https://en.wikipedia.org/wiki/Wave_equation#Introduction

Does the wave equation

$$ (\partial_t -c^2 \nabla^2) u=0 $$

imply the metric of the universe is Minkowski (-like)

$$ g= (+,-c^2, -c^2 ,-c^2 ) $$

See the d'Alembert operator https://en.wikipedia.org/wiki/D%27Alembert_operator

I came across the wave equation in my classical mechanics course in an effort to reproduce coupled oscillator behavior from an action and was flabbergasted when I just started using the d'Alembert operator without even realizing.

https://en.wikipedia.org/wiki/Wave_equation#Introduction

Does the wave equation

$$ (\partial_t{}^2 -c^2 \nabla^2) u=0 $$

imply the metric of the universe is Minkowski (-like)

$$ g= (+,-c^2, -c^2 ,-c^2 ) $$

See the d'Alembert operator https://en.wikipedia.org/wiki/D%27Alembert_operator

I came across the wave equation in my classical mechanics course in an effort to reproduce coupled oscillator behavior from an action and was flabbergasted when I just started using the d'Alembert operator without even realizing.