An Exact Fluctuating 1/2-BPS Configuration

This work explores the role of thermodynamic fluctuations in the two parameter giant and superstar configurations characterized by an ensemble of arbitrary liquid droplets or irregular shaped fuzzballs. Our analysis illustrates that the chemical and state-space geometric descriptions exhibit an intriguing set of exact pair correction functions and the global correlation lengths. The first principle of statistical mechanics shows that the possible canonical fluctuations may precisely be ascertained without any approximation. Interestingly, our intrinsic geometric study exemplifies that there exist exact fluctuating 1/2-BPS statistical configurations which involve an ensemble of microstates describing the liquid droplets or fuzzballs. The Gaussian fluctuations over an equilibrium chemical and state-space configurations accomplish a well-defined, non-degenerate, curved and regular intrinsic Riemannian manifolds for all physically admissible domains of black hole parameters. An explicit computation demonstrates that the underlying chemical correlations involve ordinary summations, whilst the state-space correlations may simply be depicted by standard polygamma functions. Our construction ascribes definite stability character to the canonical energy fluctuations and to the counting entropy associated with an arbitrary choice of excited boxes from an ensemble of ample boxes constituting a variety of Young tableaux.Comment: Minor changes, added references, 30 pages, 4 figures, PACS numbers: 04.70.-s: Physics of black holes; 04.70.-Bw: Classical black holes; 04.50.Gh Higher-dimensional black holes, black strings, and related objects; 04.60.Cf Gravitational aspects of string theory, accepted for publication in JHE

State-space Manifold and Rotating Black Holes

We study a class of fluctuating higher dimensional black hole configurations obtained in string theory/ $M$-theory compactifications. We explore the intrinsic Riemannian geometric nature of Gaussian fluctuations arising from the Hessian of the coarse graining entropy, defined over an ensemble of brane microstates. It has been shown that the state-space geometry spanned by the set of invariant parameters is non-degenerate, regular and has a negative scalar curvature for the rotating Myers-Perry black holes, Kaluza-Klein black holes, supersymmetric $AdS_5$ black holes, $D_1$-$D_5$ configurations and the associated BMPV black holes. Interestingly, these solutions demonstrate that the principal components of the state-space metric tensor admit a positive definite form, while the off diagonal components do not. Furthermore, the ratio of diagonal components weakens relatively faster than the off diagonal components, and thus they swiftly come into an equilibrium statistical configuration. Novel aspects of the scaling property suggest that the brane-brane statistical pair correlation functions divulge an asymmetric nature, in comparison with the others. This approach indicates that all above configurations are effectively attractive and stable, on an arbitrary hyper-surface of the state-space manifolds. It is nevertheless noticed that there exists an intriguing relationship between non-ideal inter-brane statistical interactions and phase transitions. The ramifications thus described are consistent with the existing picture of the microscopic CFTs. We conclude with an extended discussion of the implications of this work for the physics of black holes in string theory.Comment: 44 pages, Keywords: Rotating Black Holes; State-space Geometry; Statistical Configurations, String Theory, M-Theory. PACS numbers: 04.70.-s Physics of black holes; 04.70.Bw Classical black holes; 04.70.Dy Quantum aspects of black holes, evaporation, thermodynamics; 04.50.Gh Higher-dimensional black holes, black strings, and related objects. Edited the bibliograph

On The Phase Structure and Thermodynamic Geometry of R-Charged Black Holes

We study the phase structure and equilibrium state space geometry of R-charged black holes in $D = 5$, 4 and 7 and the corresponding rotating $D3$, $M2$ and $M5$ branes. For various charge configurations of the compact black holes in the canonical ensemble we demonstrate new liquid-gas like phase coexistence behaviour culminating in second order critical points. The critical exponents turn out to be the same as that of four dimensional asymptotically AdS black holes in Einstein Maxwell theory. We further establish that the regions of stability for R-charged black holes are, in some cases, more constrained than is currently believed, due to properties of some of the response coefficients. The equilibrium state space scalar curvature is calculated for various charge configurations, both for the case of compact as well as flat horizons and its asymptotic behaviour with temperature is established.Comment: 1 + 33 pages, LaTeX, 25 figures. References adde

On the Thermodynamic Geometry and Critical Phenomena of AdS Black Holes

In this paper, we study various aspects of the equilibrium thermodynamic state space geometry of AdS black holes. We first examine the Reissner-Nordstrom-AdS (RN-AdS) and the Kerr-AdS black holes. In this context, the state space scalar curvature of these black holes is analysed in various regions of their thermodynamic parameter space. This provides important new insights into the structure and significance of the scalar curvature. We further investigate critical phenomena, and the behaviour of the scalar curvature near criticality, for KN-AdS black holes in two mixed ensembles, introduced and elucidated in our earlier work arXiv:1002.2538 [hep-th]. The critical exponents are identical to those in the RN-AdS and Kerr-AdS cases in the canonical ensemble. This suggests an universality in the scaling behaviour near critical points of AdS black holes. Our results further highlight qualitative differences in the thermodynamic state space geometry for electric charge and angular momentum fluctuations of these.Comment: 1 + 37 Pages, LaTeX, includes 31 figures. A figure and a clarification added

Thermodynamic instability of doubly spinning black objects

We investigate the thermodynamic stability of neutral black objects with (at least) two angular momenta. We use the quasilocal formalism to compute the grand canonical potential and show that the doubly spinning black ring is thermodynamically unstable. We consider the thermodynamic instabilities of ultra-spinning black objects and point out a subtle relation between the microcanonical and grand canonical ensembles. We also find the location of the black string/membrane phases of doubly spinning black objects.Comment: 25 pages, 7 figures v2: matches the published versio

Thermodynamic Geometry and Phase Transitions in Kerr-Newman-AdS Black Holes

We investigate phase transitions and critical phenomena in Kerr-Newman-Anti de Sitter black holes in the framework of the geometry of their equilibrium thermodynamic state space. The scalar curvature of these state space Riemannian geometries is computed in various ensembles. The scalar curvature diverges at the critical point of second order phase transitions for these systems. Remarkably, however, we show that the state space scalar curvature also carries information about the liquid-gas like first order phase transitions and the consequent instabilities and phase coexistence for these black holes. This is encoded in the turning point behavior and the multi-valued branched structure of the scalar curvature in the neighborhood of these first order phase transitions. We re-examine this first for the conventional Van der Waals system, as a preliminary exercise. Subsequently, we study the Kerr-Newman-AdS black holes for a grand canonical and two "mixed" ensembles and establish novel phase structures. The state space scalar curvature bears out our assertion for the first order phase transitions for both the known and the new phase structures, and closely resembles the Van der Waals system.Comment: 1 + 41 pages, LaTeX, 46 figures. Discussions, clarifications and references adde

Thermodynamical Metrics and Black Hole Phase Transitions

An important phase transition in black hole thermodynamics is associated with the divergence of the specific heat with fixed charge and angular momenta, yet one can demonstrate that neither Ruppeiner's entropy metric nor Weinhold's energy metric reveals this phase transition. In this paper, we introduce a new thermodynamical metric based on the Hessian matrix of several free energy. We demonstrate, by studying various charged and rotating black holes, that the divergence of the specific heat corresponds to the curvature singularity of this new metric. We further investigate metrics on all thermodynamical potentials generated by Legendre transformations and study correspondences between curvature singularities and phase transition signals. We show in general that for a system with n-pairs of intensive/extensive variables, all thermodynamical potential metrics can be embedded into a flat (n,n)-dimensional space. We also generalize the Ruppeiner metrics and they are all conformal to the metrics constructed from the relevant thermodynamical potentials.Comment: Latex, 25 pages, reference added, typos corrected, English polished and the Hawking-Page phase transition clarified; to appear in JHE

Developing a utility index for the Aberrant Behavior Checklist (ABC-C) for fragile X syndrome

Purpose This study aimed to develop a utility index (the ABC-UI) from the Aberrant Behavior Checklist-Community (ABC-C), for use in quantifying the benefit of emerging treatments for fragile X syndrome (FXS). Methods The ABC-C is a proxy-completed assessment of behaviour and is a widely used measure in FXS. A subset of ABC-C items across seven dimensions was identified to include in health state descriptions. This item reduction process was based on item performance, factor analysis and Rasch analysis performed on an observational study dataset, and consultation with five clinical experts and a methodological expert. Dimensions were combined into health states using an orthogonal design and valued using time trade-off (TTO), with lead-time TTO methods used where TTO indicated a state valued as worse than dead. Preference weights were estimated using mean, individual level, ordinary least squares and random-effects maximum likelihood estimation [RE (MLE)] regression models. Results A representative sample of the UK general public (n = 349; mean age 35.8 years, 58.2 % female) each valued 12 health states. Mean observed values ranged from 0.92 to 0.16 for best to worst health states. The RE (MLE) model performed best based on number of significant coefficients and mean absolute error of 0.018. Mean utilities predicted by the model covered a similar range to that observed. Conclusions The ABC-UI estimates a wide range of utilities from patient-level FXS ABC-C data, allowing estimation of FXS health-related quality of life impact for economic evaluation from an established FXS clinical trial instrument

NIK Stabilization in Osteoclasts Results in Osteoporosis and Enhanced Inflammatory Osteolysis

Maintenance of healthy bone requires the balanced activities of osteoclasts (OCs), which resorb bone, and osteoblasts, which build bone. Disproportionate action of OCs is responsible for the bone loss associated with postmenopausal osteoporosis and rheumatoid arthritis. NF-κB inducing kinase (NIK) controls activation of the alternative NF-κB pathway, a critical pathway for OC differentiation. Under basal conditions, TRAF3-mediated NIK degradation prevents downstream signaling, and disruption of the NIK:TRAF3 interaction stabilizes NIK leading to constitutive activation of the alternative NF-κB pathway.Using transgenic mice with OC-lineage expression of NIK lacking its TRAF3 binding domain (NT3), we now find that alternative NF-κB activation enhances not only OC differentiation but also OC function. Activating NT3 with either lysozyme M Cre or cathepsinK Cre causes high turnover osteoporosis with increased activity of OCs and osteoblasts. In vitro, NT3-expressing precursors form OCs more quickly and at lower doses of RANKL. When cultured on bone, they exhibit larger actin rings and increased resorptive activity. OC-specific NT3 transgenic mice also have an exaggerated osteolytic response to the serum transfer model of arthritis.Constitutive activation of NIK drives enhanced osteoclastogenesis and bone resorption, both in basal conditions and in response to inflammatory stimuli

Relationship Between Sonic Hedgehog Protein, Brain-Derived Neurotrophic Factor and Oxidative Stress in Autism Spectrum Disorders

The etiology of autism spectrum disorders (ASD) is not well known but oxidative stress has been suggested to play a pathological role. We report here that the serum levels of Sonic hedgehog (SHH) protein and brain-derived neurotrophic factor (BDNF) might be linked to oxidative stress in ASD. By using the whole blood or polymorphonuclear leukocytes, we demonstrated that autistic children produced a significantly higher level of oxygen free radicals (OFR). In addition, we found significantly higher levels of serum SHH protein in children with mild as well as severe form of autism. We also found that the serum level of BDNF was significantly reduced in autistic children with mild form of the disorder but not with severe form of the disorder. Our findings are the first to report a correlation between SHH, BDNF and OFR in autistic children, suggesting a pathological role of oxidative stress and SHH in autism spectrum disorders