Abstract
Motivated by a recent work on asymptotically Ad $$S_4$$ black holes in M-theory, we investigate both thermodynamics and the thermodynamical geometry of Reissner–Nordstrom-AdS black holes from M2-branes. More precisely, we study AdS black holes in $$AdS_{4}\times S^{7}$$ , with the number of M2-branes interpreted as a thermodynamical variable. In this context, we calculate various thermodynamical quantities including the chemical potential, and examine their phase transitions along with the corresponding stability behaviors. In addition, we also evaluate the thermodynamical curvatures of the Weinhold, Ruppeiner, and Quevedo metrics for M2-branes geometry to study the stability of such a black object. We show that the singularities of these scalar curvature’s metrics reproduce similar stability results to those obtained by the phase transition diagram via the heat capacities in different ensembles either when the number of the M2 branes or the charge is held fixed. Also, we note that all results derived in Belhaj et al. (Eur Phys J C 76(2):73, 2016) are recovered in the limit of the vanishing charge.
Highlights
Waals gas [12,13,14,15,16,17,18,19]
We discuss the geothermodynamics (GDM) of the charged AdS black holes in Ad S4 × S7: Our analysis will focus on the singular limits of certain thermodynamical quantities, including the heat capacities and scalar curvatures, which are relevant in the study of the stability of such black hole solutions
Since the GDM approach fails to explain the correspondence between phase transitions and singularities of the scalar curvature for phantom Reissner–Nordstrom AdS black holes, as reported in [39,40,41,42], it is legitimate and well justified hereafter to check the thermodynamic geometry of black holes metric by metric and to see the divergent points of the specific heat correspond exactly to the singularities derived by GTD method
Summary
Waals gas [12,13,14,15,16,17,18,19]. Emphasis has been put on the free energy and its behavior in the fixed charge ensemble. We consider thermodynamical geometry of the M2-branes black holes in the extended phase space and study the stability problem when either N or the charge is held fixed. We discuss the geothermodynamics (GDM) of the charged AdS black holes in Ad S4 × S7: Our analysis will focus on the singular limits of certain thermodynamical quantities, including the heat capacities and scalar curvatures, which are relevant in the study of the stability of such black hole solutions. Since the GDM approach fails to explain the correspondence between phase transitions and singularities of the scalar curvature for phantom Reissner–Nordstrom AdS black holes, as reported in [39,40,41,42], it is legitimate and well justified hereafter to check the thermodynamic geometry of black holes metric by metric and to see the divergent points of the specific heat correspond exactly to the singularities derived by GTD method. The Weinhold metric [43] is defined as the second derivative of the internal energy with respect to the entropy and other extensive quantities in the energy representation, while the Ruppeiner metric [44] is related to the Weinhold metric by a conformal factor of the temperature [45]; we have ds
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
