All Available Metrics¶
All the currently available pre-defined metrics are listed here.
Minkowski Space-Time¶
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einsteinpy.symbolic.predefined.minkowski.MinkowskiCartesian(c=c)[source]¶ Minkowski(flat) space-time in Cartesian coordinates. Space-time without any curvature or matter.
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einsteinpy.symbolic.predefined.minkowski.Minkowski(c=c)¶ Minkowski(flat) space-time in Cartesian coordinates. Space-time without any curvature or matter.
Vacuum Solutions¶
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einsteinpy.symbolic.predefined.vacuum_solutions.Schwarzschild(c=c, sch=r_s)[source]¶ Schwarzschild exterior metric in curvature coordinates Schwarzschild, Sitz. Preuss. Akad. Wiss., p189, (1916) Stephani (13.19) p157
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einsteinpy.symbolic.predefined.vacuum_solutions.Kerr(c=c, sch=r_s, a=a)[source]¶ Kerr Metric in Boyer Lindquist coordinates.
- Parameters
c (Basic or int or float) – Any value to assign to speed of light. Defaults to
c.sch (Basic or int or float) – Any value to assign to Schwarzschild Radius of the central object. Defaults to
r_s.a (Basic or int or float) – Spin factor of the heavy body. Usually, given by
J/(Mc), whereJis the angular momentum. Defaults toa.
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einsteinpy.symbolic.predefined.vacuum_solutions.KerrNewman(c=c, G=G, eps_0=eps_0, sch=r_s, a=a, Q=Q)[source]¶ Kerr-Newman Metric in Boyer Lindquist coordinates.
- Parameters
c (Basic or int or float) – Any value to assign to speed of light. Defaults to
c.G (Basic or int or float) – Any value to assign to the Newton’s (or gravitational) constant. Defaults to
G.eps_0 (Basic or int or float) – Any value to assign to the electric constant or permittivity of free space. Defaults to
eps_0.sch (Basic or int or float) – Any value to assign to Schwarzschild Radius of the central object. Defaults to
r_s.a (Basic or int or float) – Spin factor of the heavy body. Usually, given by
J/(Mc), whereJis the angular momentum. Defaults toa.Q (Basic or int or float) – Any value to assign to eletric charge of the central object. Defaults to
Q.
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einsteinpy.symbolic.predefined.vacuum_solutions.ReissnerNordstorm(c=c, G=G, eps_0=eps_0, sch=r_s, Q=Q)[source]¶ The Reissner–Nordström metric in spherical coordinates A static solution to the Einstein–Maxwell field equations, which corresponds to the gravitational field of a charged, non-rotating, spherically symmetric body of mass M.
- Parameters
c (Basic or int or float) – Any value to assign to speed of light. Defaults to
c.G (Basic or int or float) – Any value to assign to the Newton’s (or gravitational) constant. Defaults to
G.eps_0 (Basic or int or float) – Any value to assign to the electric constant or permittivity of free space. Defaults to
eps_0.sch (Basic or int or float) – Any value to assign to Schwarzschild Radius of the central object. Defaults to
r_s.Q (Basic or int or float) – Any value to assign to eletric charge of the central object. Defaults to
Q.
De Sitter and Anti De Sitter¶
This module contains pre-defined functions to obtain instances of various forms of Anti-De-Sitter and De-Sitter space-times.
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einsteinpy.symbolic.predefined.de_sitter.AntiDeSitter()[source]¶ Anti-de Sitter space
Hawking and Ellis (5.9) p131
C-Metric¶
Godel¶
Davidson¶
Bessel Gravitational Wave¶
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einsteinpy.symbolic.predefined.bessel_gravitational_wave.BesselGravitationalWave(C=C)[source]¶ Exact gravitational wave solution without diffraction. Class. Quantum Grav., 16:L75–78, 1999. D. Kramer.
An exact solution describing an axisymmetric gravitational wave propagating in the z-direction in closed form. This solution to Einstein’s vacuum field equations has the remarkable property that the curvature invariants decrease monotonically with increasing radial distance from the axis and vanish at infinity. The solution is regular at the symmetry axis.
