Acoustic Schwarzschild-like black hole and analogous Hawking radiation in Einstein-bumblebee gravity

Abstract

We derive an acoustic Schwarzschild-like black hole and study its analogous Hawking radiation in Einstein-bumblebee theory by using Gross-Pitaevskii theory in the background of Schwarzschild-like spacetime. This black hole have two kinds of event horizons: one is the gravitational horizon $r_h=2M$(black hole horizon), the others are the internal and external acoustic horizons $2M<r_{ac-}\leq4M,\;r_{ac}\geq4M$(dumb hole horizon) which depend on the tuning parameter $ξ$ and Lorentz violation coupling constant $\ell$. The corresponding Hawking temperature $T_h$ depends only on $\ell$, however $T_{ac}$ depends on $\ell$ and $ξ$. The dumb hole temperature $T_{ac}$ has a maximum $T_{acm}=T_h/8$. When considering the scalar particles radiating from the dumb hole, we find that in low frequency, the grey-body factor increases with the tuning parameter $ξ$, but decreases with $\ell$. In the high frequency, it approaches to $1$. Its energy emission rate is similar to the Planck&#39;s black spectrum where there has a maximum at a given peak frequency $ω_m$. The energy emission rate also increases with the tuning parameter $ξ$, but decreases with $\ell$. This opposite dependence relationship is the most experimentally valuable feature and can directly benchmark against observations of real astrophysical black holes.