Reduced Kiselev black hole

The Kiselev model describes a black hole surrounded by a fluid with equations of state $p_r\mathrm{/}\rho =-1$ and $p_t\mathrm{/}\rho =(3w+1)\mathrm{/}2$ respectively in radial and tangential directions. It has been extensively studied in the parameter region $-1<w<-1\mathrm{/}3$. If one rids off the black hole and turns to the region $-1\mathrm{/}3<w<0$, i.e. $p_t>0$, then a new horizon of black hole type will emerge. This case has been mentioned in Kiselev’s pioneer work but seldom investigated in the literature. Referring to it as reduced Kiselev black hole, we revisit this case with attention to its causal structure, thermodynamics, shadow cast and weak-field limit. An alternative interpretation and extensions of the black hole are also discussed.