Null Geodesics and Thermodynamics of Hairy Kiselev Black Hole surrounded by Cosmological Fields

In this paper, we study the photon-orbit dynamics and thermodynamics of the Hairy Kiselev black hole with surrounding matter fields, including stiff fluid ([Formula: see text]), dust ([Formula: see text]), radiation ([Formula: see text]), dark energy ([Formula: see text]), and quintessence ([Formula: see text]). We analyze how the strength of the surrounding matter fields affects the stability of the photon orbits. Our analysis reveals that the effective potential, influenced by the matter fields, gives rise to stable photon orbits for [Formula: see text], whereas no stable orbits are found for [Formula: see text]. A Lyapunov stability study further strengthens this outcome, where [Formula: see text] is observed. Turning to the thermodynamic analysis, the central result of our work reveals a striking negative Hawking temperature for dark energy ([Formula: see text]) and quintessence ([Formula: see text]) matter fields at the cosmological horizon. The negative Hawking temperature is explained from the thermodynamic perspective and, from the geometric perspective, by the orientation of the Killing vector relative to the observer’s static patch. This behavior is further supported by the heat capacity analysis. Finally, the fermion tunneling rate obtained under the generalized uncertainty principle (GUP) shows that the temperature is reduced by a factor of [Formula: see text], indicating that quantum gravity effects at the Planck scale further suppress Hawking radiation across all investigated matter distributions. The result from the generalized uncertainty principle has the same algebraic form, further supporting the negative Hawking temperature as a natural outcome for dark energy and quintessence matter fields.