- The speed of sound , relative to the fluid, is well defined.
- The velocity of the fluid , relative to the laboratory, is well defined.

Then, relative to the laboratory, the velocity of a sound ray propagating, with respect to the fluid, along the direction defined by the unit vector is

This defines a sound cone in spacetime given by the condition , i.e., That is Solving this quadratic equation for as a function of provides a double cone associated with each point in space and time. This is associated with a conformal class of Lorentzian metrics [376, 387, 391, 389, 284] where is an unspecified but non-vanishing function. The virtues of the geometric approach are its extreme simplicity and the fact that the basic structure is
dimension-independent. Moreover this logic rapidly (and relatively easily) generalises to more complicated physical
situations.^{3}

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