State-space correlations and stabilities

Abstract

The state-space pair correlation functions and notion of stability of extremal and non-extremal black holes in string theory and M-theory are considered from the viewpoints of thermodynamic Ruppeiner geometry. From the perspective of intrinsic Riemannian geometry, the stability properties of these black branes are divulged from the positivity of principle minors of the space-state metric tensor. We have explicitly analyzed the state-space configurations for (i) the two and three charge extremal black holes, (ii) the four and six charge non-extremal black branes, which both arise from the string theory solutions. An extension is considered for the D6-D4-D2-D0 multi-centered black branes, fractional small black branes and two charge rotating fuzzy rings in the setup of Mathur's fuzzball configurations. The state-space pair correlations and nature of stabilities have been investigated for three charged bubbling black brane foams, and thereby the M-theory solutions are brought into the present consideration. In the case of extremal black brane configurations, we have pointed out that the ratio of diagonal space-state correlations varies as inverse square of the chosen parameters, while the off diagonal components vary as inverse of the chosen parameters. We discuss the significance of this observation for the non-extremal black brane configurations, and find similar conclusion that the state-space correlations extenuate as the chosen parameters are increased. In either of the above configurations, notion of scaling property suggests that the brane-brane pair correlations, which find an asymmetric nature in comparison with the other state-space pair correlations, weaken relatively faster and they relatively swiftly come into an equilibrium statistical configuration. Novel aspects of the state-space interactions may be envisaged from the coarse graining counting entropy of underlying CFT microstates.

On the Microscopic Perspective of Black Branes Thermodynamic Geometry

“…We find that such thermodynamic systems have a regular state-space geometry which turns out to be non-degenerate, and corresponds in general to an interacting statistical systems, whenever there exists a non-zero state-space scalar curvature. Recently, we have explored the complete set of non-trivial relative state-space correlation functions for string theory and M -theory black brane configurations [60,61]. Similar considerations are valid over the black holes in general relativity [67][68][69][70], attractor black holes [6][7][8][9]13,16] and Legendre transformed finite parameter chemical configurations [57,58], quantum field theory and QCD backgrounds [59].…”

Intrinsic geometric analysis of the network reliability and voltage stability

“…Form the very out-set of our geometric proposition, the voltage stability of the network and safety modes are an immediate consequence of the admissible network parameterization. With the help of correlation techniques [33][34][35][36] and critical point of an arbitrary network, the set of appropriate parameters and components can be identified for any finite component network. Interestingly, the global quantities of our model provide required set of safety alerts for the owner as well as to the regulator of the network.…”

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

“…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.…”

“…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.…”