0., state)
f_vec
assert isinstance(f_vec, np.ndarray)
assert_allclose(f_vec_expected, f_vec, rtol=1e-8)
def test_compare_vt_schwarzschild():
"""
Tests, if the value of timelike component of 4-Velocity in Schwarzschild spacetime, \
calculated using ``einsteinpy.coordindates.utils.v0()`` is the same as that calculated by \
brute force
"""
# Calculated using v0()
M = 1e24 * u.kg
sph = SphericalDifferential(0. * u.s, 1. * u.m, np.pi / 2 * u.rad,
0.1 * u.rad, -0.1 * u.m / u.s,
-0.01 * u.rad / u.s, 0.05 * u.rad / u.s)
ms = Schwarzschild(coords=sph, M=M)
x_vec = sph.position()
ms_mat = ms.metric_covariant(x_vec)
v_vec = sph.velocity(ms)
sph.v_t = (ms, ) # Setting v_t
vt_s = sph.v_t # Getting v_t
# Calculated by brute force
A = ms_mat[0, 0]
C = ms_mat[1, 1] * v_vec[1]**2 + ms_mat[2, 2] * v_vec[2]**2 + ms_mat[
3, 3] * v_vec[3]**2 - _c**2
D = -4 * A * C
vt_sb = np.sqrt(D) / (2 * A)
assert_allclose(vt_s.value, vt_sb, rtol=1e-8)