Abstract
In this paper, we investigate the thermodynamics and phase transitions of a four-dimensional rotating Kaluza–Klein black hole solution in the presence of Maxwell electrodynamics. Calculating the conserved and thermodynamic quantities shows that the first law of thermodynamics is satisfied. To find the stable black hole’s criteria, we check the stability in the canonical ensemble by analyzing the behavior of the heat capacity. We also consider a massive scalar perturbation minimally coupled to the background geometry of the four-dimensional static Kaluza–Klein black hole and investigate the quasinormal modes by employing the Wentzel–Kramers–Brillouin (WKB) approximation. The anomalous decay rate of the quasinormal modes spectrum is investigated by using the sixth-order WKB formula and quasi-resonance modes of the black hole are studied with averaging of Padé approximations as well.
Highlights
From thermodynamic considerations, we know that under certain conditions, a thermodynamic system can experience a phase transition
Davies found that a discontinuity of the heat capacity represents the second-order phase transition in black holes (BHs) about 40 years ago [11,12,13] while the analysis of phase structure was done by Hut [14]
We focus on perturbations of minimal coupled massive scalar fields in the background of four-dimensional static KK BHs to investigate the effects of the free parameters p and q on the scalar quasinormal modes (QNMs) spectrum
Summary
We know that under certain conditions, a thermodynamic system can experience a phase transition. A minimally coupled scalar field describes the QNMs in the area of scalar–tensor theories, and observing quasi-resonance modes and anomalous decay rate of QN modes motivates one to investigate these models as well. We focus on perturbations of minimal coupled massive scalar fields in the background of four-dimensional static KK BHs to investigate the effects of the free parameters p and q on the scalar QNM spectrum. We should note that some of the observational constraints on free parameters and physical properties of the mentioned KK BH solution (such as analysis of the gyroscope precession frequency [43], X-ray reflection spectroscopy [44], and shadow, quasinormal modes and quasiperiodic oscillations [45]) have been studied before
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