Anais Smailagic

Feynman path integral on the non-commutative plane

We formulate Feynman path integral on a non commutative plane using coherent states. The propagator for a free particle exhibits UV cut-off induced by the parameter of non commutativity.We formulate the Feynman path integral on a non-commutative plane using coherent states. The propagator for a free particle exhibits UV cutoff induced by the parameter of non-commutativity.

Non-commutative geometry inspired higher-dimensional charged black holes

Abstract We obtain a new, exact, solution of the Einsteins equation in higher dimensions. The source is given by a static spherically symmetric, Gaussian distribution of mass and charge. The resulting metric describes a regular, i.e. curvature singularity free, charged black hole in higher dimensions. The metric smoothly interpolates between Reissner–Nordstrom geometry at large distance, and de Sitter spacetime at short distance. Thermodynamical properties of the black hole are investigated and the form of the Area Law is determined. We study pair creation and show that the upper bound on the discharge time increases with the number of extra dimensions.

UV divergence-free QFT on noncommutative plane

We formulate noncommutative qauntum field theory in terms of fields defined as mean value over coherent states of the noncommutative plane. No -product is needed in this formulation and noncommutativity is carried by a modified Fourier transform of fields. As a result the theory is UV finite and the cutoff is provided by the noncommutative parameter θ.

Lorentz invariance, unitarity and UV-finiteness of QFT on noncommutative spacetime

Ultraviolet finite quantum field theory on even-dimensional noncommutative spacetime is formulated using coordinate coherent states. 2D spacetime is foliated into families of orthogonal, noncommutative, two planes. Lorentz invariance is recovered if one imposes a single noncommutative parameter θ in the theory. Unitarity is checked at the one-loop level and no violation is found. Being UV finite NCQFT does not present any UV/IR mixing.

Isotropic representation of the noncommutative 2D harmonic oscillator

We show that 2D noncommutative harmonic oscillator has an isotropic representation in terms of commutative coordinates. The noncommutativity in the new mode, induces energy level splitting, and is equivalent to an external magnetic field effect. The equivalence of the spectra of the isotropic and anisotropic representation is traced back to the existence of SU(2) invariance of the noncommutative model.

Trace anomaly on a quantum spacetime manifold

In this paper we investigate the trace anomaly in a space-time where single events are delocalized as a consequence of short distance quantum coordinate fluctuations. We obtain a modified form of heat kernel asymptotic expansion which does not suffer from short distance divergences. Calculation of the trace anomaly is performed using an IR regulator in order to circumvent the absence of UV infinities. The explicit form of the trace anomaly is presented and the corresponding 2D Polyakov effective action and energy-momentum tensor are obtained. The vacuum expectation value of the energy-momentum tensor in the Boulware, Hartle-Hawking and Unruh vacua is explicitly calculated in a rt section of a recently found, noncommutative inspired, Schwarzschild-like solution of the Einstein equations. The standard short distance divergences in the vacuum expectation values are regularized in agreement with the absence of UV infinities removed by quantum coordinate fluctuations.

Maxwell’s Equal Area Law and the Hawking-Page Phase Transition

We study the phases of a Schwarzschild black hole in the Anti-deSitter background geometry. Exploiting fluid/gravity duality, we construct the Maxwell equal area isotherm   in the temperature-entropy plane, in order to eliminate negative heat capacity BHs. The construction we present here is reminiscent of the isobar cut in the pressure-volume plane which eliminates unphysical part of the Van der Walls curves below the critical temperature. Our construction also modifies the Hawking-Page phase transition. Stable BHs are formed at the temperature , while pure radiation persists for . turns out to be below the standard Hawking-Page temperature and there are no unstable BHs as in the usual scenario. Also, we show that, in order to reproduce the correct BH entropy , one has to write a black hole equation of state, that is, , in terms of the geometrical volume .

Black holes production in self-complete quantum gravity

A regular black hole model, which has been proposed by Hayward (2006) in [24], is reconsidered in the framework of higher dimensional TeV unification and self-complete quantum gravity scenario (Dvali and Gomez (2010) [36], Dvali, Folkerts and Germani (2010) [37], Spallucci and Ansoldi (2011) [38]). We point out the “quantum” nature of these objects and compute their cross section production by taking into account the key role played by the existence of a minimal length l0. We show that the threshold energy is related to l0. We recover, in the high energy limit, the standard “black-disk” form of the cross section, while it vanishes, below threshold, faster than any power of the invariant mass energy −s.

Regular black holes from semi-classical down to Planckian size

In this paper, we review various models of curvature singularity free black holes (BHs). In the first part of the review, we describe semi-classical solutions of the Einstein equations which, however, contains a “quantum” input through the matter source. We start by reviewing the early model by Bardeen where the metric is regularized by-hand through a short-distance cutoff, which is justified in terms of nonlinear electro-dynamical effects. This toy-model is useful to point-out the common features shared by all regular semi-classical black holes. Then, we solve Einstein equations with a Gaussian source encoding the quantum spread of an elementary particle. We identify, the a priori arbitrary, Gaussian width with the Compton wavelength of the quantum particle. This Compton–Gauss model leads to the estimate of a terminal density that a gravitationally collapsed object can achieve. We identify this density to be the Planck density, and reformulate the Gaussian model assuming this as its peak density. All these models, are physically reliable as long as the BH mass is big enough with respect to the Planck mass. In the truly Planckian regime, the semi-classical approximation breaks down. In this case, a fully quantum BH description is needed. In the last part of this paper, we propose a nongeometrical quantum model of Planckian BHs implementing the Holographic Principle and realizing the “classicalization” scenario recently introduced by Dvali and collaborators. The classical relation between the mass and radius of the BH emerges only in the classical limit, far away from the Planck scale.

Gaussian black holes in Rastall gravity

In this short note we present the solution of Rastall gravity equations sourced by a Gaussian matter distribution. We find that the black hole metric shares all the common features of other regular, General Relativity BH solutions discussed in the literature: there is no curvature singularity and the Hawking radiation leaves a remnant at zero temperature in the form of a massive ordinary particle.