Entropic force law in the presence of a noncommutative inspired spacetime for a solar system scale

We first study some aspects of a physically inspired kind of a noncommutative spherically symmetric spacetime based on the Gaussian-smeared mass distribution for a solar system scale. This leads to the elimination of a singularity appeared in the origin of the spacetime. Afterwards, we investigate some features of Verlinde's scenario in the presence of the mentioned spacetime and derive several quantities such as Unruh-Verlinde temperature, the energy and the entropic force on three different types of holographic screens, namely the static, the stretched horizon and the accelerating surface.Comment: 11 pages, 3 figure

Gravitational energy of a noncommutative Vaidya black hole

In this paper we evaluate the components of the energy-momentum pseudotensors of Landau and Lifshitz for the noncommutative Vaidya spacetime. The effective gravitational mass experienced by a neutral test particle present at any finite distance in the gravitational field of the noncommutative Vaidya black hole is derived. Using the effective mass parameter one finds that the naked singularity is massless and this supports Seifert's conjecture.Comment: 10 pages, no figure, to appear in Can. J. Phy

Planck-scale nonthermal correlations in a noncommutative geometry inspired Vaidya black hole

Using the noncommutative geometry inspired Vaidya metric obtained in terms of coordinate coherent states and also utilizing the generalized uncertainty principle (GUP), we show that the nonthermal nature of the Hawking spectrum leads to Planck-scale nonthermal correlations between emitted modes of evaporation. Our analysis thus exhibits that owing to self-gravitational effects plus noncommutativity and GUP influences, information can emerge in the form of Planck-scale correlated emissions from the black hole.Comment: 16 pages, no figure, minor revisio

Emergent GUP from Modified Hawking Radiation in Einstein-NED Theory

We present a general procedure for constructing exact black hole (BH) solutions with the magnetic charge in the context of nonlinear electrodynamics (NED) theory as well as in the coherent state approach to noncommutative geometry (NCG). In this framework, the Lagrangian density for the noncommutative Hayward BH is obtained and the weak energy condition (WEC) is satisfied. The noncommutative Hayward solution depends on two kind of charges which for the vanishing of them yields the Schwarzschild solution. Moreover, in order to find a link between the BH evaporation and uncertainty relations, we may calculate the Hawking temperature and find the effect of the Lagrangian density of BHs on the Hawking radiation. Therefore, a generalized uncertainty principle (GUP) emerges from the modified Hawking temperature in Einstein-NED theory. The origin of this GUP is the combined influence of a nonlinear magnetic source and an intrinsic property of the manifold associated with a fictitious charge. Finally, we find that there is an upper bound on the Lagrangian uncertainty of the BHs which are sourced by the NED field and/or the fictitious charge.Comment: 24 pages, 3 figures, 1 table, new issues in Introduction and new References are added, Title is changed, minor revisions in Abstract and Conclusion

Thermodynamical features of Verlinde's approach for a non-commutative Schwarzschild-anti-deSitter black hole in a broad range of scales

We try to study the thermodynamical features of a non-commutative inspired Schwarzschild-anti-deSitter black hole in the context of entropic gravity model, particularly for the model that is employed in a broad range of scales, from the short distances to the large distances. At small length scales, the Newtonian force is failed because one finds a linear relation between the entropic force and the distance. In addition, there are some deviations from the standard Newtonian gravity at large length scales.Comment: 17 pages, 4 figures, accepted for publication in EPJ Plu

Bounds on the degrees of birational maps with arithmetically Cohen-Macaulay graphs

A rational map whose source and image are projectively embedded varieties has an {\em Arithmetically Cohen-Macaulay graph} if the Rees algebra of one (hence any) of its base ideals is a Cohen-Macaulay ring. If the map is birational onto the image one considers how this property forces an upper bound on the degree of a representative of the map. In the plane case a complete description is given of the Cremona maps with Cohen-Macaulay graph, while in arbitrary dimension $n$ it is shown that a Cremona map with Cohen-Macaulay graph has degree at most $n^2$.Comment: Last version to appear in Journal of Algebr

Some examples of different descriptions of energy-momentum density in the context of Bianchi IX cosmological model

Based on the Bianchi type IX metric, we calculate the energy and momentum density components of the gravitational field for the five different definitions of energy-momentum, namely, Tolman, Papapetrou, Landau-Lifshitz, M{\o}ller and Weinberg. The energy densities of M{\o}ller and Weinberg become zero for the spacetime under consideration. In the other prescriptions, i.e., Tolman, Papapetrou and Landau-Lifshitz complexes, we find different non-vanishing energy-momentum densities for the given spacetime, supporting the well-known argument in General Relativity that the different definitions may lead to different distributions even in the same spacetime background.Comment: 11 pages, no figure, typos corrected, accepted for publication in Indian J. Phy

On A Generalization of Weak Armendariz Rings

We introduce the notion of J-Armendariz rings, which are a generalization of weak Armendariz rings and investigate their properties. We show that any local ring is J-Armendariz, and then fined a local ring that is not weak Armendariz.Comment:

Vehicle as a Resource (VaaR)

Intelligent vehicles are considered key enablers for intelligent transportation systems. They are equipped with resources/components to enable services for vehicle occupants, other vehicles on the road, and third party recipients. In-vehicle sensors, communication modules, and on-board units with computing and storage capabilities allow the intelligent vehicle to work as a mobile service provider of sensing, data storage, computing, cloud, data relaying, infotainment, and localization services. In this paper, we introduce the concept of Vehicle as a Resource (VaaR) and shed light on the services a vehicle can potentially provide on the road or parked. We anticipate that an intelligent vehicle can be a significant service provider in a variety of situations, including emergency scenarios

On Central Skew Armendariz rings

For a ring endomirphism, we introduce the central skew Armendariz rings, which are a generalization of skew Armendariz rings and central Armendariz rings, and investigate their properties.Comment: 9 page