Thermodynamics and Null Geodesics of a Schwarzschild Black Hole Surrounded by a Dehnen Type Dark Matter Halo

TL;DR

This paper introduces a new black hole solution embedded in a Dehnen dark matter halo, analyzing its thermodynamics and null geodesics to understand the influence of dark matter parameters on stability and photon orbits.

Contribution

It presents a novel black hole model within a Dehnen dark matter halo and investigates its thermodynamic properties and null geodesic behavior, including stability and chaos analysis.

Findings

Dark matter parameters significantly affect thermodynamic stability.

Null geodesics and photon orbit radii are influenced by dark matter properties.

Circular null geodesics can exhibit chaotic behavior under certain conditions.

Abstract

In this work, we derive a novel black hole solution surrounded by a Dehnen-(1,4,0) type dark matter halo by embedding a Schwarzschild black hole within the halo, constituting a composite dark matter-black hole system. The thermodynamics of the resulting effective black hole spacetime is then studied with particular attention to the influence of the dark matter parameters on various thermodynamic properties. We examine the specific heat and free energy to assess the thermodynamic stability of the model. Furthermore, the null geodesics and the effective potential of light rays are studied to investigate how the dark matter parameters affect these geodesics and the radii of circular orbits. The stability of circular null geodesics is analyzed using dynamical systems and Lyapunov exponents, which represents the dynamical behaviour of the circular photon orbits. Finally, we studied if the circular geodesics exhibit chaotic behaviour using the chaos-bound condition.