Euro Spallucci

Noncommutative geometry inspired Schwarzschild black hole

We investigate the behavior of a noncommutative radiating Schwarzschild black hole. It is shown that coordinate noncommutativity cures usual problems encountered in the description of the terminal phase of black hole evaporation. More in detail, we find that: the evaporation end-point is a zero temperature extremal black hole even in the case of electrically neutral, non-rotating, objects; there exists a finite maximum temperature that the black hole can reach before cooling down to absolute zero; there is no curvature singularity at the origin, rather we obtain a regular de Sitter core at short distance.

Non-commutative geometry inspired charged black holes

We find a new, non-commutative geometry inspired, solution of the coupled Einstein–Maxwell field equations describing a variety of charged, self-gravitating objects, including extremal and non-extremal black holes. The metric smoothly interpolates between de Sitter geometry, at short distance, and Reissner–Nordstrom geometry far away from the origin. Contrary to the ordinary Reissner–Nordstrom spacetime there is no curvature singularity in the origin neither “naked” nor shielded by horizons. We investigate both Hawking process and pair creation in this new scenario.

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.

“Kerrr” black hole: The lord of the string

Kerrr in the title is not a typo. The third “r” stands for regular, in the sense of pathology-free rotating black hole. We exhibit a long search-for, exact, Kerrlike, solution of the Einstein equations with novel features: i) no curvature ring singularity; ii) no “anti-gravity” universe with causality violating timelike closed world-lines ; iii) no “super-luminal” matter disk. The ring singularity is replaced by a classical, circular, rotating string with Planck tension representing the inner engine driving the rotation of all the surrounding matter. The resulting geometry is regular and smoothly interpolates among inner Minkowski space, borderline deSitter and outer Kerr universe. The key ingredient to cure all unphysical features of the ordinary Kerr black hole is the choice of a “noncommutative geometry inspired” matter source as the input for the Einstein equations, in analogy with spherically symmetric black holes described in earlier works.

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.

Gauge Theory of the String Geodesic Field

A relativistic string is usually represented by the Nambu-Goto action in terms of the extremal area of a 2-dimensional timelike submanifold of Minkowski space. Alternatively, a family of classical solutions of the string equation of motion can be globally described in terms of the associated geodesic field. In this paper we propose a new gauge theory for the geodesic field of closed and open strings. Our approach solves the technical and conceptual problems affecting previous attempts to describe strings in terms of local field variables. The connection between the geodesic field, the string current and the Kalb-Ramond gauge potential is discussed and clarified. A non-abelian generalization and the generally covariant form of the model are also discussed.