Quantum gravity effects on spectroscopy of Kerr-Newman black hole in gravity’s rainbow

Quantum gravity effects on spectroscopy for the charged rotating gravity’s rainbow are investigated. By utilizing an action invariant obtained from particles tunneling through the event horizon, the entropy and area spectrum for the modified Kerr-Newman black hole are derived. The equally spaced entropy spectrum characteristic of Bekenstein’s original derivation is recovered. And, the entropy spectrum is independent of the energy of the test particles, although the gravity’s rainbow itself is the energy dependent. Such, the quantum gravity effects of gravity’s rainbow has no influence on the entropy spectrum. On the other hand, due to the spacetime quantum effects, the obtained area spectrum is different from the original Bekenstein spectrum. It is not equidistant and has the dependence on the horizon area. And that, by analyzing the area spectrum from a specific rainbow functions, a minimum area with Planck scale is derived for the event horizon. At this, the area quantum is zero and the black hole radiation stops. Thus, the black hole remnant for the gravity’s rainbow is obtained from the area quantization. In addition, the entropy for the modified Kerr-Newman black hole is calculated and the quantum correction to the area law is obtained and discussed.

-rigidity of Lagrangian submanifolds and punctured holomorphic disks in the cotangent bundle

Our main result is the $\mathbb {\mathcal {C}}^{0}$ -rigidity of the area spectrum and the Maslov class of Lagrangian submanifolds. This relies on the existence of punctured pseudoholomorphic disks in cotangent bundles with boundary on the zero section, whose boundaries represent any integral homology class. We discuss further applications of these punctured disks in symplectic geometry.

Register of the human brain acoustic area spectrum

Last years, there were developed methods based on the human brain and body acoustic signals application. We consider human brain micro vibrations as an ancient, highly reliable, relatively rapid channel of the central nervous system with all the organism cells and structures. There is offered a method of the human brain acoustic area spectrum analysis and registration. Experimental sample “Register of the human brain micro vibrations spectrum is developed. The model of the human brain acoustic area generation is offered – neurovascular reflex and related with human brain blood vessels smooth muscularity nerve cells metabolism. In comparison with classical EEG, it is demonstrated that acoustic encephalogram also reflects human brain neuroreflex activity. Piezoelectric sensors, which feature in silicone membrane existence, are investigated. Such type of construction allowed to register human brain mechanical vibrations in the gamut from 0.1 up to 27 Hz. Spectral analysis is specific in that signal integration time is 160 seconds. Meanwhile, 12600 spectral harmonics of the human brain reticular activating system were reliably extracted. For convenience, all the acoustic area spectrum of the human brain was shrunk into segmental frame of reference which is frequency structured matrix of functional conditions multiplicity “multiple arousal” of 24х625 frequency cells size. All the developed technologies and device might be used for the organism adaptation estimations, psycho-emotional conditions estimations and functional-topical diagnosis of the internal parts of the human body.

Edge modes of gravity. Part II. Corner metric and Lorentz charges

In this second paper of the series we continue to spell out a new program for quantum gravity, grounded in the notion of corner symmetry algebra and its representations. Here we focus on tetrad gravity and its corner symplectic potential. We start by performing a detailed decomposition of the various geometrical quantities appearing in BF theory and tetrad gravity. This provides a new decomposition of the symplectic potential of BF theory and the simplicity constraints. We then show that the dynamical variables of the tetrad gravity corner phase space are the internal normal to the spacetime foliation, which is conjugated to the boost generator, and the corner coframe field. This allows us to derive several key results. First, we construct the corner Lorentz charges. In addition to sphere diffeomorphisms, common to all formulations of gravity, these charges add a local $$ \mathfrak{sl} $$ sl (2, ℂ) component to the corner symmetry algebra of tetrad gravity. Second, we also reveal that the corner metric satisfies a local $$ \mathfrak{sl} $$ sl (2, ℝ) algebra, whose Casimir corresponds to the corner area element. Due to the space-like nature of the corner metric, this Casimir belongs to the unitary discrete series, and its spectrum is therefore quantized. This result, which reconciles discreteness of the area spectrum with Lorentz invariance, is proven in the continuum and without resorting to a bulk connection. Third, we show that the corner phase space explains why the simplicity constraints become non-commutative on the corner. This fact requires a reconciliation between the bulk and corner symplectic structures, already in the classical continuum theory. Understanding this leads inevitably to the introduction of edge modes.

SIMULTANEOUS ASSAYS OF METFORMIN HCL AND GLIBENCLAMIDE MIXTURE USING TWO ANALYTICAL METHODS OF SPECTROPHOTOMETRY

Objective: Area Under Curve method (AUC) and the Multiple Wavelength Spectrophotometric (MWS) method are practice and simple methods for simultaneous assays of Metformin HCl and Glibenclamide on the tablet dosage form. Methods: The AUC method is measured for the absorption spectrum with a concentration 4 mg/l Metformin HCl by calculating the area spectrum at wavelength 230-240 nm and the absorption spectrum with a concentration 8.7 mg/l Glibenclamide by calculating the area at wavelength 225-235 nm. The MWS by determining the absorption spectrum and the five wavelength points for the absorption value at 225 nm, 229.4 nm, 236.6 nm, 233 nm, and 243 nm and calculated using matrix operations. Results: The validation test of the AUC method for Metformin HCl obtained accuracy = 99.35%, linearity = 0.9881, precision = 0.39%, LOD = 0.4459 mg/l. LOQ = 1.4864 mg/l and for Glibenclamide obtained accuracy = 100.79%, linearity = 0.9993, precision = 0.65%, LOD=0.4372 mg/l, LOQ = 1.4072 mg/l and the MWS method for Metformin HCl obtained accuracy = 100.76%, linearity 0.9949, precision = 0.65%, LOD = 0.9103 mg/l, LOQ = 3.0431 mg/l, and for Glibenclamide with accuracy = 100.07%, linearity = 0.9993. precision = 0.36%, LOD = 0.9205 mg/l. LOQ = 3.0431 mg/l , and appropriate the requirements of ICH guidelines. Conclusion: These Methods successively applied to determine of Metformin HCl and Glibenclamide mixture in tablet dosage form and fulfill the validation requirements.

Area and entropy quantization of quantum-corrected Schwarzschild black hole surrounded by quintessence

In this paper, the minimal change in the area and the entropy of quantum-corrected Schwarzschild black hole immersed in the quintessence matter is investigated. Utilizing two different approaches, namely, the periodicity of the outgoing wave and the black hole adiabatic property, the area spectrum is derived, which is independent of both the length scale coming from quantum deformation of the Schwarzschild black hole, and the quintessential state parameter, and which is in agreement with the uniform area spacing originally found by Bekenstein.

An Area Rescaling Ansatz and Black Hole Entropy from Loop Quantum Gravity

Considering the possibility of ‘renormalization’ of the gravitational constant on the horizon, leading to a dependence on the level of the associated Chern-Simons theory, a rescaled area spectrum is proposed for the nonrotating black hole horizon in loop quantum gravity. The statistical mechanical calculation leading to the entropy provides a unique choice of the rescaling function for which the Bekenstein-Hawking area law is yielded without the need to choose the Barbero-Immirzi parameter (γ). γ is determined, rather than being chosen, by studying the limit in which the ‘renormalized’ gravitational constant on the horizon asymptotically approaches the ‘bare’ value. The possible physical dynamics behind the ‘renormalization’ is discussed.