<p>This paper investigates the thermodynamic properties of rotating Lifshitz black branes in quartic quasitopological gravity coupled to a dilaton field. We derive the field equations and identify a conserved quantity, <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathcal {C}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">C</mi> </math></EquationSource> </InlineEquation>, along the radial coordinate. Due to the complexity of the equations, exact analytical solutions are unattainable; therefore, we analyze the asymptotic behavior of the solutions both near the horizon and at infinity. We compute the conserved and thermodynamic quantities, including temperature, angular velocity, entropy, energy density, and angular momentum density. By evaluating the conserved quantity <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathcal {C}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">C</mi> </math></EquationSource> </InlineEquation> at both boundaries, we establish a direct relation between these thermodynamic variables, leading to a Smarr-type formula. We demonstrate that the first law of thermodynamics is rigorously satisfied for these rotating black branes. Furthermore, our analysis of thermal stability, based on the heat capacity and the Hessian determinant, reveals that the black brane solution is thermally unstable for the considered parameter space.</p>

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Thermodynamics of rotating Lifshitz dilaton black branes in quartic quasitopological gravity

  • M. Ghanaatian,
  • F. Esmaeili,
  • A. Bazrafshan,
  • Gh. Forozani

摘要

This paper investigates the thermodynamic properties of rotating Lifshitz black branes in quartic quasitopological gravity coupled to a dilaton field. We derive the field equations and identify a conserved quantity, \(\mathcal {C}\) C , along the radial coordinate. Due to the complexity of the equations, exact analytical solutions are unattainable; therefore, we analyze the asymptotic behavior of the solutions both near the horizon and at infinity. We compute the conserved and thermodynamic quantities, including temperature, angular velocity, entropy, energy density, and angular momentum density. By evaluating the conserved quantity \(\mathcal {C}\) C at both boundaries, we establish a direct relation between these thermodynamic variables, leading to a Smarr-type formula. We demonstrate that the first law of thermodynamics is rigorously satisfied for these rotating black branes. Furthermore, our analysis of thermal stability, based on the heat capacity and the Hessian determinant, reveals that the black brane solution is thermally unstable for the considered parameter space.