Schwarzschild Geometry Utilities

einsteinpy.utils.schwarzschild_utils.schwarzschild_radius(mass, c=<<class 'astropy.constants.codata2014.CODATA2014'> name='Speed of light in vacuum' value=299792458.0 uncertainty=0.0 unit='m / s' reference='CODATA 2014'>, G=<<class 'astropy.constants.codata2014.CODATA2014'> name='Gravitational constant' value=6.67408e-11 uncertainty=3.1e-15 unit='m3 / (kg s2)' reference='CODATA 2014'>)

Schwarzschild radius is the radius defining the event horizon of a Schwarzschild black hole. It is characteristic radius associated with every quantity of mass.

Parameters

mass (kg) –

Returns

r – Schwarzschild radius for a given mass

Return type

m

einsteinpy.utils.schwarzschild_utils.schwarzschild_radius_dimensionless(M, c=299792458.0, G=6.67408e-11)
Parameters

  • M (float) – Mass of massive body

  • c (float) – Speed of light, defaults to value of speed of light in SI units.

  • G (float) – Gravitational Constant, defaults to its value in SI units

Returns

Rs – Schwarzschild radius for a given mass

Return type

float

einsteinpy.utils.schwarzschild_utils.time_velocity(pos_vec, vel_vec, mass)

Velocity of time calculated from einstein’s equation. See http://www.physics.usu.edu/Wheeler/GenRel/Lectures/GRNotesDecSchwarzschildGeodesicsPost.pdf

Parameters

  • pos_vector (array) – Vector with r, theta, phi components in SI units

  • vel_vector (array) – Vector with velocities of r, theta, phi components in SI units

  • mass (kg) – Mass of the body

Returns

Velocity of time

Return type

one

einsteinpy.utils.schwarzschild_utils.metric(r, theta, M, c=299792458.0, G=6.67408e-11)

Returns the Schwarzschild Metric

Parameters

  • r (float) – Distance from the centre

  • theta (float) – Angle from z-axis

  • M (float) – Mass of the massive body

  • c (float) – Speed of light

Returns

Numpy array of shape (4,4)

Return type

array

einsteinpy.utils.schwarzschild_utils.christoffels(r, theta, M, c=299792458.0, G=6.67408e-11)

Returns the 3rd rank Tensor containing Christoffel Symbols for Schwarzschild Metric

Parameters

  • r (float) – Distance from the centre

  • theta (float) – Angle from z-axis

  • M (float) – Mass of the massive body

  • c (float) – Speed of light

Returns

Numpy array of shape (4,4,4)

Return type

array