Thermal stability with emission energy and Joule–Thomson expansion of regular BTZ-like black hole
Abstract
Abstract We investigate the thermodynamic properties and Joule–Thomson expansion for conical or BTZ-like black holes. To analyze the thermal stability, we discuss the temperature and thermal stability relative to the horizon radius for different values of model parameters $$\beta _0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>β</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:math> and $$\alpha _2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>α</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math> . Moreover, we analyze thermodynamical geometries like Ruppeiner, Weinhold and Hendi Panahiyah Eslam Momennia formulation and calculate respective scalar curvatures for BTZ-like black holes. Interestingly, the black holes have no singularity in some cases, i.e., completely regular. We obtain the inversion temperatures and inversion curves and investigate the similarities and differences between van der Waals and charged fluids. To discuss this expansion, we use a BTZ-like black hole. Further, we establish the position of the inversion point versus different values of mass $$\mu $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>μ</mml:mi> </mml:math> , and the parameters $$\beta _0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>β</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:math> and $$\alpha _2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>α</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math> for such a BTZ-like black hole. The Joule–Thomson coefficient $$\mu $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>μ</mml:mi> </mml:math> at this point disappears. A crucial trait upon which we relied to inspect the sign of quantity $$\mu $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>μ</mml:mi> </mml:math> to get the cooling-heating areas. We also investigate the energy emission depending upon the frequency $$\omega $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ω</mml:mi> </mml:math> .