Hawking radiation from acoustic black holes in hydrodynamic flow of electrons

Acoustic black holes are formed when a fluid flowing with subsonic velocities, accelerates and becomes supersonic. When the flow is directed from the subsonic to supersonic region, the surface on which the normal component of fluid velocity equals the local speed of sound acts as an acoustic horizon. This is because no acoustic perturbation from the supersonic region can cross it to reach the subsonic part of the fluid. One can show that if the fluid velocity is locally irrotational, the field equations for acoustic perturbations of the velocity potential are identical to that of a massless scalar field propagating in a black hole background. One, therefore, expects Hawking radiation in the form of a thermal spectrum of phonons. There have been numerous investigations of this possibility, theoretically, as well as experimentally, in systems ranging from cold atom systems to quark-gluon plasma formed in relativistic heavy-ion collisions. Here we investigate this possibility in the hydrodynamic flow of electrons. Resulting Hawking radiation in this case should be observable in terms of current fluctuations. Further, current fluctuations on both sides of the acoustic horizon should show correlations expected for pairs of Hawking particles.Comment: 7 pages, 2 figure

A realisation of Lorentz algebra in Lorentz violating theory

A Lorentz non-invariant higher derivative effective action in flat spacetime, characterised by a constant vector, can be made invariant under infinitesimal Lorentz transformations by restricting the allowed field configurations. These restricted fields are defined as functions of the background vector in such a way that background dependance of the dynamics of the physical system is no longer manifest. We show here that they also provide a field basis for the realisation of Lorentz algebra and allow the construction of a Poincar\'e invariant symplectic two form on the covariant phase space of the theory.Comment: text body edited, reference adde