We study thermodynamics and quantum tunneling of the Reissner–Nordström black hole with deficit solid angle and quintessence. We employ black hole thermodynamical laws and Parikh–Wilczek’s semiclassical tunneling process to obtain expressions of some thermodynamics quantities, Boltzmann factor, and entropy variation of the black hole. Regarding black hole background as dynamical and using conservation laws for energy and charge, we detect the existence of unthermal radiation spectrum and dependence of Boltzmann factor on the background geometry, and on energy and charge of the radiant particle. We explicitly plot variations of temperature, heat capacity, Boltzmann factor, and entropy change for various values of deficit solid angle [Formula: see text] and quintessence density [Formula: see text]. When varying the black hole entropy, there exists a phase transition, which shifts to lower entropy for increasing [Formula: see text] and decreasing [Formula: see text]. We show that temperature, heat capacity, and quantum tunneling rate are decreased in presence of quintessence and deficit angle parameters.
The effects of head‐on collision on dust acoustic (DA) solitary and shock waves in dusty plasma are investigated considering positively charged inertial dust, Boltzmann distributed negatively charged heavy ions, positively charged light ions, and superthermal electrons in the plasma system. The nonlinear Korteweg‐de‐Vries (KdV) Burger equations are derived taking the extended Poincaré‐Lighthill‐Kuo method into account to study the characteristic properties of nonlinearity and production of solitary shock due to collisions. The study reveals that the amplitudes and widths of the DA shock waves are decreasing with increasing viscosity, electron to dust density ratio, and dust to ion temperature ratio, while they are increasing due to the presence of superthermal electrons. The nonlinearity of DA waves are enhanced with increasing density ratio of electron to dust and temperature ratio of dust to ion and electron, respectively, but it is reducing with superthermal electrons. The phase shifts of DA solitary waves are found to decrease with rising superthermality of electrons and increase with the density ratio of electron to
dust.
We derive thermodynamic quantities such as the Hawking temperature, mass, entropy, heat capacity and study the thermodynamic phase transitions of rotating Bardeen black holes surrounded by quintessence-like matter. Interpreting the cosmological parameter as thermodynamic pressure and its conjugate variable as volume, the first law of black hole thermodynamics has been modified in the Anti-de Sitter (AdS) space. It then has been used to investigate the thermodynamics of the rotating Bardeen–AdS black hole with quintessence matter. Properties of the thermodynamic volume have also been analyzed through the study of compressibility and sound speed of the black hole. The black hole sound speed is associated with the adiabatic compressibility, and it equals the light speed for nonrotating black holes and decreases with increasing angular momentum. The nonrotating black holes are adiabatically incompressible, and as the angular momentum attains a maximum value in the extremal case, the compressibility grows maximum. We further derive the equation of state in the extended phase space and explore the critical behaviors of the black hole in the canonical ensemble. Graphs of phase transitions and critical behaviors show an accentuated influence of quintessence matter on the thermodynamic phase transitions and stability of the black holes and support the van der Waals-like phase transition behavior.
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