2008/01/27 by Bhupendra Nath Tiwari, Tiwari, Bhupendra Nath
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories #hep-th #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.0801.4087
489 pages, Latex, French, English Abstract
openalex publication_date 2008/01/27 · arxiv created 2011/08/23 · arxiv updated 2011/08/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study thermodynamic geometry of certain black holes and black branes with and without generalized uncertainty principle or stringy α′ -corrections to the entropy. From this perspective, we analyze Ruppenier geometry of Reissner-Nordström black holes and show that it is well defined and corresponds to a non-interacting statistical system. We investigate that the Weinhold geometry of dilatonic black holes is regular everywhere and that of large mass Reissner-Nordström black holes in the Poincaré patch of AdS4 contains certain narrow range of thermodynamically unstable regions in the statespace. We obtain that the generalized uncertainty principle corrected Ruppenier geometry of Reissner-Nordström black holes correspond to a non-interacting statistical system unlike the magnetically charged black holes. We show that the stringy α′ -corrections do not introduce singularity in the statespace geometry of non-supersymmetric extremal black holes in D= 4 . Interestingly, the degree of scalar curvature and that of the determinant of this Ruppenier geometry can be written as an integer multiple of the order of α′ -correction. We further show that the statespace geometry of Gauss- Bonnet corrected supersymmetric extremal black holes in D=4 as well as non-extremal D1D5 and D2D6NS5 black branes in D=10 is regular everywhere. Furthermore, the thermodynamic geometry of four dimensional rotating Kerr-Newman extremal black holes in Einstein-Maxwell theory is everywhere ill-defined and that of the Kaluza-Klein black holes in Einstein-Maxwell theory or the one arrising from heterotic string compactification is ill-defined only at the points of the ergo-branch.