KerrSpacetime

class kerrgeopy.spacetime.KerrSpacetime(a, M=None)

Bases: object

Class representing spacetime around a black hole with mass \(M\) and spin parameter \(a\)

Parameters:

• a (double) – dimensionless angular momentum

• M (double) – mass of the black hole

Variables:

• a – dimensionless angular momentum

• M – mass of the black hole

• inner_horizon – radius of the inner horizon

• outer_horizon – radius of the outer horizon

__init__(a, M=None)

Methods

__init__(a[, M])
four_velocity(t, r, theta, phi, constants, ...)	Computes the four velocity of a given trajectory
is_stable(p, e, x)	Determines whether a given orbit is stable or not
metric(t, r, theta, phi)	Returns the matrix representation of the metric at a given point expressed in Boyer-Lindquist coordinates.
norm(t, r, theta, phi, v)	Computes the norm of a vector at a given point in spacetime expressed in Boyer-Lindquist coordinates
separatrix(e, x)	Computes the value of p at the separatrix for a given value of e and x

four_velocity(t, r, theta, phi, constants, upsilon_r, upsilon_theta, initial_phases)

Computes the four velocity of a given trajectory

Parameters:

• t (function) – time component of trajectory

• r (function) – radial component of trajectory

• theta (function) – polar component of trajectory

• phi (function) – azimuthal component of trajectory

• constants (tuple(double, double, double)) – tuple of constants of motion in the form \((\mathcal{E},\mathcal{L},\mathcal{Q})\)

• upsilon_r (double) – radial frequency

• upsilon_theta (double) – polar frequency

• initial_phases (tuple, optional) – tuple of initial phases \((q_{t_0},q_{r_0},q_{\theta_0},q_{\phi_0})\)

Returns:

components of the four velocity (i.e. \((u^t,u^r,u^\theta,u^\phi)\))

Return type:

tuple(function, function, function, function)

is_stable(p, e, x)

Determines whether a given orbit is stable or not

Parameters:

• p (double) – dimensionless semi-latus rectum

• e (double) – orbital eccentricity

• x (double) – cosine of the orbital inclination

Return type:

bool

metric(t, r, theta, phi)

Returns the matrix representation of the metric at a given point expressed in Boyer-Lindquist coordinates.

Parameters:

• t (double) – time coordinate

• r (double) – radial coordinate

• theta (double) – polar coordinate

• phi (double) – azimuthal coordinate

Return type:

numpy.ndarray

norm(t, r, theta, phi, v)

Computes the norm of a vector at a given point in spacetime expressed in Boyer-Lindquist coordinates

Parameters:

• t (double) – time coordinate

• r (double) – radial coordinate

• theta (double) – polar coordinate

• phi (double) – azimuthal coordinate

• v (array_like) – vector to compute the norm of

Returns:

norm of v

Return type:

double

separatrix(e, x)

Computes the value of p at the separatrix for a given value of e and x

Parameters:

• e (double) – orbital eccentricity

• x (double) – cosine of the orbital inclination

Return type:

double