Black hole production in the presence of a maximal momentum in horizon wave function formalism

We study the Horizon Wave Function (HWF) description of a generalized uncertainty principle (GUP) black hole in the presence of two natural cutoffs as a minimal length and a maximal momentum. This is motivated by a metric which allows the existence of sub-Planckian black holes, where the black hole mass [Formula: see text] is replaced by [Formula: see text]. Considering a wave-packet with a Gaussian profile, we evaluate the HWF and the probability that the source might be a (quantum) black hole. By decreasing the free parameter, the general form of probability distribution, [Formula: see text], is preserved, but this resulted in reducing the probability for the particle to be a black hole accordingly. The probability for the particle to be a black hole grows when the mass is increasing slowly for larger positive [Formula: see text], and for a minimum mass value it reaches to [Formula: see text]. In effect, for larger [Formula: see text] the magnitude of [Formula: see text] and [Formula: see text] increases, matching with our intuition that either the particle ought to be more localized or more massive to be a black hole. The scenario undergoes a change for some values of [Formula: see text] significantly, where there is a minimum in [Formula: see text], so this expresses that every particle can have some probability of decaying to a black hole. In addition, for sufficiently large [Formula: see text], we find that every particle could be fundamentally a quantum black hole.

(1+1)-dimensional Dirac oscillator with deformed algebra with minimal uncertainty in position and maximal in momentum

[Formula: see text]-dimensional Dirac oscillator with minimal uncertainty in position and maximal in momentum is investigated. To obtain energy spectrum, SUSY QM technique is applied. It is shown that the Dirac oscillator has two branches of spectrum, the first one gives the standard spectrum of the Dirac oscillator when the parameter of deformation goes to zero and the second branch does not have nondeformed limit. Maximal momentum brings an upper bound for the energy and it gives rise to the conclusion that the energy spectrum contains a finite number of eigenvalues. We also calculate partition function for the spectrum of the first type. The partition function allows us to derive thermodynamic functions of the oscillator which are obtained numerically.

Phase space of a test particle in the presence of natural cutoffs

Physics at very high energies (close to the Planck energy scale) is in the center of modern physics challenges. At the high energy scales, or equivalently very short distances, the very notion of spacetime acquires a complicated structure. In this scale, there are limitations on the complete resolution of adjacent points in spacetime manifold. While the effect of a minimal measurable length on algebraic structure of a free particle’s phase space has been studied in the literature, the simultaneous effects of minimal length and maximal momentum have not been explored in this subject so far. Here, we are going to fill this gap. We study some properties of the algebraic structure of quantum field theories in the presence of natural cutoffs as a minimal length and a maximal momentum in a free particle’s phase space. Especially, we pay attention on the phase space trajectories of systems in the presence of natural cutoffs.

Some applications of the most general form of the higher-order GUP with minimal length uncertainty and maximal momentum

In this paper, using the new type of D-dimensional nonperturbative Generalized Uncertainty Principle (GUP) which has predicted both a minimal length uncertainty and a maximal observable momentum,1 first, we obtain the maximally localized states and express their connections to [P. Pedram, Phys. Lett. B 714, 317 (2012)]. Then, in the context of our proposed GUP and using the generalized Schrödinger equation, we solve some important problems including particle in a box and one-dimensional hydrogen atom. Next, implying modified Bohr–Sommerfeld quantization, we obtain energy spectra of quantum harmonic oscillator and quantum bouncer. Finally, as an example, we investigate some statistical properties of a free particle, including partition function and internal energy, in the presence of the mentioned GUP.

Natural cutoffs effect on charged rotating TeV-scale black hole thermodynamics

We study the thermodynamics of charged rotating black hole in large extra dimensions scenario where quantum gravity effects are taken into account. We consider the effects of minimal length, minimal momentum, and maximal momentum as natural cutoffs on the thermodynamics of charged rotating TeV-scale black holes. In this framework, the effect of the angular momentum and charge on the thermodynamics of the black hole are discussed. We focus also on frame dragging and Sagnac effect of the micro black holes.

Quantum gravity effects on charged microblack holes thermodynamics

The charged black hole thermodynamics is corrected in terms of the quantum gravity effects. Most of the quantum gravity theories support the idea that near the Planck scale, the standard Heisenberg uncertainty principle should be reformulated by the so-called Generalized Uncertainty Principle (GUP) which provides a perturbation framework to perform required modifications of the black hole quantities. In this paper, we consider the effects of the minimal length and maximal momentum as GUP type I and the minimal length, minimal momentum and maximal momentum as GUP type II on thermo dynamics of the charged TeV-scale black holes. We also generalized our study to the universe with the extra dimensions based on the ADD model. In this framework, the effect of the electrical charge on thermodynamics of the black hole and existence of the charged black hole remnants as a potential candidate for the dark matter particles are discussed.

On the Heisenberg algebra in Bargmann–Fock space with natural cutoffs

We construct a generalized Hilbert space representation of quantum mechanics in [Formula: see text]-dimensions based on Bargmann–Fock space with natural cutoffs as a minimal length, minimal momentum and maximal momentum in order to have a general framework for Heisenberg algebra in Bargmann–Fock space.