def event_horizon(M,
a,
theta=np.pi / 2,
coord="BL",
c=constant.c.value,
G=constant.G.value):
"""
Calculate the radius of event horizon of Kerr black hole
Parameters
----------
M : float
Mass of massive body
a : float
Black hole spin factor
theta : float
Angle from z-axis in Boyer-Lindquist coordinates in radians. Mandatory for coord=='Spherical'. Defaults to pi/2.
coord : str
Output coordinate system. 'BL' for Boyer-Lindquist & 'Spherical' for spherical. Defaults to 'BL'.
Returns
-------
~numpy.array
[Radius of event horizon(R), angle from z axis(theta)] in BL/Spherical coordinates
"""
Rs = schwarzschild_radius_dimensionless(M, c, G)
Rh = 0.5 * (Rs + np.sqrt((Rs**2) - 4 * (a**2)))
if coord == "BL":
ans = np.array([Rh, theta], dtype=float)
else:
ans = utils.CartesianToSpherical_pos(
utils.BLToCartesian_pos(np.array([Rh, theta, 0.0]), a))[:2]
return ans
def radius_ergosphere(Rs, a, theta=np.pi / 2, coord="BL"):
"""
Calculate the radius of ergospere of Kerr black hole at a specific azimuthal angle
Parameters
----------
Rs : float
Schwarzschild Radius
a : float
Black hole spin factor
theta : float
Angle from z-axis in Boyer-Lindquist coordinates in radians. Defaults to pi/2.
coord : str
Output coordinate system. 'BL' for Boyer-Lindquist & 'Spherical' for spherical. Defaults to 'BL'.
Returns
-------
~numpy.array
[Radius of ergosphere(R), angle from z axis(theta)] in BL/Spherical coordinates
"""
Re = 0.5 * (Rs + np.sqrt((Rs**2) - 4 * (a**2) * (np.cos(theta)**2)))
if coord == "BL":
ans = np.array([Re, theta], dtype=float)
else:
ans = utils.CartesianToSpherical_pos(
utils.BLToCartesian_pos(np.array([Re, theta, 0.0]), a))[:2]
return ans
def test_BL2C_8dim(vec, a):
list1 = list()
for v in vec:
nv = np.hstack((
v[0],
utils.BLToCartesian_pos(v[1:4], a),
v[4],
utils.BLToCartesian_vel(v[1:4], v[5:8], a),
))
list1.append(nv)
arr1 = np.array(list1)
arr2 = utils.BL2C_8dim(vec, a)
assert_allclose(arr1, arr2, rtol=0.0, atol=1e-5)
def test_BL2C_8dim():
vec = np.array([
[21.0, 300, 0.33, 4.0, 1.0, -10.0, -1, -2],
[1.0, 3, 0.1, 5.0, 1.0, 100.0, -11, 2],
[1.0, 3, 0.1, 0, 1.0, 0, -11, 2],
])
a = 0.4
list1 = list()
for v in vec:
nv = np.hstack((
v[0],
utils.BLToCartesian_pos(v[1:4], a),
v[4],
utils.BLToCartesian_vel(v[1:4], v[5:8], a),
))
list1.append(nv)
arr1 = np.array(list1)
arr2 = utils.BL2C_8dim(vec, a)
assert_allclose(arr1, arr2, rtol=0.0, atol=1e-5)
Returns
-------
~numpy.array
[Radius of event horizon(R), angle from z axis(theta)] in BL/Spherical coordinates
"""
Rh = 0.5 * (
Rs + np.sqrt((Rs ** 2) - 4 * (a ** 2 + (charge_length_scale(Q, c, G, Cc)) ** 2))
)
if coord == "BL":
ans = np.array([Rh, theta], dtype=float)
else:
ans = utils.CartesianToSpherical_pos(
utils.BLToCartesian_pos(np.array([Rh, theta, 0.0]), a)
)[:2]
return ans
def metric(c, G, Cc, r, theta, Rs, a, Q):
=======
Cc=constant.coulombs_const.value,
):
>>>>>>> 0e311bec1be2508a28ebd8a3f8b7b944db997269
"""
Returns the Kerr-Newman Metric
Parameters
----------
def test_BLtoCartesian_pos(pos_vec, a, ans_vec):
ans = utils.BLToCartesian_pos(pos_vec, a)
assert_allclose(ans, ans_vec, rtol=0.0, atol=1e-5)
def test_cycle_pos(pos_vec, a):
pos_vec2 = utils.CartesianToBL_pos(pos_vec, a)
pos_vec3 = utils.BLToCartesian_pos(pos_vec2, a)
assert_allclose(pos_vec, pos_vec3, rtol=0.0, atol=1e-5)
def test_BLtoCartesian_pos():
pos_vec = np.array([12, 20 * np.pi / 180, 60 * np.pi / 180])
a = 0.0
ans_vec = np.array([2.052121, 3.55437, 11.27631])
ans = utils.BLToCartesian_pos(pos_vec, a)
assert_allclose(ans, ans_vec, rtol=0.0, atol=1e-5)