A rotating black hole in a Hernquist dark matter halo: horizon geometry, thermodynamics, and quantum emission

Abstract

We investigate the geometrical, thermodynamic, and quantum emission properties of a rotating black hole immersed in a Hernquist dark matter halo. Starting from a static black hole spacetime surrounded by a Hernquist distribution, we construct its rotating counterpart through the noncomplexification formulation of the Newman-Janis algorithm and analyze the modifications induced by the independent halo parameters $\rho$ and $r_s$ and the rotation parameter $a$. The horizon structure is determined from the roots of the radial function $\Delta(r)$, while the stationary limit surfaces and the corresponding ergoregions are obtained from the condition $g_{tt}=0$. We show that the Hernquist contribution displaces the outer event horizon toward larger radii and modifies the size of the ergoregion, whereas rotation controls the oblateness of the horizon and the strength of frame dragging. We further derive the surface gravity, Hawking temperature, Bekenstein-Hawking entropy, and heat capacity. The quantum tunneling rate is obtained from the Hamilton-Jacobi method, leading to the corresponding occupation number and a thermal estimate of the particle creation density. Finally, we estimate the Hawking luminosity and evaporation timescales within a Stefan-Boltzmann approximation. All standard Kerr and Schwarzschild results are recovered in the appropriate limiting cases.