Unruh effect in curved space and hydrodynamics

Conservation laws and gradient decomposition form the basis of the hydrodynamic description. The report will discuss the construction and solution of a system of hydrodynamic equations for an accelerated medium in space with constant curvature. Analysis of the resulting equations allows us to obtain new elements of gravitational-hydrodynamic duality by connecting transport coefficients in curved and flat spaces. Another consequence of the obtained equations is the confirmation, from a new point of view, of the generalized Unruh effect in four-dimensional (A)dS space, which is determined by acceleration in five-dimensional space. The talk will also present a recent result concerning critical phenomena in an accelerated medium associated with the behavior of lower Matsubara modes at the Rindler horizon.