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

Abstract

We examine the statistical nature of the charged anticharged non-extremal black holes in string theory. From the perspective of the intrinsic Riemannian Geometry, the first principle of the statistical mechanics shows that the stability properties of general nonextremal nonlarge charged black brane solutions are divulged from the positivity of the corresponding principle minors of the space-state metric tensor. Under the addition of the Kaluza-Klein monopoles, a novel aspect of the Gaussian fluctuations demonstrates that the canonical fluctuations can be ascertained without any approximation. We offer the state-space geometric implication for the most general non-extremal black brane configurations in string theory.Keywords: Intrinsic Geometry; String Theory; Physics of black holes; Classical black holes; Quantum aspects of black holes, evaporation, thermodynamics; Higher-dimensional black holes, black strings, and related objects; Statistical Fluctuation; Flow Instability.PACS numbers: 2.40.- Ky; 04.70.Bw; 04.70.Dy; 04.50.Gh; 47.29.Ky Generic higher charged non-extremal black branes in string theory [1,2,3,4,5,6,7,8] and M -theory [9,10,11,12] possess rich state-space geometric structures. 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. We wish to explicate the nature of the state-space pair correlation functions and the associated stability properties of the higher charged black brane solutions containing an ensemble of branes and antibranes. In the past, there have been several notions analyzed in condensed matter physics [21,22,23,24,25]. Here, we shall consider eight charged anticharged string theory black brane configurations and analyze the state-space pair correlation functions and their relative scaling relations. Given the definite state-space description of consistent non-extremal black brane macroscopic solutions, we expose (i) for what conditions the considered black hole configuration is stable, (ii) how its state-space correlation functions scale in terms of the numbers of the branes and antibranes. 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].Before analyzing the state-space properties of the eight parameter black brane configuration, let us first provide a brief introduction to the thermodynamic geometry [21,30,13]....

Geodesic motion in a charged 2D stringy black hole spacetime

“…1 In particular, the charged dilatonic black holes (BHs) have been studied extensively in the literature [2][3][4][5][6][7][8][9] and such BHs have diverse connections to supergravity, 2 Kaluza-Klein, 3 string 4 and conformal field theories. 5 The study of geodesics for test particles in given spacetime is one way to understand the gravitational field around the BH and therefore, to investigate the given spacetime, first step may be to consider the motion of test particles in it.…”