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We examine the effect of variable viscosity parameter ($\alpha$) inrelativistic, low angular momentum advective accretion flow around rotatingblack holes. Following the recent simulation studies of magnetohydrodynamicdisk that reveal the radial variation of $\alpha(r)$, we theoreticallyinvestigate the properties of the global transonic accretion flow considering aone-dimensional power law prescription of viscosity parameter as $\alpha(r)\propto r^{\theta}$, where the viscosity exponent $\theta$ is a constant. Indoing so, we adopt the relativistic equation of state and solve the fluidequations that govern the flow motion inside the disk. We find that dependingon the flow parameters, accretion flow experiences centrifugally supportedshock transition and such shocked accretion solutions continue to exist forwide ranges of the flow energy, angular momentum, accretion rate and viscosityexponent, respectively. Due to shock compression, the hot and dense post-shockflow (hereafter PSC) can produce the high energy radiations after reprocessingthe soft photons from the pre-shock flow via inverse Comptonization. Since PSCis usually described using shock radius ($r_s$), compression ratio ($R$) andshock strength ($S$), we study the role of $\theta$ in deciding $r_s$, $R$ and$S$, respectively. Moreover, we obtain the parameter space for shock and findthat possibility of shock formation diminishes as $\theta$ is increased.Finally, we compute the limiting value of $\theta$ ($i.e., \theta^{\rm max}$)that admits shock and find that flow can sustain more viscosity when itaccretes onto rapidly rotating ($a_{\rm k} \rightarrow 1$) black hole incomparison to weakly rotating ($a_{\rm k} \rightarrow 0$) black hole.

Properties of relativistic hot accretion flow around rotating black hole with radially varying viscosity