  Binary pulsars are ideal to test the foundations of General Relativity, such
as Lorentz symmetry, which requires that experiments produce the same results
in all free-falling (i.e.inertial) frames. We here break this symmetry in the
gravitational sector by specifying a preferred time direction, and thus a
preferred frame, at each spacetime point. We then examine the consequences of
this gravitational Lorentz symmetry breaking in the orbital evolution of binary
pulsars, focusing on the dissipative effects. We find that Lorentz symmetry
breaking modifies these effects, and thus the orbital dynamics, in two
different ways. First, it generically causes the emission of dipolar radiation,
which makes the orbital separation decrease faster than in General Relativity.
Second, the quadrupole component of the emission is also modified. The orbital
evolution depends critically on the sensitivities of the stars, which measure
how their binding energies depend on the motion relative to the preferred
frame. We calculate the sensitivities numerically and compute the predicted
orbital decay rate of binary pulsars in Lorentz-violating gravity. By testing
these predictions against observations, we place very stringent constraints on
gravitational Lorentz violation.
