Effect Of Noncommutative Geometry Research Articles

Effects of non-commutative geometry on black hole properties

In this study, we investigate the signatures of a non-commutative black hole solution. Initially, we calculate the thermodynamic properties of the system, including entropy, heat capacity, and Hawking radiation. For the latter quantity, we employ two distinct methods: surface gravity and the topological approach. Additionally, we examine the emission rate and remnant mass within this context. Remarkably, the lifetime of the black hole, after reaching its final state due to the evaporation process, is expressed analytically up to a grey-body factor. We estimate the lifetime for specific initial and final mass configurations. Also, we analyze the tensorial quasinormal modes using the 6th-order WKB method. Finally, we study the deflection angle, i.e., gravitational lensing, in both the weak and strong deflection limits.

Gravitational amplitudes in black hole evaporation: the effect of non-commutative geometry

Recent work in the literature has studied the quantum-mechanical decay of a Schwarzschild-like black hole, formed by gravitational collapse, into almost-flat spacetime and weak radiation at a very late time. The relevant quantum amplitudes have been evaluated for bosonic and fermionic fields, showing that no information is lost in collapse to a black hole. On the other hand, recent developments in non-commutative geometry have shown that, in general relativity, the effects of non-commutativity can be taken into account by keeping the standard form of the Einstein tensor on the left-hand side of the field equations and introducing a modified energy–momentum tensor as a source on the right-hand side. The present paper, relying on the recently obtained non-commutativity effect on a static, spherically symmetric metric, considers from a new perspective the quantum amplitudes in black hole evaporation. The general relativity analysis of spin-2 amplitudes is shown to be modified by a multiplicative factor F depending on a constant non-commutativity parameter and on the upper limit R of the radial coordinate. Limiting forms of F are derived which are compatible with the adiabatic approximation here exploited. Approximate formulae for the particle emission rate are also obtained within this framework.

A NOTE ON NON-COMMUTATIVITY AND MASS GENERATION

We argue that it is the effect of non-commutative geometry of spacetime that leads to the generation of mass, thus pleasingly complementing earlier results.

NONCOMMUTATIVE DECRUMPLING INFLATION AND RUNNING OF THE SPECTRAL INDEX

We present a new inflation model, known as noncommutative decrumpling inflation, in which space has noncommutative geometry with time variability of the number of spatial dimensions. Within the framework of noncommutative decrumpling inflation, we compute both the spectral index and its running. Our results show the effects of both time variability of the number of spatial dimensions and noncommutative geometry on the spectral index and its running. Two classes of examples have been studied and comparisons made with the standard slow-roll formulae. We conclude that the effects of noncommutative geometry on the spectral index and its running are much smaller than the effects of time variability of spatial dimensions.

Possible effects of noncommutative geometry on weakCPviolation and unitarity triangles

The possible effects of noncommutative geometry on weak $\mathrm{CP}$ violation and unitarity triangles are discussed by taking into account a simple version of the momentum-dependent quark mixing matrix in the noncommutative standard model. In particular, we calculate nine rephasing invariants of $\mathrm{CP}$ violation and illustrate the noncommutative $\mathrm{CP}$-violating effect in a couple of charged D-meson decays. We also show how inner angles of the deformed unitarity triangles are related to $\mathrm{CP}$-violating asymmetries in some typical ${B}_{d}$ and ${B}_{s}$ transitions into $\mathrm{CP}$ eigenstates. B-meson factories are expected to help probe or constrain noncommutative geometry at low energies in the near future.