def test_compare_kerr_kerrnewman_christoffels(c, G, Cc, r, theta, M, a): # christoffel symbols for kerr and kerr-newman metric should be equal when Q=0 scr = M * G / (c**2) a_scaled = kerr_utils.scaled_spin_factor(a, M, c, G) c1 = kerr_utils.christoffels(c, r, theta, scr, a_scaled) c2 = kerrnewman_utils.christoffels(c, G, Cc, r, theta, scr, a_scaled, 0.0) assert_allclose(c1, c2, rtol=1e-8)
def test_compare_kerr_kerrnewman_dmetric_dx(c, G, Cc, r, theta, M, a): # differentiation of metric for kerr and kerr-newman metric should be equal when Q=0 scr = M * G / (c**2) a_scaled = kerr_utils.scaled_spin_factor(a, M, c, G) m1 = kerr_utils.dmetric_dx(c, r, theta, scr, a_scaled) m2 = kerrnewman_utils.dmetric_dx(c, G, Cc, r, theta, scr, a_scaled, 0.0) assert_allclose(m1, m2, rtol=1e-10)
def test_compare_kerr_kerrnewman_metric_inv(test_input): c, G, Cc, r, theta, M, a = test_input # inverse of metric for kerr and kerr-newman metric should be equal when Q=0 scr = 2 * M * G / (c**2) a_scaled = kerr_utils.scaled_spin_factor(a, M) m1 = kerr_utils.metric_inv(r, theta, M, a_scaled) m2 = kerrnewman_utils.metric_inv(r, theta, M, a_scaled, 0.0) assert_allclose(m1, m2, rtol=1e-10)
def test_compare_kerr_kerrnewman_christoffels(test_input): # christoffel symbols for Kerr and Kerr-Newman metric should be equal when Q=0 c, G, Cc, r, theta, M, a = test_input scr = 2 * M * G / (c ** 2) a_scaled = kerr_utils.scaled_spin_factor(a, M) c1 = kerr_utils.christoffels(r, theta, M, a_scaled) c2 = kerrnewman_utils.christoffels(r, theta, M, a_scaled, 0.0) assert_allclose(c1, c2, rtol=1e-8)
def test_compare_kerr_kerrnewman_dmetric_dx(test_input): c, G, Cc, r, theta, M, a = test_input # differentiation of metric for Kerr and Kerr-Newman metric should be equal when Q=0 scr = 2 * M * G / (c ** 2) a_scaled = kerr_utils.scaled_spin_factor(a, M) m1 = kerr_utils.dmetric_dx(r, theta, M, a_scaled) m2 = kerrnewman_utils.dmetric_dx(r, theta, M, a_scaled, 0.0) assert_allclose(m1, m2, rtol=1e-10)
def test_compare_kerr_kerrnewman_time_velocity(pos_vec, vel_vec, mass, a01): # time velocity for kerr & kerr-newman should be same when Q=0 a = kerr_utils.scaled_spin_factor(a01, mass.to(u.kg).value, constant.c.value, constant.G.value) t1 = kerr_utils.kerr_time_velocity(pos_vec, vel_vec, mass, a) t2 = kerrnewman_utils.kerrnewman_time_velocity(pos_vec, vel_vec, mass, a, 0.0 * u.C) assert_allclose(t1.value, t2.value, rtol=1e-10)
def test_compare_kerr_kerrnewman_time_velocity(): # time velocity for Kerr & Kerr-Newman should be same when Q=0 pos_vec = np.array([1.0, np.pi / 2, 0.1]) vel_vec = np.array([-0.1, -0.01, 0.05]) mass = 1e24 * u.kg a01 = 0.85 a = kerr_utils.scaled_spin_factor(a01, mass.to(u.kg).value) t1 = kerr_utils.kerr_time_velocity(pos_vec, vel_vec, mass, a) t2 = kerrnewman_utils.kerrnewman_time_velocity(pos_vec, vel_vec, mass, a, 0.0 * u.C) assert_allclose(t1.value, t2.value, rtol=1e-10)
def test_christoffels1(c, G, Cc, r, theta, M, a, Q): # compare christoffel symbols output by optimized function and by brute force scr = M * G / (c**2) a_scaled = kerr_utils.scaled_spin_factor(a, M, c, G) chl1 = kerrnewman_utils.christoffels(c, G, Cc, r, theta, scr, a_scaled, Q) # calculate by formula invg = kerrnewman_utils.metric_inv(c, G, Cc, r, theta, scr, a_scaled, Q) dmdx = kerrnewman_utils.dmetric_dx(c, G, Cc, r, theta, scr, a_scaled, Q) 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 l = t % 4 for m in range(4): chl2[i, k, l] += invg[i, m] * (dmdx[l, m, k] + dmdx[k, m, l] - dmdx[m, k, l]) chl2 = np.multiply(chl2, 0.5) assert_allclose(chl2, chl1, rtol=1e-10)
def test_scaled_spin_factor(): a = 0.8 M = 5e24 a1 = kerr_utils.scaled_spin_factor(a, M) a2 = schwarzschild_radius_dimensionless(M) * a * 0.5 assert_allclose(a2, a1, rtol=1e-9)
def test_scaled_spin_factor_raises_error(a): try: kerr_utils.scaled_spin_factor(a, 3e20) assert False except ValueError: assert True
def test_scaled_spin_factor(): a = 0.8 M = 5e24 * u.kg a1 = kerr_utils.scaled_spin_factor(a, M.value) a2 = utils.schwarzschild_radius(M).value * a * 0.5 assert_allclose(a2, a1, rtol=1e-9)