import numpy as np
from astropy import units as u
from einsteinpy import constant
from einsteinpy.coordinates.conversion import (
BoyerLindquistConversion,
CartesianConversion,
SphericalConversion,
)
_c = constant.c.value
[docs]
class Cartesian(CartesianConversion):
"""
Class for defining 3-Position & 4-Position in Cartesian Coordinates \
using SI units
"""
@u.quantity_input(t=u.s, x=u.m, y=u.m, z=u.m)
def __init__(self, t, x, y, z):
"""
Constructor
Parameters
----------
t : float
Time
x : float
x-Component of 3-Position
y : float
y-Component of 3-Position
z : float
z-Component of 3-Position
"""
super().__init__(t.si.value, x.si.value, y.si.value, z.si.value)
self.t = t
self.x = x
self.y = y
self.z = z
self.system = "Cartesian"
self._dimension = {
"t": self.t,
"x": self.x,
"y": self.y,
"z": self.z,
"system": self.system,
}
self._dimension_order = ("t", "x", "y", "z")
def __str__(self):
return f"Cartesian Coordinates: \n \
t = ({self.t}), x = ({self.x}), y = ({self.y}), z = ({self.z})"
def __repr__(self):
return f"Cartesian Coordinates: \n \
t = ({self.t}), x = ({self.x}), y = ({self.y}), z = ({self.z})"
def __getitem__(self, item):
"""
Method to return coordinates
Objects are subscriptable with both explicit names of \
parameters and integer indices
Parameters
----------
item : str or int
Name of the parameter or its index
If ``system`` is provided, while initializing, \
name of the coordinate is returned
"""
if isinstance(item, (int, np.integer)):
return self._dimension[self._dimension_order[item]]
return self._dimension[item]
[docs]
def position(self):
"""
Returns Position 4-Vector in SI units
Returns
-------
tuple
4-Tuple, containing Position 4-Vector in SI units
"""
return (_c * self.t.si.value, self.x.si.value, self.y.si.value, self.z.si.value)
[docs]
def to_spherical(self, **kwargs):
"""
Method for conversion to Spherical Polar Coordinates
Other Parameters
----------------
**kwargs : dict
Keyword Arguments
Returns
-------
~einsteinpy.coordinates.core.Spherical
Spherical representation of the Cartesian Coordinates
"""
t, r, theta, phi = self.convert_spherical()
return Spherical(t * u.s, r * u.m, theta * u.rad, phi * u.rad)
[docs]
def to_bl(self, **kwargs):
"""
Method for conversion to Boyer-Lindquist (BL) Coordinates
Parameters
----------
**kwargs : dict
Keyword Arguments
Expects two arguments, ``M and ``a``, as described below
Other Parameters
----------------
M : float
Mass of gravitating body
Required to calculate ``alpha``, the rotational length \
parameter
a : float
Spin Parameter of gravitating body
0 <= a <= 1
Required to calculate ``alpha``, the rotational length \
parameter
Returns
-------
~einsteinpy.coordinates.core.BoyerLindquist
Boyer-Lindquist representation of the Cartesian Coordinates
"""
M, a = kwargs["M"], kwargs["a"]
t, r, theta, phi = self.convert_bl(M=M, a=a)
return BoyerLindquist(t * u.s, r * u.m, theta * u.rad, phi * u.rad)
[docs]
class Spherical(SphericalConversion):
"""
Class for defining 3-Position & 4-Position in Spherical Polar Coordinates \
using SI units
"""
@u.quantity_input(t=u.s, r=u.m, theta=u.rad, phi=u.rad)
def __init__(self, t, r, theta, phi):
"""
Constructor
Parameters
----------
t : float
Time
r : float
r-Component of 3-Position
theta : float
theta-Component of 3-Position
phi : float
phi-Component of 3-Position
"""
super().__init__(t.si.value, r.si.value, theta.si.value, phi.si.value)
self.t = t
self.r = r
self.theta = theta
self.phi = phi
self.system = "Spherical"
self._dimension = {
"t": self.t,
"r": self.r,
"theta": self.theta,
"phi": self.phi,
"system": self.system,
}
self._dimension_order = ("t", "r", "theta", "phi")
def __str__(self):
return f"Spherical Polar Coordinates: \n \
t = ({self.t}), r = ({self.r}), theta = ({self.theta}), phi = ({self.phi})"
def __repr__(self):
return f"Spherical Polar Coordinates: \n \
t = ({self.t}), r = ({self.r}), theta = ({self.theta}), phi = ({self.phi})"
def __getitem__(self, item):
"""
Method to return coordinates
Objects are subscriptable with both explicit names of \
parameters and integer indices
Parameters
----------
item : str or int
Name of the parameter or its index
If ``system`` is provided, while initializing, \
name of the coordinate is returned
"""
if isinstance(item, (int, np.integer)):
return self._dimension[self._dimension_order[item]]
return self._dimension[item]
[docs]
def position(self):
"""
Returns Position 4-Vector in SI units
Returns
-------
tuple :
4-Tuple, containing Position 4-Vector in SI units
"""
return (
_c * self.t.si.value,
self.r.si.value,
self.theta.si.value,
self.phi.si.value,
)
[docs]
def to_cartesian(self, **kwargs):
"""
Method for conversion to Cartesian Coordinates
Other Parameters
----------------
**kwargs : dict
Keyword Arguments
Returns
-------
~einsteinpy.coordinates.core.Cartesian
Cartesian representation of the Spherical Polar Coordinates
"""
t, x, y, z = self.convert_cartesian()
return Cartesian(t * u.s, x * u.m, y * u.m, z * u.m)
[docs]
def to_bl(self, **kwargs):
"""
Method for conversion to Boyer-Lindquist (BL) Coordinates
Parameters
----------
**kwargs : dict
Keyword Arguments
Expects two arguments, ``M and ``a``, as described below
Other Parameters
----------------
M : float
Mass of gravitating body
Required to calculate ``alpha``, the rotational length \
parameter
a : float
Spin Parameter of gravitating body
0 <= a <= 1
Required to calculate ``alpha``, the rotational length \
parameter
Returns
-------
~einsteinpy.coordinates.core.BoyerLindquist
Boyer-Lindquist representation of the Spherical \
Polar Coordinates
"""
M, a = kwargs["M"], kwargs["a"]
t, r, theta, phi = self.convert_bl(M=M, a=a)
return BoyerLindquist(t * u.s, r * u.m, theta * u.rad, phi * u.rad)
[docs]
class BoyerLindquist(BoyerLindquistConversion):
"""
Class for defining 3-Position & 4-Position in Boyer-Lindquist Coordinates \
using SI units
"""
@u.quantity_input(t=u.s, r=u.m, theta=u.rad, phi=u.rad)
def __init__(self, t, r, theta, phi):
"""
Constructor
Parameters
----------
t : float
Time
r : float
r-Component of 3-Position
theta : float
theta-Component of 3-Position
phi : float
phi-Component of 3-Position
"""
super().__init__(t.si.value, r.si.value, theta.si.value, phi.si.value)
self.t = t
self.r = r
self.theta = theta
self.phi = phi
self.system = "BoyerLindquist"
self._dimension = {
"t": self.t,
"r": self.r,
"theta": self.theta,
"phi": self.phi,
"system": self.system,
}
self._dimension_order = ("t", "r", "theta", "phi")
def __str__(self):
return f"Boyer-Lindquist Coordinates: \n \
t = ({self.t}), r = ({self.r}), theta = ({self.theta}), phi = ({self.phi})"
def __repr__(self):
return f"Boyer-Lindquist Coordinates: \n \
t = ({self.t}), r = ({self.r}), theta = ({self.theta}), phi = ({self.phi})"
def __getitem__(self, item):
"""
Method to return coordinates
Objects are subscriptable with both explicit names of \
parameters and integer indices
Parameters
----------
item : str or int
Name of the parameter or its index
If ``system`` is provided, while initializing, \
name of the coordinate is returned
"""
if isinstance(item, (int, np.integer)):
return self._dimension[self._dimension_order[item]]
return self._dimension[item]
[docs]
def position(self):
"""
Returns Position 4-Vector in SI units
Returns
-------
tuple :
4-Tuple, containing Position 4-Vector in SI units
"""
return (
_c * self.t.si.value,
self.r.si.value,
self.theta.si.value,
self.phi.si.value,
)
[docs]
def to_cartesian(self, **kwargs):
"""
Method for conversion to Cartesian Coordinates
Parameters
----------
**kwargs : dict
Keyword Arguments
Expects two arguments, ``M and ``a``, as described below
Other Parameters
----------------
M : float
Mass of gravitating body
Required to calculate ``alpha``, the rotational length \
parameter
a : float
Spin Parameter of gravitating body
0 <= a <= 1
Required to calculate ``alpha``, the rotational length \
parameter
Returns
-------
~einsteinpy.coordinates.core.Cartesian
Cartesian representation of the Boyer-Lindquist Coordinates
"""
M, a = kwargs["M"], kwargs["a"]
t, x, y, z = self.convert_cartesian(M=M, a=a)
return Cartesian(t * u.s, x * u.m, y * u.m, z * u.m)
[docs]
def to_spherical(self, **kwargs):
"""
Method for conversion to Spherical Polar Coordinates
Parameters
----------
**kwargs : dict
Keyword Arguments
Expects two arguments, ``M and ``a``, as described below
Other Parameters
----------------
M : float
Mass of gravitating body
Required to calculate ``alpha``, the rotational length \
parameter
a : float
Spin Parameter of gravitating body
0 <= a <= 1
Required to calculate ``alpha``, the rotational length \
parameter
Returns
-------
~einsteinpy.coordinates.core.Spherical
Spherical Polar representation of the \
Boyer-Lindquist Coordinates
"""
M, a = kwargs["M"], kwargs["a"]
t, r, theta, phi = self.convert_spherical(M=M, a=a)
return Spherical(t * u.s, r * u.m, theta * u.rad, phi * u.rad)
