pttools.bubble.relativity

Functions for calculating quantities from Einstein’s special theory of relativity

Functions

pttools.bubble.relativity.gamma(v)

Lorentz gamma, \(\gamma = (1 - v^2)^{-\frac{1}{2}}\).

Parameters:

v (float | float64 | ndarray) – [fluid] speed \(v\)

Returns:

Lorentz \(\gamma\)

Return type:

float | float64 | ndarray

pttools.bubble.relativity.gamma2(v)

Square of Lorentz gamma, \(\gamma^2 = \frac{1}{1 - v^2}\).

Parameters:

v (float | float64 | ndarray) – [fluid] speed \(v\)

Returns:

\(\gamma^2\)

Return type:

float | float64 | ndarray

pttools.bubble.relativity.lorentz(xi, v)

Lorentz transformation of fluid speed \(v\) between moving frame and plasma frame:

\[\mu = \frac{\xi - v}{1 - v\xi}\]

. Hindmarsh et al., 2021 eq. 7.32 This function is its own inverse:

\[v = \frac{\xi - \mu}{1 - \mu\xi}\]

. However, be careful with the signs.

Parameters:

• xi (float | float64 | ndarray) – \(\xi = \frac{r}{t}\)

• v (float | float64 | ndarray) – fluid speed \(v\)

Return type:

float | float64 | ndarray