Schwarzschild Geometry Utilities

einsteinpy.utils.schwarzschild_utils.schwarzschild_radius(mass)

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.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(c, r, theta, Rs)

Returns the Schwarzschild Metric

Parameters

  • c (float) – Speed of light

  • r (float) – Distance from the centre

  • theta (float) – Angle from z-axis

  • Rs (float) – Schwarzschild Radius

Returns

Numpy array of shape (4,4)

Return type

array

einsteinpy.utils.schwarzschild_utils.christoffels(c, r, theta, Rs)

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

Parameters

  • c (float) – Speed of light

  • r (float) – Distance from the centre

  • theta (float) – Angle from z-axis

  • Rs (float) – Schwarzschild Radius

Returns

Numpy array of shape (4,4,4)

Return type

array