differential module¶
This module contains the basic classes for time differentials of coordinate systems and the transformations:
-
class
einsteinpy.coordinates.differential.
CartesianDifferential
(t, x, y, z, v_x, v_y, v_z)[source]¶ Bases:
einsteinpy.coordinates.conversion.CartesianConversion
Class for defining 3-Velocity & 4-Velocity in Cartesian Coordinates using SI units
Constructor
- Parameters
t (Quantity) – Time
x (Quantity) – x-Component of 3-Position
y (Quantity) – y-Component of 3-Position
z (Quantity) – z-Component of 3-Position
v_x (Quantity, optional) – x-Component of 3-Velocity
v_y (Quantity, optional) – y-Component of 3-Velocity
v_z (Quantity, optional) – z-Component of 3-Velocity
-
position
()[source]¶ Returns Position 4-Vector in SI units
- Returns
4-Tuple, containing Position 4-Vector in SI units
- Return type
-
property
v_t
¶ Returns the Timelike component of 4-Velocity
-
velocity
(metric)[source]¶ Returns Velocity 4-Vector in SI units
- Parameters
metric (*) – Metric object, in which the coordinates are defined
- Returns
4-Tuple, containing Velocity 4-Vector in SI units
- Return type
-
spherical_differential
(**kwargs)[source]¶ Converts to Spherical Polar Coordinates
- Parameters
**kwargs (dict) – Keyword Arguments
- Returns
Spherical Polar representation of velocity
- Return type
-
bl_differential
(**kwargs)[source]¶ 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
Boyer-Lindquist representation of velocity
- Return type
-
class
einsteinpy.coordinates.differential.
SphericalDifferential
(t, r, theta, phi, v_r, v_th, v_p)[source]¶ Bases:
einsteinpy.coordinates.conversion.SphericalConversion
Class for defining 3-Velocity & 4-Velocity in Spherical Polar Coordinates using SI units
Constructor
- Parameters
-
position
()[source]¶ Returns Position 4-Vector in SI units
- Returns
4-Tuple, containing Position 4-Vector in SI units
- Return type
-
property
v_t
¶ Returns the Timelike component of 4-Velocity
-
velocity
(metric)[source]¶ Returns Velocity 4-Vector in SI units
- Parameters
metric (*) – Metric object, in which the coordinates are defined
- Returns
4-Tuple, containing Velocity 4-Vector in SI units
- Return type
-
cartesian_differential
(**kwargs)[source]¶ Converts to Cartesian Coordinates
- Parameters
**kwargs (dict) – Keyword Arguments
- Returns
Cartesian representation of velocity
- Return type
-
bl_differential
(**kwargs)[source]¶ 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
Boyer-Lindquist representation of velocity
- Return type
-
class
einsteinpy.coordinates.differential.
BoyerLindquistDifferential
(t, r, theta, phi, v_r, v_th, v_p)[source]¶ Bases:
einsteinpy.coordinates.conversion.BoyerLindquistConversion
Class for defining 3-Velocity & 4-Velocity in Boyer-Lindquist Coordinates using SI units
Constructor.
- Parameters
-
position
()[source]¶ Returns Position 4-Vector in SI units
- Returns
4-Tuple, containing Position 4-Vector in SI units
- Return type
-
property
v_t
¶ Returns the Timelike component of 4-Velocity
-
velocity
(metric)[source]¶ Returns Velocity 4-Vector in SI units
- Parameters
metric (*) – Metric object, in which the coordinates are defined
- Returns
4-Tuple, containing Velocity 4-Vector in SI units
- Return type
-
cartesian_differential
(**kwargs)[source]¶ 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
Cartesian representation of velocity
- Return type
CartesianDifferential
-
spherical_differential
(**kwargs)[source]¶ 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
Spherical representation of velocity
- Return type
SphericalDifferential