Analog gravity in nonisentropic fluids

Abstract

The analog acoustic metric has been originally derived for adiabatic acoustic perturbations propagating in an isentropic irrotational ideal fluid. In the framework of a Lagrangian hydrodynamic description we demonstrate that under certain conditions the usual acoustic metric can be derived for nonisentropic fluids. In a special case when the pressure takes a special form and the nonadiabatic perturbations are neglected the adiabatic acoustic perturbations corresponding to massless phonons propagate in an analog metric of the usual type. * bilic@irb.hr † hnikolic@irb.hr

Analog Schwarzschild Black Hole from a Nonisentropic Fluid

“…Instead, we adopt the approach of Ref. [17], which is different from the approaches in Refs. [3,4,15] basically, in two assumptions.…”

“…where c 1 (s) is an arbitrary function of s. The specific entropy s is generally a function of θ [17], so (20) implies s = s( t + g(r)). Then, from (14), we obtain ω = c 1 (s)…”

“…In general, the fluid can be described as a classical field theory in terms of a scalar field θ(x) and the kinetic term X = g µν θ ,µ θ ,ν through the prescription [17]:…”

“…Unfortunately, their solution is subject to a slightly modified analog geometry that is not exactly supported by fluid dynamics. For nonisentropic fluids, recently studied in [17], one is more flexible and has the possibility to choose ω(x), such that the analog metric exactly reproduces the Schwarzschild metric. Since g µν is the flat metric that is not proportional to the Schwarzschild metric, one would naively expect G µν to be equal to the Schwarzschild metric only if c s in (1) is not equal to unity.…”

Influence of matter geometry on shocked flows-I: Accretion in the Schwarzschild metric

“…Quasi-spherical flow, or the conical flow, as is it mentioned in the literature (see, e.g. section 4.1 of Chakrabarti and Das (2001); Nag et al (2012); Bilić et al (2014)), is considered to be idealmost to model low angular momentum inviscid accretion since weakly rotating advection dominated accretion is best described by such geometric structure. A rather non-trivial axially symmetric accretion configuration requires the matter to be in hydrostatic equilibrium along the vertical direction.…”