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"""
This is a test module, that tests the non-coordinate conversion utilities in ``einsteinpy.coordinates.utils``.
"""
import astropy.units as u
import numpy as np
import pytest
from numpy.testing import assert_allclose
from einsteinpy.coordinates import BoyerLindquistDifferential, SphericalDifferential
from einsteinpy.coordinates.utils import lorentz_factor, v0
from einsteinpy.metric import Schwarzschild, Kerr, KerrNewman
from einsteinpy import constant
_c = constant.c.value
def test_lorentz_factor():
"""
Tests, if the value of Lorentz Factor, calculated using \
``einsteinpy.coordindates.utils.lorentz_factor()`` is the same as, \
that calculated by brute force
"""
# Calculated using v0()
gamma = lorentz_factor(-0.1, -0.01, 0.05)
# Calculated by brute force
v_vec = np.array([-0.1, -0.01, 0.05])
v_norm2 = v_vec[0]**2 + v_vec[1]**2 + v_vec[2]**2
gamma_b = 1 / np.sqrt(1 - v_norm2 / _c ** 2)
assert_allclose(gamma, gamma_b, rtol=1e-8)
@pytest.fixture
def sph():
return SphericalDifferential(
0. * u.s,
1. * u.m,
np.pi / 2 * u.rad,
0.1 * u.rad,
0. * u.m / u.s,
0.1 * u.rad / u.s,
951 * u.rad / u.s
)
@pytest.fixture
def bl():
return BoyerLindquistDifferential(
0. * u.s,
1. * u.m,
np.pi / 2 * u.rad,
0.1 * u.rad,
0. * u.m / u.s,
0.1 * u.rad / u.s,
951 * u.rad / u.s
)
def test_v0(sph, bl):
"""
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 * u.kg
ms = Schwarzschild(coords=sph, M=M)
mk = Kerr(coords=bl, M=M, a=0.5 * u.one)
mk0 = Kerr(coords=bl, M=M, a=0. * u.one)
mkn = KerrNewman(coords=bl, M=M, a=0.5 * u.one, Q=0. * u.C)
mkn0 = KerrNewman(coords=bl, M=M, a=0. * u.one, Q=0. * u.C)
v4vec_s = sph.velocity(ms)
v4vec_k = bl.velocity(mk)
v4vec_k0 = bl.velocity(mk0)
v4vec_kn = bl.velocity(mkn)
v4vec_kn0 = bl.velocity(mkn0)
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():
"""
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)
@pytest.fixture
def sph2():
return 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
)
@pytest.fixture
def bl2():
return BoyerLindquistDifferential(
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
)
def test_compare_vt_schwarzschild_kerr_kerrnewman(sph2, bl2):
"""
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 * u.kg
ms = Schwarzschild(coords=sph2, M=M)
mk = Kerr(coords=bl2, M=M, a=0.5 * u.one)
mk0 = Kerr(coords=bl2, M=M, a=0. * u.one)
mkn = KerrNewman(coords=bl2, M=M, a=0.5 * u.one, Q=0. * u.C)
mkn0 = KerrNewman(coords=bl2, M=M, a=0. * u.one, Q=0. * u.C)
v_vec_ms = sph2.velocity(ms)
v_vec_mk = bl2.velocity(mk)
v_vec_mk0 = bl2.velocity(mk0)
v_vec_mkn = bl2.velocity(mkn)
v_vec_mkn0 = bl2.velocity(mkn0)
assert_allclose(v_vec_ms, v_vec_mk0, rtol=1e-8)
assert_allclose(v_vec_mk, v_vec_mkn, rtol=1e-8)
assert_allclose(v_vec_mkn0, v_vec_ms, rtol=1e-8)
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