Black Hole with Quantum Potential

In this work, we investigate black hole (BH) physics in the context of quantum corrections. These quantum corrections were introduced recently by replacing classical geodesics with quantal (Bohmian) trajectories and hence form a quantum Raychaudhuri equation (QRE). From the QRE, we derive a modified Schwarzschild metric, and use that metric to investigate BH singularity and thermodynamics. We find that these quantum corrections change the picture of Hawking radiation greatly when the size of BH approaches the Planck scale. They prevent the BH from total evaporation, predicting the existence of a quantum BH remnant, which may introduce a possible resolution for the catastrophic behavior of Hawking radiation as the BH mass approaches zero. Those corrections also turn the spacelike singularity of the black hole to be timelike, and hence this may ameliorate the information loss problem.Comment: 16 pages, 6 figures; Accepted in Nucl.Phys.

A Proposal for Testing Gravity's Rainbow

Various approaches to quantum gravity such as string theory, loop quantum gravity and Horava-Lifshitz gravity predict modifications of the energy-momentum dispersion relation. Magueijo and Smolin incorporated the modified dispersion relation (MDR) with the general theory of relativity to yield a theory of gravity's rainbow. In this paper, we investigate the Schwarzschild metric in the context of gravity's rainbow. We investigate rainbow functions from three known modified dispersion relations that were introduced by Amelino-Camelia, et el. in [arXiv:hep-th/9605211, arXiv:0806.0339v2, arXiv:astro-ph/9712103] and by Magueijo-Smolin in [arXiv:hep-th/0112090]. We study the effect of the rainbow functions on the deflection of light, photon time delay, gravitational red-shift, and the weak equivalence principle. We compare our results with experiments to obtain upper bounds on the parameters of the rainbow functions.Comment: 6 pages, no figures, to appear in Europhysics Letter

Time Crystals from Minimum Time Uncertainty

Motivated by the Generalized Uncertainty Principle, covariance, and a minimum measurable time, we propose a deformation of the Heisenberg algebra and show that this leads to corrections to all quantum mechanical systems. We also demonstrate that such a deformation implies a discrete spectrum for time. In other words, time behaves like a crystal. As an application of our formalism, we analyze the effect of such a deformation on the rate of spontaneous emission in a hydrogen atom.Comment: 11 pages, to appear in Eur. Phys. J.

Remnant for all Black Objects due to Gravity's Rainbow

We argue that a remnant is formed for all black objects in gravity's rainbow. This will be based on the observation that a remnant depends critically on the structure of the rainbow functions, and this dependence is a model independent phenomena. We thus propose general relations for the modified temperature and entropy of all black objects in gravity's rainbow. We explicitly check this to be the case for Kerr, Kerr-Newman-dS, charged-AdS, and higher dimensional Kerr-AdS black holes. We also try to argue that a remnant should form for black Saturn in gravity's rainbow. This work extends our previous results on remnants of Schwarzschild black holes [ arXiv:1402.5320] and black rings [arXiv:1409.5745].Comment: 21 pages, 13 figures, Accepted in Nucl.Phys.

Some Implications of Two Forms of the Generalized Uncertainty Principle

Various theories of quantum gravity predict the existence of a minimum length scale, which leads to the modification of the standard uncertainty principle to the Generalized Uncertainty Principle (GUP). In this paper, we study two forms of the GUP and calculate their implications on the energy of the harmonic oscillator and the Hydrogen atom more accurately than previous studies. In addition, we show how the GUP modifies the Lorentz force law and the time-energy uncertainty principle.Comment: 9 pages, 3 figure

Remnants of Black Rings from Gravity's Rainbow

In this paper, we investigate a spinning black ring and a charged black ring in the context of gravity's rainbow. By incorporating rainbow functions proposed by Amelino-Camelia, et al. in [arXiv:hep-th/9605211, arXiv:0806.0339v2] in the metric of the black rings, a considerable modification happens to their thermodynamical properties. We calculate corrections to the temperature, entropy and heat capacity of the black rings. These calculations demonstrate that the behavior of Hawking radiation changes considerably near the Planck scale in gravity's rainbow, where it is shown that black rings do not evaporate completely and a remnant is left as the black rings evaporate down to Planck scale.Comment: 14 pages, 6 figure

Zakat on Bonds in Islamic Jurisprudence (Fiqh): Theory and Practice

Bonds are one of the contemporary financial instruments that need more understanding, clarification and research, and most studies focus on the theoretical side of bonds without addressing the practical side. Fiqh opinions focused on the provisions of zakat of bonds, their quorum and the amount of zakat. But none of the Fiqh opinions or books specialized in zakat clarified the ways for calculating zakat of bonds of all kinds in detail. In this research, the Fiqh opinion will be linked to the calculation of zakat on various bonds through the use of the principles of financial accounting. Thus, this research will provide a practical and applied reference for calculating zakat of bonds, and to be a reference in this field for each of the bond owners and the seeker of Sharia knowledge through calculating zakat of bonds and clarified more by applied mathematical examples

Electronic conductance of quantum wire with serial periodic potential structures

A theory based on the total transfer matrix is presented to investigate the electronic conductance in a quantum wire with serial periodic potentials. We apply the formalism in computation of the electronic conductance in a wire with different physical parameters of the wire structure. The numerical results could be used in designing some future quantum electronic devices