Thermodynamic geometry and extremal black holes in string theory

Abstract

We study a generalisation of thermodynamic geometry to degenerate quantum ground states at zero temperatures exemplified by charged extremal black holes in type II string theories. Several examples of extremal charged black holes with non degenerate thermodynamic geometries and finite but non zero state space scalar curvatures are established. These include black holes described by D1-D5-P and D2-D6-NS5-P brane systems and also two charged small black holes in Type II string theories. We also explore the modifications to the state space geometry and the scalar curvature due to the higher derivative contributions and string loop corrections as well as an exact entropy expression from quantum information theory. Our construction describes state space geometries arising out of a possible limiting thermodynamic characterisation of degenerate quantum ground states at zero temperatures.

A new approach toward geometrical concept of black hole thermodynamics

“…Although extracting phase transition in terms of curvature singularity is the main reason to consider the geometrical approach in thermodynamics, there are several examples in which the curvature singularities of the known metrics (Weinhold and Ruppeiner metrics and their Legendre transformations) are not located at the phase transition points and they have number of singularities in which are before/after the phase transition points [23][24][25][26].…”

State-Space Geometry, Nonextremal Black Holes and Kaluza–klein Monopoles

“…In sequel, we enlist the complete set of non-trivial relative state-space correlation functions of the nonextremal nonlarge charged anticharged black brane configurations. See for an introduction references [14,15,16,18,19,20]. A similar analysis remains valid for the black holes in general relativity [27, ], attractor black holes [31,32,33,34,35,36,37,38,39] and Legendre transformed finite parameter chemical configurations [40,41], quantum field theory and hot QCD backgrounds [42,43] with finite chemical potentials and the strongly coupled quarkonium configurations [44,45].…”

“…Some examples of such state-space configurations involve statistical properties of the extremal and non-extremal black branes [13,14,15,16,17,18,19,20]. In this paper, we focus our attention on the thermodynamic perspectives of the higher charged anticharged black brane configurations in string theory.…”

“…Following the notions we have developed in the Refs. [14,15,16,18,17,19,20], the subsequent analysis is devoted to the state-space geometric implications of the eight charge non-extremal black branes. In the 2 present work, we examine the nature of the state-space of the non-extremal black hole under the contribution of finitely many non-trivially circularly fibered KK-monopoles.…”

“…Following developments introduced in the Refs. [14,15,16,18,17,19,20], we have explicitly extended the analysis of the state-space geometry for the four charge and four anticharge non-extremal black brane configurations in the string theory. The present consideration of the eight parameter black brane configurations, where the underlying leading order statistical entropy is written as a function of the charges {n i } and anticharges {m i } and describes the stability properties under the Gaussian fluctuations.…”