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Miraculously, stationary black hole spacetimes arise as explicit (i.e., exact expression can be written down!) solutions to the (vacuum) Einstein equation.
This expression can be written as (16).
The following expression can be written from the above identity.
Then, using Eq. (12), the EVM expression can be written as Eq. (14).
Likewise, a similar expression can be written for the terminals' side.
Finally, compiling I 1 and I 2, the EVM expression can be written as Eq. (18).
Similar(36)
The base inertial parameters expressions can be written as a linear combination of the inertial parameters and determining their symbolic expressions provides a deeper insight into their physical meaning.
Thanks to the Math Input Panel in Windows 7, the mathematical expressions can be written by hand with a mouse, digitizer pen or touch screen, converted to text and easily inserted into a Microsoft Word document — or any other program that supports Mathematical Markup Language.
Using a finite difference approximation and Koopmans' theorem [13 16], the above expressions can be written as: (3) (4).
These expressions can be written under a unified form as follows, P y ̃ y ̃ = P y ° y ° + σ p 2 I (26).
Using a finite difference approximation and Koopmans' theorem [25 28], the above expressions can be written as: μ ≈ − 1 2 ( I + A ) ≈ 1 2 ( ε L + ε H ) (6) η ≈ 1 2 ( I − A ) ≈ 1 2 ( ε L − ε H ) (7).
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com