scri.asymptotic_bondi_data.constraints

Functions

bianchi_0(self[, lhs, rhs])	Return the left- and/or right-hand sides of the Psi0 component of the Bianchi identity
bianchi_1(self[, lhs, rhs])	Return the left- and/or right-hand sides of the Psi1 component of the Bianchi identity
bianchi_2(self[, lhs, rhs])	Return the left- and/or right-hand sides of the Psi2 component of the Bianchi identity
bondi_constraints(self[, lhs, rhs])	Compute Bondi-gauge constraint equations
constraint_3(self[, lhs, rhs])	Return the left- and/or right-hand sides of the Psi3 expression in Bondi gauge
constraint_4(self[, lhs, rhs])	Return the left- and/or right-hand sides of the Psi4 expression in Bondi gauge
constraint_mass_aspect(self[, lhs, rhs])	Return the left- and/or right-hand sides of the mass-aspect reality condition in Bondi gauge

scri.asymptotic_bondi_data.constraints.bianchi_0(self, lhs=True, rhs=True)

Return the left- and/or right-hand sides of the Psi0 component of the Bianchi identity

In Bondi coordinates, the Bianchi identities simplify, resulting in this expression (among others) for the time derivative of ψ₀:

ψ̇₀ = ðψ₁ + 3 σ ψ₂

Parameters:

lhs: bool [defaults to True]

If True, return the left-hand side of the equation above

rhs: bool [defaults to True]

If True, return the right-hand side of the equation above

If both parameters are True, a tuple with elements (lhs_value, rhs_value) is

returned; otherwise just the requested value is returned.

scri.asymptotic_bondi_data.constraints.bianchi_1(self, lhs=True, rhs=True)

Return the left- and/or right-hand sides of the Psi1 component of the Bianchi identity

In Bondi coordinates, the Bianchi identities simplify, resulting in this expression (among others) for the time derivative of ψ₁:

ψ̇₁ = ðψ₂ + 2 σ ψ₃

Parameters:

lhs: bool [defaults to True]

If True, return the left-hand side of the equation above

rhs: bool [defaults to True]

If True, return the right-hand side of the equation above

If both parameters are True, a tuple with elements (lhs_value, rhs_value) is

returned; otherwise just the requested value is returned.

scri.asymptotic_bondi_data.constraints.bianchi_2(self, lhs=True, rhs=True)

Return the left- and/or right-hand sides of the Psi2 component of the Bianchi identity

In Bondi coordinates, the Bianchi identities simplify, resulting in this expression (among others) for the time derivative of ψ₂:

ψ̇₂ = ðψ₃ + σ ψ₄

Parameters:

lhs: bool [defaults to True]

If True, return the left-hand side of the equation above

rhs: bool [defaults to True]

If True, return the right-hand side of the equation above

If both parameters are True, a tuple with elements (lhs_value, rhs_value) is

returned; otherwise just the requested value is returned.

scri.asymptotic_bondi_data.constraints.bondi_constraints(self, lhs=True, rhs=True)

Compute Bondi-gauge constraint equations

Bondi gauge establishes some relations that the data must satisfy:

ψ̇₀ = ðψ₁ + 3 σ ψ₂

ψ̇₁ = ðψ₂ + 2 σ ψ₃

ψ̇₂ = ðψ₃ + 1 σ ψ₄

ψ₃ = -∂ðσ̄/∂u

ψ₄ = -∂²σ̄/∂u²

Im[ψ₂] = -Im[ð²σ̄ + σ ∂σ̄/∂u]

This function returns a 6-tuple of 2-tuples, corresponding to these 6 equations and their left- and right-hand sides.

scri.asymptotic_bondi_data.constraints.constraint_3(self, lhs=True, rhs=True)

Return the left- and/or right-hand sides of the Psi3 expression in Bondi gauge

In Bondi coordinates, the value of ψ₃ is given by a time derivative and an angular derivative of the (conjugate) shear:

ψ₃ = -∂ðσ̄/∂u

Parameters:

lhs: bool [defaults to True]

If True, return the left-hand side of the equation above

rhs: bool [defaults to True]

If True, return the right-hand side of the equation above

If both parameters are True, a tuple with elements (lhs_value, rhs_value) is

returned; otherwise just the requested value is returned.

scri.asymptotic_bondi_data.constraints.constraint_4(self, lhs=True, rhs=True)

Return the left- and/or right-hand sides of the Psi4 expression in Bondi gauge

In Bondi coordinates, the value of ψ₄ is given by the second time derivative of the (conjugate) shear:

ψ₄ = -∂²σ̄/∂u²

Parameters:

lhs: bool [defaults to True]

If True, return the left-hand side of the equation above

rhs: bool [defaults to True]

If True, return the right-hand side of the equation above

If both parameters are True, a tuple with elements (lhs_value, rhs_value) is

returned; otherwise just the requested value is returned.

scri.asymptotic_bondi_data.constraints.constraint_mass_aspect(self, lhs=True, rhs=True)

Return the left- and/or right-hand sides of the mass-aspect reality condition in Bondi gauge

In Bondi coordinates, the Bondi mass aspect is always real, resulting in this relationship:

Im[ψ₂] = -Im[ð²σ̄ + σ ∂σ̄/∂u]

Parameters:

lhs: bool [defaults to True]

If True, return the left-hand side of the equation above

rhs: bool [defaults to True]

If True, return the right-hand side of the equation above

If both parameters are True, a tuple with elements (lhs_value, rhs_value) is

returned; otherwise just the requested value is returned.