- 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 isSolving 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 [607, 622, 626, 624, 470]

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}

Living Rev. Relativity 14, (2011), 3
http://www.livingreviews.org/lrr-2011-3 |
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