In this paper, we study the Joule-Thomson Expansion process for two types of black holes: AdS-Einstein-Maxwell-power-Yang-Mills (AEMPYM) and AdS-Kerr-Sen (AKS). Our study focuses on understanding how various parameters influence the Joule-Thomson Coefficient, the inversion curve, and the ratio of minimum inversion temperature to critical temperature. For the AKS black hole, we observe that the isenthalpic curves can exhibit either cooling or heating behavior. This behavior is determined by the inversion curve, which is affected by the black hole’s mass and specific parameters such as b (parameter signifies the ionic charge of the black hole) and a (rotation parameter). In the case of the AEMPYM black hole, our findings reveal that the ratio of minimum inversion temperature to critical temperature approaches a specific value as Maxwell’s charge increases. This ratio remains constant for certain parameter values, while it varies for others. Specifically, when the parameter <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10714_2025_3393_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">$q$</EquationSource> <EquationSource Format="MATHML"><math> <mi>q</mi> </math></EquationSource> </InlineEquation> (real positive parameter of AEMPYM black hole) is greater than 1, the ratio is almost equal to 1/2 as Maxwell’s charge <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10714_2025_3393_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">$C$</EquationSource> <EquationSource Format="MATHML"><math> <mi>C</mi> </math></EquationSource> </InlineEquation> increases. When q equals 1/2, the ratio is exactly 1/2 for all values of <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10714_2025_3393_Article_IEq3.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">$C$</EquationSource> <EquationSource Format="MATHML"><math> <mi>C</mi> </math></EquationSource> </InlineEquation>. For values of <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10714_2025_3393_Article_IEq4.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">$q$</EquationSource> <EquationSource Format="MATHML"><math> <mi>q</mi> </math></EquationSource> </InlineEquation> between 1/2 and 1, the ratio is close to 1/2, and for values of <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10714_2025_3393_Article_IEq5.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">$q$</EquationSource> <EquationSource Format="MATHML"><math> <mi>q</mi> </math></EquationSource> </InlineEquation> between 0 and 1/2, the ratio decreases, moving away from 1/2. For the AKS black hole, we find that specific parameter values, such as <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10714_2025_3393_Article_IEq6.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="85" /> </InlineMediaObject> <EquationSource Format="TEX">$a = 0.00951$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>a</mi> <mo>=</mo> <mn>0.00951</mn> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10714_2025_3393_Article_IEq7.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="83" /> </InlineMediaObject> <EquationSource Format="TEX">$b = 0.00475$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>b</mi> <mo>=</mo> <mn>0.00475</mn> </mrow> </math></EquationSource> </InlineEquation>, yield a ratio of minimum inversion temperature to a critical temperature that is approximately 1/2. This consistency across different parameter values highlights the robustness of our findings. Finally, we compare our results with those reported in the existing literature, providing a comprehensive summary in detailed tables. This comparison not only validates our findings but also situates them within the broader context of black hole thermodynamics and the Joule-Thomson effect.

Cooling and heating regions of Joule-Thomson expansion for AdS black holes: Einstein-Maxwell-power-Yang-Mills and Kerr Sen black holes

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发表日期：

2025年3月26日

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Mohammad Reza Alipour,
Saeed Noori Gashti,
Mohammad Ali S. Afshar,
Jafar Sadeghi

摘要

In this paper, we study the Joule-Thomson Expansion process for two types of black holes: AdS-Einstein-Maxwell-power-Yang-Mills (AEMPYM) and AdS-Kerr-Sen (AKS). Our study focuses on understanding how various parameters influence the Joule-Thomson Coefficient, the inversion curve, and the ratio of minimum inversion temperature to critical temperature. For the AKS black hole, we observe that the isenthalpic curves can exhibit either cooling or heating behavior. This behavior is determined by the inversion curve, which is affected by the black hole’s mass and specific parameters such as b (parameter signifies the ionic charge of the black hole) and a (rotation parameter). In the case of the AEMPYM black hole, our findings reveal that the ratio of minimum inversion temperature to critical temperature approaches a specific value as Maxwell’s charge increases. This ratio remains constant for certain parameter values, while it varies for others. Specifically, when the parameter $q$ $q$ (real positive parameter of AEMPYM black hole) is greater than 1, the ratio is almost equal to 1/2 as Maxwell’s charge $C$ $C$ increases. When q equals 1/2, the ratio is exactly 1/2 for all values of $C$ $C$ . For values of $q$ $q$ between 1/2 and 1, the ratio is close to 1/2, and for values of $q$ $q$ between 0 and 1/2, the ratio decreases, moving away from 1/2. For the AKS black hole, we find that specific parameter values, such as $a = 0.00951$ $a = 0.00951$ and $b = 0.00475$ $b = 0.00475$ , yield a ratio of minimum inversion temperature to a critical temperature that is approximately 1/2. This consistency across different parameter values highlights the robustness of our findings. Finally, we compare our results with those reported in the existing literature, providing a comprehensive summary in detailed tables. This comparison not only validates our findings but also situates them within the broader context of black hole thermodynamics and the Joule-Thomson effect.