Duality Covariant Formulation of Extended Supergravity: Central Charges,BPS States and Black-Hole Entropy

In these lectures we give a geometrical formulation of N-extrended supergravities which generalizes N = 2 special geometry of N = 2 theories. In all these theories duality symmetries are related to the notion of “flat symplectic bundles” and central charges may be defined as “sections” over these bundles. Attractor points giving rise to “fixed scalars” of the horizon geometry and Bekenstein-Hawking entropy formula for extremal black-holes are discussed in some details.     

Emergent horizon,Hawking radiation and chaos in the collapsed polymer model of a black hole

We have proposed that the interior of a macroscopic Schwarzschild black hole (BH) consists of highly excited, long, closed, interacting strings and, as such, can be modeled as a collapsed polymer. It was previously shown that the scaling relations of the collapsed‐polymer model agree with those of the BH. The current paper further substantiates this proposal with an investigation into some of its dynamical consequences. In particular, we show that the model predicts, without relying on gravitational effects, an emergent horizon. We further show that the horizon fluctuates quantum mechanically as it should and that the strength of the fluctuations is inversely proportional to the BH entropy. It is then demonstrated that the emission of Hawking radiation is realized microscopically by the quantum‐induced escape of small pieces of string, with the rate of escape and the energy per emitted piece both parametrically matching the Hawking temperature. We also show, using standard methods from statistical mechanics and chaos theory, how our model accounts for some other known properties of BHs. These include the accepted results for the scrambling time and the viscosity‐to‐entropy ratio, which in our model apply not only at the horizon but throughout the BH interior.     

On the existence of non‐supersymmetric black hole attractors for two‐parameter Calabi‐Yau's and attractor equations

We look for possible nonsupersymmetric black hole attractor solutions for type II compactification on (the mirror of) CY₃(2,128) expressed as a degree‐12 hypersurface in WCP ⁴[1,1,2,2,6]. In the process, (a) for points away from the conifold locus, we show that the existence of a non‐supersymmetric attractor along with a consistent choice of fluxes and extremum values of the complex structure moduli, could be connected to the existence of an elliptic curve fibered over C ⁸ which may also be “arithmetic” (in some cases, it is possible to interpret the extremization conditions for the black‐hole superpotential as an endomorphism involving complex multiplication of an arithmetic elliptic curve), and (b) for points near the conifold locus, we show that existence of non‐supersymmetric black‐hole attractors corresponds to a version of A₁‐singularity in the space Image( Z ⁶→ R ²/ Z ₂ (↪ R ³)) fibered over the complex structure moduli space. The (derivatives of the) effective black hole potential can be thought of as a real (integer) projection in a suitable coordinate patch of the Veronese map: CP ⁵→ CP ²⁰, fibered over the complex structure moduli space. We also discuss application of Kallosh's attractor equations (which are equivalent to the extremization of the effective black‐hole potential) for nonsupersymmetric attractors and show that (a) for points away from the conifold locus, the attractor equations demand that the attractor solutions be independent of one of the two complex structure moduli, and (b) for points near the conifold locus, the attractor equations imply switching off of one of the six components of the fluxes. Both these features are more obvious using the attractor equations than the extremization of the black hole potential.     

Black hole attractors and the entropy function in four‐ and five‐dimensional N = 2 supergravity

In this overview of selected aspects of the black hole attractor mechanism, after introducing the necessary foundations, we examine the relationship between two ways to describe the attractor phenomenon in four‐dimensional N = 2 supergravity: the entropy function and the black hole potential. We also exemplify their practical application to finding solutions to the attractor equations for a conifold prepotential. Next we describe an extension of the original definition of the entropy function to a class of rotating black holes in five‐dimensional N = 2 supergravity based on cubic polynomials, exploiting a connection between four‐ and five‐dimensional black holes. This link allows further the derivation of five‐dimensional first‐order differential flow equations governing the profile of the fields from infinity to the event horizon and construction of non‐supersymmetric interpolating solutions in four dimensions by dimensional reduction. Finally, since four‐dimensional extremal black holes in N = 2 supergravity can be viewed as certain two‐dimensional string compactifications with fluxes, we discuss implications of the conifold example in the context of the entropic principle, which postulates as a probability measure on the space of these string compactifications the exponentiated entropy of the corresponding black holes.     

Dirac quasinormal modes of Born-Infeld black hole spacetimes

Quasinormal modes (QNMs) for massless and massive Dirac perturbations of Born-Infeld black holes (BHs) in higher dimensions are investigated. Solving the corresponding master equation in accordance with hypergeometric functions and the QNMs are evaluated. We discuss the relationships between QNM frequencies and spacetime dimensions. Meanwhile, we also discuss the stability of the Born-Infeld BH by calculating the temporal evolution of the perturbation field. Both the perturbation frequencies and the decay rate increase with increasing dimension of spacetime n. This shows that the Born-Infeld BHs become more and more unstable at higher dimensions. Furthermore, the traditional finite difference method is improved, so that it can be used to calculate the massive Dirac field. We also elucidate the dynamic evolution of Born-Infeld BHs in a massive Dirac field. Because the number of extra dimensions is related to the string scale, there is a relationship between the spacetime dimension n and the properties of Born-Infeld BHs that might be advantageous for the development of extra-dimensional brane worlds and string theory.     

Numerical simulations of black-hole binaries and gravitational wave emission

We review recent progress in numerical relativity simulations of black-hole (BH) spacetimes. Following a brief summary of the methods employed in the modeling, we summarize the key results in two major areas of BH physics: (i) BHs as sources of gravitational waves (GWs) and (ii) astrophysical systems involving BHs. We conclude with a list of the most urgent tasks for numerical relativity in these areas.     

Preferential mode of cyclization of tetrahydrofuran amino acids containing peptides: some theoretical insights

Theoretical insights have been provided for the observed preference of cyclodimerization over intramolecular cyclization reactions in linear tripeptides containing “2,5‐cis” (2S,5R)‐tetrahydrofuran amino acid as well as in those containing “2,5‐trans” (2S,5S)‐tetrahydrofuran amino acid, using quantum chemical methods. The geometries of species involved as well as the feasibility of cyclization reactions are studied at the B3LYP/6‐31G(d,p) level of theory in gas phase as well as in solvent phase. Thermodynamic data from Hessian calculations favor the intermolecular cyclization. Analysis of optimized geometries reveals the existence of additional stabilizing hydrogen bonding interactions in intermolecularly cyclized products. The existence of these second‐order interactions is substantiated by topological (atoms in molecules (AIM)) and natural bond orbital (NBO) analyses. Such interactions are absent in the intramolecular cyclization products. Further justification for the presence of stabilizing interactions in intermolecularly cyclized products comes from the molecular electrostatic potentials and electron density surfaces. Kinetic control favoring the intermolecularly cyclized products due to additional entropy of activation in the intramolecular case is surmised. Copyright © 2009 John Wiley & Sons, Ltd.     

Thermal consequences of a regular black hole with cosmological constant and Einstein–Aether black hole

We discuss the thermodynamics of regular black hole (RBH) with cosmological constant and Einstein–Aether black hole (BH) with coupling constant in the presence of thermal corrections. For these BHs, we develop various thermodynamical quantities such as entropy, pressure, specific heats, Gibbs free energy and Helmholtz free energy. Thermal stability is also being analyzed through γ factor, Gibbs free energy and Helmholtz free energy. It is found that RBH with cosmological constant and Einstein–Aether show stable behavior with the increase of the values of cosmological and coupling constants.     

QCD universality recovered via the Total Available Quadri‐Scalar

After presenting a brief review of the phenomenology of the Leading Effect, we define a new variable, the “Total Available Quadri‐Scalar” (A_TOT) and propose it as the invariant quantity effectively available for the production of the multihadronic final states. The introduction and definition of this new varaible is justified by means of simple geometrical‐kinematical considerations and we show that A_TOT reduces to the so‐called effective energy in the single specific situation where the use of the latter applies. Using A_TOT to re‐plot existing data, the quantity <n_ch> is shown to be a “Universality Feature” – that is, independent from the colliding particles, the collider nominal energy, and even from the hadronic invariant mass – as imposed by QCD universality.     

Higher derivative correction to Kaluza–Klein black hole solution

We investigate the attractor mechanism in a Kaluza–Klein black hole solution in the presence of higher derivative terms. In particular, we discuss the attractor behavior of static black holes by using the effective potential approach as well as the entropy function formalism. We consider different higher derivative terms with a general coupling to the moduli field. For the R ² theory, we use an effective potential approach, looking for solutions which are analytic near the horizon and showing that they exist and enjoy attractor behavior. The attractor point is determined by extremization of the modified effective potential at the horizon. We study the effect of the general higher derivative corrections of R ⁿ terms. Using the entropy function we define the modified effective potential and we find the conditions to have the attractor solution. In particular for a single charged Kaluza–Klein black hole solution we show that a higher derivative correction dresses the singularity for an appropriate coupling, and we can find the attractor solution.     

Testing the quantum effects near the event horizon with respect to the black hole shadow

In recent years, the study of quantum effects near the event horizon of a black hole (BH) has attracted extensive attention. It has become one of the important methods to explore BH quantum properties using the related properties of a quantum deformed BH. In this work, we study the effect of a quantum deformed BH on the BH shadow in two-dimensional Dilaton gravity. In this model, quantum effects are reflected by the quantum correction parameter m. By calculation, we find that: (1) the shape of the shadow boundary of a rotating BH is determined by the BH spin a, the quantum correction parameter m, and the BH type parameter n; (2) when the spin \begin{document}$ a=0 $\end{document}, the shape of the BH shadow is a perfect circle; when \begin{document}$ a\neq 0 $\end{document}, the shape is distorted; if the quantum correction parameter \begin{document}$ m=0 $\end{document}, their shapes reduce to the cases of a Schwarzschild BH and Kerr BH, respectively; (3) the degree of distortion of the BH shadow is different for various quantum correction parameters m; with an increase in the parameter m, the boundary of the BH shadow expands; (4) the size of the BH shadow varies greatly with respect to various quantum deformed BHs (n), and the change in BH shadow shape caused by parameter n is similar to that caused by parameter m, which indicates that there is a "degenerate phenomenon" between the two parameters. Because the value of m in actual physics should be very small, the current observations of the event horizon telescope (EHT) cannot distinguish quantum effects from the BH shadow. In future BH shadow measurements, it will be possible to distinguish quantum deformed BHs, which will help to better understand the quantum effects of BHs.     

Quantum effects on the black hole shadow and deflection angle in the presence of plasma

In this study, the optical properties of a renormalization group improved (RGI) Schwarzschild black hole (BH) are investigated in a plasma medium. Beginning with the equations of motion in a plasma medium, we aim to present the modifications in the shadow radius of the RGI BH. To this end, we compute the deflection angle of light in the weak gravity regime for uniform and non-uniform plasma media. Importantly, owing to the plasma media, we discover that the equations of motion for light obtained from the radiating and infalling/rest gas have to be modified. This, in turn, changes and modifies the expression for the intensity observed far away from the BH. Finally, we obtain the shadow images for the RGI BH for different plasma models. Although quantum effects change the background geometry, such effects are minimal, and practically detecting these effects using the current technology based on supermassive BH shadows is impossible. The parameter Ω encodes the quantum effects, and in principle, one expects such quantum effects to play significant roles only for very small BHs. However, the effects of plasma media can play an important role in the optical appearance of BHs, as they affect and modify the equations of motion.     

Weak deflection angle and shadow cast by the charged-Kiselev black hole with cloud of strings in plasma

In this study, the gravitational deflection angle of photons in the weak field limit (or the weak deflection angle) and shadow cast by the electrically charged and spherically symmetric static Kiselev black hole (BH) in the string cloud background are investigated. The influences of the BH charge Q, quintessence parameter γ, and string cloud parameter a on the weak deflection angle are studied using the Gauss-Bonnet theorem, in addition to studying the influences on the radius of photon spheres and size of the BH shadow in the spacetime geometry of the charged-Kiselev BH in string clouds. Moreover, we study the effects of plasma (uniform and non-uniform) on the weak deflection angle and shadow cast by the charged-Kiselev BH surrounded by the clouds of strings. In the presence of a uniform/nonuniform plasma medium, an increase in the string cloud parameter a increases the deflection angle α. In contrast, a decrease in the BH charge Q decreases the deflection angle. Further, we observe that an increase in the BH charge Q causes a decrease in the size of the shadow of the BH. We notice that, with an increase in the values of the parameters γ and a, the size of the BH shadow increases, and therefore, the intensity of the gravitational field around the charged-Kiselev BH in string clouds increases. Thus, the gravitational field of the charged-Kiselev BH in the string cloud background is stronger than the field produced by the pure Reissner-Nordstrom BH. Moreover, we use the data released by the Event Horizon Telescope (EHT) collaboration, for the supermassive BHs M87* and Sgr A*, to obtain constraints on the values of the parameters γ and a.     

振动筛系统的两类余维三分岔与非常规混沌演化

建立了振动筛系统的动力学模型,推导出了其周期运动的Poincaré 映射,基于Poincaré 映射方法着重研究了系统Flip-Hopf-Hopf余维三分岔、三次强共振条件下的Hopf-Hopf余维三分岔以及三种非常规的混沌演化过程.研究结果表明,此两类余维三分岔点附近的动力学行为变得更加复杂和新颖,在分岔点附近出现了三角形吸引子、3T²环面分岔以及“五角星型”、“轮胎型”概周期吸引子,揭示了环面爆破、环面倍化以及T²环面分岔向混沌演化的过程,这些结果对于振动筛系统的动力学优化设计提供了理论参考. 关键词： 余维三分岔 非常规混沌演化 T²环面分岔')" href="#">T²环面分岔     

Uplifting the Iwasawa

The Iwasawa manifold is uplifted to seven‐folds of either G₂ holonomy or SU(3) structure, explicit new metrics for the same having been constructed in this work. We uplift the Iwasawa manifold to a G₂ manifold through “size” deformation (of the Iwasawa metric), via Hitchin's Flow equations, showing also the impossibility of the uplift for “shape” and “size” deformations (of the Iwasawa metric). Using results of Dall'Agata and Prezas, Phys. Rev. D 69 , 066004 (2004) [arXiv:hep‐th/0311146] [1], we also uplift the Iwasawa manifold to a 7‐fold with SU(3) structure through “size” and “shape” deformations via generalisation of Hitchin's Flow equations. For seven‐folds with SU(3)‐structure, the result could be interpreted as M5‐branes wrapping two‐cycles embedded in the seven‐fold (as in [1]) ‐ a warped product of either a special hermitian six‐fold or a balanced six‐fold with the unit interval. There can be no uplift to seven‐folds of SU(3) structure involving non‐trivial “size” and “shape” deformations (of the Iwasawa metric) retaining the “standard complex structure” ‐ the uplift generically makes one move in the space of almost complex structures such that one is neither at the standard complex structure point nor at the “edge”. Using the results of Konopelchenko and Landolfi, J. Geom. Phys. 29 , 319 (1999) [arXiv:math.DG/9804144] [2], we show that given two “shape deformation” functions, and the dilaton, one can construct a Riemann surface obtained via Weierstraß representation for the conformal immersion of a surface in R ^l, for a suitable l, with the condition of having conformal immersion being a quadric in CP ^l‐1.     

Moduli and (un)attractor black hole thermodynamics

We investigate four-dimensional spherically symmetric black hole solutions in gravity theories with massless, neutral scalars non-minimally coupled to gauge fields. In the non-extremal case, we explicitly show that, under the variation of the moduli, the scalar charges appear in the first law of black hole thermodynamics. In the extremal limit, the near horizon geometry is AdS ₂ × S ² and the entropy does not depend on the values of moduli at infinity. We discuss the attractor behaviour by using Sen’s entropy function formalism as well as the effective potential approach and their relation with the results previously obtained through special geometry method. We also argue that the attractor mechanism is at the basis of the matching between the microscopic and macroscopic entropies for the extremal non-BPS Kaluza–Klein black hole.     

Current–voltage characteristics of Al/Rhodamine-101/n-GaAs structures in the wide temperature range

The forward bias current–voltage (I–V) characteristics of Al/Rhodamine-101/n-GaAs structure have been investigated in the temperature range of 80–350 K. It has been seen a decrease in ideality factor (n) and an increase in the zero-bias barrier height (BH) with an increase in temperature. It has been seen that such a behavior of the BH and n obey Gaussian distribution of the BHs due to the BH inhomogeneities at the metal/semiconductor (MS) interface. The very strong temperature dependence of ideality factor of the structure has shown that the current processes occurring in the organic layer at the MS interface would be a possible candidate such as trap-charge limited conduction in determining the current at the intermediate and high bias regimes. Furthermore, it has been show that the Rh101 can be used to vary effective BHs for the metal/GaAs Schottky diodes. As a result, it has been determined that the BH value for conventional Al/n-GaAs SBD is remarkably higher than our own values of 0.68 eV obtained for the Al/Rh101/n-GaAs at 290 K.     

Comparison of thermodynamic behaviors of two regular-AdS black holes

Considering the negative cosmological constant of an anti-de Sitter (AdS) background as a positive thermodynamic pressure in the extended phase space, we investigate the P−υ critical behavior and of the cooling–heating phase transition of the regular Hayward-AdS (HAdS) black hole (BH), and compare the difference of some thermodynamic processes in both the HAdS BH and the Bardeen-AdS (BAdS) BH. We found that the phase transition of the BAdS BH tends to be more the van der Waals (vdW) phase transition. For the cooling–heating phase transition, we obtained the inversion curves of the HAdS BH are always higher than the BAdS BH under the same pressure and magnetic charge. We also compare the smallest existence mass, the zero-temperature remnant, and the critical magnetic charge for these two BHs. The results suggested that the inner horizon and the outer horizon of the Hayward BH are easier to merge, and the singularity is easier to expose.     

Local information‐distance thermodynamics of molecular fragments

The Fisher information contained in a probability distribution is summarized. The corresponding measures of the information distance, relative to the reference probability density, are introduced and discussed. These concepts are designed as analogues of the Kullback‐Leibler directed divergence and Kullback's divergence. For these alternative measures of the missing information the equilibrium (“stockholder”) scheme of Hirshfeld, of a division of the molecular electron density into the subsystem components, is derived from the minimum principle of the local or global entropy deficiency relative to the free‐subsystem (“promolecule”) reference. The local information distance densities are used to describe instantaneous electron distributions in molecular subsystems within a thermodynamic‐like approach to the density fluctuations and irreversible processes. The key concepts of such a local irreversible “thermodynamics” are introduced. They include the corresponding local affinities (forces) and the conjugate fluxes (responses), which together determine the local entropy deficiency source. These quantities depend on the adopted measure of the information distance and selected state‐parameters. For each such representation the relevant Onsager‐type reciprocity relations can be derived, which reflect the symmetries between the linear effects of affinities on fluxes.     

Quantum information paradox: Real or fictitious?

One of the outstanding puzzles of theoretical physics is whether quantum information indeed gets lost in the case of black hole (BH) evaporation or accretion. Let us recall that quantum mechanics (QM) demands an upper limit on the acceleration of a test particle. On the other hand, it is pointed out here that, if a Schwarzschild BH exists, the acceleration of the test particle would blow up at the event horizon in violation of QM. Thus the concept of an exact BH is in contradiction with QM and quantum gravity (QG). It is also reminded that the mass of a BH actually appears as an integration constant of Einstein equations. And it has been shown that the value of this integration constant is actually zero! Thus even classically, there cannot be finite mass BHs though zero mass BH is allowed. It has been further shown that during continued gravitational collapse, radiation emanating from the contracting object gets trapped within it by the runaway gravitational field. As a consequence, the contracting body attains a quasi-static state where outward trapped radiation pressure gets balanced by inward gravitational pull and the ideal classical BH state is never formed in a finite proper time. In other words, continued gravitational collapse results in an ‘eternally collapsing object’ which is a ball of hot plasma and which is asymptotically approaching the true BH state with M = 0 after radiating away its entire mass energy. And if we include QM, this contraction must halt at a radius suggested by the highest QM acceleration. In any case no event horizon (EH) is ever formed and in reality, there is no quantum information paradox.