import numpy as np
from astropy import units as u
from einsteinpy import constant, metric
from einsteinpy.coordinates.conversion import (
BoyerLindquistConversion,
CartesianConversion,
SphericalConversion,
)
from einsteinpy.coordinates.utils import v0
from einsteinpy.utils import CoordinateError
_c = constant.c.value
[docs]
class CartesianDifferential(CartesianConversion):
"""
Class for defining 3-Velocity & 4-Velocity in Cartesian Coordinates \
using SI units
"""
@u.quantity_input(
t=u.s, x=u.m, y=u.m, z=u.m, v_x=u.m / u.s, v_y=u.m / u.s, v_z=u.m / u.s
)
def __init__(self, t, x, y, z, v_x, v_y, v_z):
"""
Constructor
Parameters
----------
t : ~astropy.units.quantity.Quantity
Time
x : ~astropy.units.quantity.Quantity
x-Component of 3-Position
y : ~astropy.units.quantity.Quantity
y-Component of 3-Position
z : ~astropy.units.quantity.Quantity
z-Component of 3-Position
v_x : ~astropy.units.quantity.Quantity, optional
x-Component of 3-Velocity
v_y : ~astropy.units.quantity.Quantity, optional
y-Component of 3-Velocity
v_z : ~astropy.units.quantity.Quantity, optional
z-Component of 3-Velocity
"""
super().__init__(
t.si.value,
x.si.value,
y.si.value,
z.si.value,
v_x.si.value,
v_y.si.value,
v_z.si.value,
)
self.t = t
self.x = x
self.y = y
self.z = z
self._v_t = None
self.v_x = v_x
self.v_y = v_y
self.v_z = v_z
self.system = "Cartesian"
def __str__(self):
return f"Cartesian Coordinates: \n\
t = ({self.t}), x = ({self.x}), y = ({self.y}), z = ({self.z})\n\
v_t: {self.v_t}, v_x: {self.v_x}, v_y: {self.v_y}, v_z: {self.v_z}"
def __repr__(self):
return f"Cartesian Coordinates: \n\
t = ({self.t}), x = ({self.x}), y = ({self.y}), z = ({self.z})\n\
v_t: {self.v_t}, v_x: {self.v_x}, v_y: {self.v_y}, v_z: {self.v_z}"
[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)
@property
def v_t(self):
"""
Returns the Timelike component of 4-Velocity
"""
return self._v_t
@v_t.setter
def v_t(self, args):
"""
Sets the value of the Time-like component of 4-Velocity
Parameters
----------
args : tuple
1-tuple containing the ~einsteinpy.metric.* object, \
in which the coordinates are defined
Raises
------
CoordinateError
If ``metric`` object has been instantiated with a coordinate system, \
other than Cartesian Coordinates.
"""
g = args[0]
if self.system != g.coords.system:
raise CoordinateError(
f"Metric object has been instantiated with a coordinate system, ( {g.coords.system} )"
" other than Cartesian Coordinates."
)
g_cov_mat = g.metric_covariant(self.position())
v_t = v0(g_cov_mat, self.v_x.si.value, self.v_y.si.value, self.v_z.si.value)
self._v_t = v_t * u.m / u.s
[docs]
def velocity(self, metric):
"""
Returns Velocity 4-Vector in SI units
Parameters
----------
metric : ~einsteinpy.metric.*
Metric object, in which the coordinates are defined
Returns
-------
tuple
4-Tuple, containing Velocity 4-Vector in SI units
"""
# Setting _v_t
self.v_t = (metric,)
return (
self._v_t.value,
self.v_x.si.value,
self.v_y.si.value,
self.v_z.si.value,
)
[docs]
def spherical_differential(self, **kwargs):
"""
Converts to Spherical Polar Coordinates
Parameters
----------
**kwargs : dict
Keyword Arguments
Returns
-------
~einsteinpy.coordinates.differential.SphericalDifferential
Spherical Polar representation of velocity
"""
t, r, theta, phi, v_r, v_th, v_p = self.convert_spherical()
return SphericalDifferential(
t * u.s,
r * u.m,
theta * u.rad,
phi * u.rad,
v_r * u.m / u.s,
v_th * u.rad / u.s,
v_p * u.rad / u.s,
)
[docs]
def bl_differential(self, **kwargs):
"""
Converts to Boyer-Lindquist Coordinates
Parameters
----------
**kwargs : dict
Keyword Arguments
Expects two arguments, ``M and ``a``, as described below
Other Parameters
----------------
M : float
Mass of the gravitating body, \
around which, spacetime has been defined
a : float
Spin Parameter of the gravitating body, \
around which, spacetime has been defined
Returns
-------
~einsteinpy.coordinates.differential.BoyerLindquistDifferential
Boyer-Lindquist representation of velocity
"""
M, a = kwargs["M"], kwargs["a"]
t, r, theta, phi, v_r, v_th, v_p = self.convert_bl(M=M, a=a)
return BoyerLindquistDifferential(
t * u.s,
r * u.m,
theta * u.rad,
phi * u.rad,
v_r * u.m / u.s,
v_th * u.rad / u.s,
v_p * u.rad / u.s,
)
[docs]
class SphericalDifferential(SphericalConversion):
"""
Class for defining 3-Velocity & 4-Velocity in Spherical Polar Coordinates \
using SI units
"""
@u.quantity_input(
t=u.s,
r=u.m,
theta=u.rad,
phi=u.rad,
v_r=u.m / u.s,
v_th=u.rad / u.s,
v_p=u.rad / u.s,
)
def __init__(self, t, r, theta, phi, v_r, v_th, v_p):
"""
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
v_r : float, optional
r-Component of 3-Velocity
v_th : float, optional
theta-Component of 3-Velocity
v_p : float, optional
phi-Component of 3-Velocity
"""
super().__init__(
t.si.value,
r.si.value,
theta.si.value,
phi.si.value,
v_r.si.value,
v_th.si.value,
v_p.si.value,
)
self.t = t
self.r = r
self.theta = theta
self.phi = phi
self._v_t = None
self.v_r = v_r
self.v_th = v_th
self.v_p = v_p
self.system = "Spherical"
def __str__(self):
return f"Spherical Polar Coordinates: \n\
t = ({self.t}), r = ({self.r}), theta = ({self.theta}), phi = ({self.phi})\n\
v_t: {self.v_t}, v_r: {self.v_r}, v_th: {self.v_th}, v_p: {self.v_p}"
def __repr__(self):
return f"Spherical Polar Coordinates: \n\
t = ({self.t}), r = ({self.r}), theta = ({self.theta}), phi = ({self.phi})\n\
v_t: {self.v_t}, v_r: {self.v_r}, v_th: {self.v_th}, v_p: {self.v_p}"
[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,
)
@property
def v_t(self):
"""
Returns the Timelike component of 4-Velocity
"""
return self._v_t
@v_t.setter
def v_t(self, args):
"""
Sets the value of the Time-like component of 4-Velocity
Parameters
----------
args : tuple
1-tuple containing the ~einsteinpy.metric.* object, \
in which the coordinates are defined
Raises
------
CoordinateError
If ``metric`` object has been instantiated with a coordinate system, \
other than Sperical Polar Coordinates.
"""
g = args[0]
if self.system != g.coords.system:
raise CoordinateError(
f"Metric object has been instantiated with a coordinate system, ( {g.coords.system} )"
" other than Spherical Polar Coordinates."
)
g_cov_mat = g.metric_covariant(self.position())
v_t = v0(g_cov_mat, self.v_r.si.value, self.v_th.si.value, self.v_p.si.value)
self._v_t = v_t * u.m / u.s
[docs]
def velocity(self, metric):
"""
Returns Velocity 4-Vector in SI units
Parameters
----------
metric : ~einsteinpy.metric.*
Metric object, in which the coordinates are defined
Returns
-------
tuple
4-Tuple, containing Velocity 4-Vector in SI units
"""
# Setting _v_t
self.v_t = (metric,)
return (
self._v_t.value,
self.v_r.si.value,
self.v_th.si.value,
self.v_p.si.value,
)
[docs]
def cartesian_differential(self, **kwargs):
"""
Converts to Cartesian Coordinates
Parameters
----------
**kwargs : dict
Keyword Arguments
Returns
-------
~einsteinpy.coordinates.differential.CartesianDifferential
Cartesian representation of velocity
"""
t, x, y, z, v_x, v_y, v_z = self.convert_cartesian()
return CartesianDifferential(
t * u.s,
x * u.m,
y * u.m,
z * u.m,
v_x * u.m / u.s,
v_y * u.m / u.s,
v_z * u.m / u.s,
)
[docs]
def bl_differential(self, **kwargs):
"""
Converts to Boyer-Lindquist coordinates
Parameters
----------
**kwargs : dict
Keyword Arguments
Expects two arguments, ``M and ``a``, as described below
Other Parameters
----------------
M : float
Mass of the gravitating body, \
around which, spacetime has been defined
a : float
Spin Parameter of the gravitating body, \
around which, spacetime has been defined
Returns
-------
~einsteinpy.coordinates.differential.BoyerLindquistDifferential
Boyer-Lindquist representation of velocity
"""
M, a = kwargs["M"], kwargs["a"]
t, r, theta, phi, v_r, v_th, v_p = self.convert_bl(M=M, a=a)
return BoyerLindquistDifferential(
t * u.s,
r * u.m,
theta * u.rad,
phi * u.rad,
v_r * u.m / u.s,
v_th * u.rad / u.s,
v_p * u.rad / u.s,
)
[docs]
class BoyerLindquistDifferential(BoyerLindquistConversion):
"""
Class for defining 3-Velocity & 4-Velocity in Boyer-Lindquist Coordinates \
using SI units
"""
@u.quantity_input(
t=u.s,
r=u.m,
theta=u.rad,
phi=u.rad,
v_r=u.m / u.s,
v_th=u.rad / u.s,
v_p=u.rad / u.s,
)
def __init__(self, t, r, theta, phi, v_r, v_th, v_p):
"""
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
v_r : float, optional
r-Component of 3-Velocity
v_th : float, optional
theta-Component of 3-Velocity
v_p : float, optional
phi-Component of 3-Velocity
"""
super().__init__(
t.si.value,
r.si.value,
theta.si.value,
phi.si.value,
v_r.si.value,
v_th.si.value,
v_p.si.value,
)
self.t = t
self.r = r
self.theta = theta
self.phi = phi
self._v_t = None
self.v_r = v_r
self.v_th = v_th
self.v_p = v_p
self.system = "BoyerLindquist"
def __str__(self):
return f"Boyer-Lindquist Coordinates: \n\
t = ({self.t}), r = ({self.r}), theta = ({self.theta}), phi = ({self.phi})\n\
v_t: {self.v_t}, v_r: {self.v_r}, v_th: {self.v_th}, v_p: {self.v_p}"
def __repr__(self):
return f"Boyer-Lindquist Coordinates: \n\
t = ({self.t}), r = ({self.r}), theta = ({self.theta}), phi = ({self.phi})\n\
v_t: {self.v_t}, v_r: {self.v_r}, v_th: {self.v_th}, v_p: {self.v_p}"
[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,
)
@property
def v_t(self):
"""
Returns the Timelike component of 4-Velocity
"""
return self._v_t
@v_t.setter
def v_t(self, args):
"""
Sets the value of the Time-like component of 4-Velocity
Parameters
----------
args : tuple
1-tuple containing the ~einsteinpy.metric.* object, \
in which the coordinates are defined
Raises
------
CoordinateError
If ``metric`` object has been instantiated with a coordinate system, \
other than Boyer-Lindquist Coordinates.
"""
g = args[0]
if self.system != g.coords.system:
raise CoordinateError(
"Metric object has been instantiated with a coordinate system, ( {g.coords.system} )"
" other than Boyer-Lindquist Coordinates."
)
g_cov_mat = g.metric_covariant(self.position())
v_t = v0(g_cov_mat, self.v_r.si.value, self.v_th.si.value, self.v_p.si.value)
self._v_t = v_t * u.m / u.s
[docs]
def velocity(self, metric):
"""
Returns Velocity 4-Vector in SI units
Parameters
----------
metric : ~einsteinpy.metric.*
Metric object, in which the coordinates are defined
Returns
-------
tuple
4-Tuple, containing Velocity 4-Vector in SI units
"""
# Setting _v_t
self.v_t = (metric,)
return (
self._v_t.value,
self.v_r.si.value,
self.v_th.si.value,
self.v_p.si.value,
)
[docs]
def cartesian_differential(self, **kwargs):
"""
Converts to Cartesian Coordinates
Parameters
----------
**kwargs : dict
Keyword Arguments
Expects two arguments, ``M and ``a``, as described below
Other Parameters
----------------
M : float
Mass of the gravitating body, \
around which, spacetime has been defined
a : float
Spin Parameter of the gravitating body, \
around which, spacetime has been defined
Returns
-------
~einsteinpy.coordinates.differentia.CartesianDifferential
Cartesian representation of velocity
"""
M, a = kwargs["M"], kwargs["a"]
t, x, y, z, v_x, v_y, v_z = self.convert_cartesian(M=M, a=a)
return CartesianDifferential(
t * u.s,
x * u.m,
y * u.m,
z * u.m,
v_x * u.m / u.s,
v_y * u.m / u.s,
v_z * u.m / u.s,
)
[docs]
def spherical_differential(self, **kwargs):
"""
Converts to Spherical Polar Coordinates
Parameters
----------
**kwargs : dict
Keyword Arguments
Expects two arguments, ``M and ``a``, as described below
Other Parameters
----------------
M : float
Mass of the gravitating body, \
around which, spacetime has been defined
a : float
Spin Parameter of the gravitating body, \
around which, spacetime has been defined
Returns
-------
~einsteinpy.coordinates.differentia.SphericalDifferential
Spherical representation of velocity
"""
M, a = kwargs["M"], kwargs["a"]
t, r, theta, phi, v_r, v_th, v_p = self.convert_spherical(M=M, a=a)
return SphericalDifferential(
t * u.s,
r * u.m,
theta * u.rad,
phi * u.rad,
v_r * u.m / u.s,
v_th * u.rad / u.s,
v_p * u.rad / u.s,
)
