In light of a general scenario of a two-level non-Hermitian $\mathcal{PT}$-symmetric Hamiltonian, we apply the tetrad-based method to analyze the possibility of analogue Hawking radiation. We carry this out by making use of the conventional null-geodesic approach, wherein the associated Hawking radiation is described as a quantum tunneling process across a classically forbidden barrier on which the event horizon imposes. An interesting aspect of our result is that our estimate for the tunneling probability is independent of the non-Hermitian parameter that defines the guiding Hamiltonian.

We examine the possibility of artificial Hawking radiation by proposing a non-$\mathcal{PT}$ -symmetric weakly pseudo-Hermitian two-band model containing a tilting parameter by pursuing Weyl semimetal blackhole analogy. We determine the tunneling probability using such a Hamiltonian through the event horizon that acts as a classically forbidden barrier.

Our aim is to link Bekenstein’s quantized form of the area of the event horizon to the Hamiltonian of the non-Hermitian Swanson oscillator which is known to be \(\mathbb{PT}\)-symmetric. We achieve this by employing a similarity transformation that maps the non-Hermitian quantum system to a scaled harmonic oscillator. Our procedure is standard and well known. To this end, we consider the unconstrained reduced Hamiltonian which is directly expressed in terms of the Schwarzschild mass and implies a periodic character of the conjugate momentum (which represents the asymptotic time coordinate), the period being the inverse Hawking temperature. This leads to quantization of the event-horizon area in terms of the harmonic-oscillator levels. Next, in the framework of the Swanson oscillator, we proceed to derive novel expressions for the Hawking temperature and the black hole entropy. Notably, the logarithmic area-correction term \(-(1/2)\ln\)(area) is consistent with our results, whereas \(-(3/2)\ln\)(area) is not.

We investigate the implications provided by the modified Painlevé-Gullstrand coordinates in the context of quintessence for the Kiselev black hole. In this regard, we set up a fully static line element in terms of lapse and shift functions, apart from including the deformation parameter signaling deviation from the standard Painlevé-Gullstrand metric. We address two specific issues pertaining to the problems of radiation and dust furnished by the corresponding barotropic index parameter and study the related consequences by performing a range of analyses to explore the influence imposed by quintessence. We also discuss the thermodynamical consequences by evaluating the expressions of the Hawking temperature and the entropy function in closed forms.