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 f_vec(self, ld, vec): chl = kerr_utils.christoffels(vec[1], vec[2], self.M.value, self.a.value) vals = np.zeros(shape=(8,), dtype=float) for i in range(4): vals[i] = vec[i + 4] vals[4] = -2.0 * ( chl[0, 0, 1] * vec[4] * vec[5] + chl[0, 0, 2] * vec[4] * vec[6] + chl[0, 1, 3] * vec[5] * vec[7] + chl[0, 2, 3] * vec[6] * vec[7] ) vals[5] = -1.0 * ( chl[1, 0, 0] * vec[4] * vec[4] + 2 * chl[1, 0, 3] * vec[4] * vec[7] + chl[1, 1, 1] * vec[5] * vec[5] + 2 * chl[1, 1, 2] * vec[5] * vec[6] + chl[1, 2, 2] * vec[6] * vec[6] + chl[1, 3, 3] * vec[7] * vec[7] ) vals[6] = -1.0 * ( chl[2, 0, 0] * vec[4] * vec[4] + 2 * chl[2, 0, 3] * vec[4] * vec[7] + chl[2, 1, 1] * vec[5] * vec[5] + 2 * chl[2, 1, 2] * vec[5] * vec[6] + chl[2, 2, 2] * vec[6] * vec[6] + chl[2, 3, 3] * vec[7] * vec[7] ) vals[7] = -2.0 * ( chl[3, 0, 1] * vec[4] * vec[5] + chl[3, 0, 2] * vec[4] * vec[6] + chl[3, 1, 3] * vec[5] * vec[7] + chl[3, 2, 3] * vec[6] * vec[7] ) return vals
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_christoffels(c, r, theta, Rs, a): # output produced by the optimized function chl1 = kerr_utils.christoffels(c, r, theta, Rs, a) # calculate by formula invg = kerr_utils.metric_inv(c, r, theta, Rs, a) dmdx = kerr_utils.dmetric_dx(c, r, theta, Rs, a) 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-8)
def f_vec(self, ld, vec): chl = kerr_utils.christoffels(_c, vec[1], vec[2], self.schwarzschild_r.value, self.a) vals = np.zeros(shape=(8, ), dtype=float) for i in range(4): vals[i] = vec[i + 4] vals[4] = -2.0 * ( chl[0][0][1] * vec[4] * vec[5] + chl[0][0][2] * vec[4] * vec[6] + chl[0][1][3] * vec[5] * vec[7] + chl[0][2][3] * vec[6] * vec[7]) vals[5] = -1.0 * (chl[1][0][0] * vec[4] * vec[4] + 2 * chl[1][0][3] * vec[4] * vec[7] + chl[1][1][1] * vec[5] * vec[5] + 2 * chl[1][1][2] * vec[5] * vec[6] + chl[1][2][2] * vec[6] * vec[6] + chl[1][3][3] * vec[7] * vec[7]) vals[6] = -1.0 * (chl[2][0][0] * vec[4] * vec[4] + 2 * chl[2][0][3] * vec[4] * vec[7] + chl[2][1][1] * vec[5] * vec[5] + 2 * chl[2][1][2] * vec[5] * vec[6] + chl[2][2][2] * vec[6] * vec[6] + chl[2][3][3] * vec[7] * vec[7]) vals[7] = -2.0 * ( chl[3][0][1] * vec[4] * vec[5] + chl[3][0][2] * vec[4] * vec[6] + chl[3][1][3] * vec[5] * vec[7] + chl[3][2][3] * vec[6] * vec[7]) return vals