We study Vaidya-type solutions in Weyl conformal gravity (WCG) using Eddington–Finkelstein-like coordinates. Our considerations focus on spherical as well as hyperbolic and planar symmetries. In particular, we find all vacuum dynamical solutions for the aforementioned symmetries. These are, in contrast to general relativity, structurally quite non-trivial. We provide a thorough analysis of their basic properties, such as, relation to other known WCG solutions, algebraic types, singularities, horizons, and symmetries. In the same vein, we also derive, classify, and discuss non-vacuum solutions with the Coulombic electric field and null dust. Other salient issues, such as the gauge equivalence of WCG solutions to Einstein spaces and the role of the Birkhoff–Riegert theorem, are also addressed.

Czechia

Petr Jizba

Tereza Lehečková

Generalized Eddington–Finkelstein coordinates and exact Vaidya-type solutions in Weyl conformal gravity

We study how the number of degrees of freedom in Weyl conformal gravity runs with the energy scale from the UV fixed point. To this end we employ two approaches. First, we utilize the Fradkin–Tseytlin prescription for the number of degrees of freedom and demonstrate that the one-loop result is highly dependent on the selected background. We then employ the counting methodology based on the a- and c-function, which are typically used to characterize the trace anomaly of conformal field theories in four dimensions. We compute these in the enhanced one-loop approximation and demonstrate that the degrees of freedom decrease monotonically from six degrees in the UV regime. This behavior is independent of the backgrounds considered. Further salient issues, such as the connection between the Fradkin–Tseytlin prescription and counting based on the a- and c-function, or the applicability of both methods in Einstein’s gravity, are also addressed.

Italy

Stefano Giaccari

Jaroslav Kňap

Brazil

Lesław Rachwał

Running of the number of degrees of freedom in quantum conformal gravity

We investigate the non-relativistic limit of the Klein–Gordon equation for mixed scalar particles and show that, in this regime, one unavoidably arrives at redefining the particle’s inertial mass. This happens because, in contrast to the case when mixing is absent, the antiparticle sector contribution cannot be neglected for particles with definite flavor. To clearly demonstrate this feature, we adopt the Feshbach–Villars formalism for Klein–Gordon particles. Furthermore, within the same framework, we also demonstrate that, in the presence of a weak gravitational field, the mass parameter that couples to gravity (gravitational mass) does not match the effective inertial mass. This, in turn, implies a violation of the weak equivalence principle. Finally, we prove that the Bargmann’s superselection rule, which prohibits oscillating particles on the basis of the Galilean transformation, is incompatible with the non-relativistic limit of the Lorentz transformation and hence does not collide with the results obtained.

Massimo Blasone

Germany

Gaetano Lambiase

Luciano Petruzziello

Weak equivalence principle violation for mixed scalar particles

The generalized uncertainty principle (GUP) is a phenomenological model whose purpose is to account for a minimal length scale (e.g., Planck scale or characteristic inverse-mass scale in effective quantum description) in quantum systems. In this paper, we study possible observational effects of GUP systems in their decoherence domain. We first derive coherent states associated to GUP and unveil that in the momentum representation they coincide with Tsallis probability amplitudes, whose nonextensivity parameter <math><mi>q</mi></math> monotonically increases with the GUP deformation parameter <math><mi>β</mi></math>. Second, for <math><mi>β</mi><mo>&lt;</mo><mn>0</mn></math> (i.e., <math><mi>q</mi><mo>&lt;</mo><mn>1</mn></math>), we show that, due to Bekner-Babenko inequality, the GUP is fully equivalent to information-theoretic uncertainty relations based on Tsallis-entropy-power. Finally, we invoke the maximal entropy principle known from estimation theory to reveal connection between the quasiclassical (decoherence) limit of GUP-related quantum theory and nonextensive thermostatistics of Tsallis. This might provide an exciting paradigm in a range of fields from quantum theory to analog gravity. For instance, in some quantum gravity theories, such as conformal gravity, aforementioned quasiclassical regime has relevant observational consequences. We discuss some of the implications.

Giuseppe Gaetano Luciano

Decoherence limit of quantum systems obeying generalized uncertainty principle: New paradigm for Tsallis thermostatistics

Starting from an ultraviolet fixed point, we study the infrared behavior of quantum Weyl gravity in terms of a functional renormalization group (RG) flow equation. To do so, we employ two classes of Bach-flat backgrounds, namely maximally symmetric spacetimes and Ricci-flat backgrounds in the improved one-loop scheme. We show that in the absence of matter fields and with a topological term included, the effective action exhibits dynamical breaking of scale symmetry. In particular, it is shown that apart from a genuine IR fixed point that is reached at a zero value of the running scale, the RG flow also exhibits bouncing behavior in the IR regime. We demonstrate that both <math><mrow><msub><mrow><mi>β</mi></mrow><mrow><mi>C</mi></mrow></msub></mrow></math> and <math><mrow><msub><mrow><mi>β</mi></mrow><mrow><mi>E</mi></mrow></msub></mrow></math> reach the RG turning point (almost) simultaneously at the same finite energy scale, irrespective of the chosen background. The IR fixed point itself is found to be IR stable in the space of the considered couplings. Ensuing scaling dimensions of both operators are also computed. Salient issues, including the connection of the observed bouncing RG flow behavior with holography and prospective implications in early Universe cosmology, are also briefly discussed.

Infrared behavior of Weyl gravity: Functional renormalization group approach

In the context of quantum field theory, we derive flavor-energy uncertainty relations for neutrino oscillations. By identifying the nonconserved flavor charges with the “clock observables,” we arrive at the Mandelstam-Tamm version of time-energy uncertainty relations. In the ultrarelativistic limit, these relations yield the well-known condition for neutrino oscillations. Ensuing nonrelativistic corrections to the latter are explicitly evaluated. The analogy among flavor states and unstable particles and a novel interpretation of our uncertainty relations, based on the unitary inequivalence of Fock spaces for flavor and massive neutrinos, are also discussed.

Luca Smaldone

Flavor-energy uncertainty relations for neutrino oscillations in quantum field theory

We analyze the functional integral for quantum conformal gravity and show that, with the help of a Hubbard–Stratonovich transformation, the action can be broken into a local quadratic-curvature theory coupled to a scalar field. A one-loop effective-action calculation reveals that strong fluctuations of the metric field are capable of spontaneously generating a dimensionally transmuted parameter which, in the weak-field sector of the broken phase, induces a Starobinsky-type f ( R )-model with a gravi-cosmological constant. A resulting non-trivial relation between Starobinsky’s parameter and the gravi-cosmological constant is highlighted and implications for cosmic inflation are briefly discussed and compared with the recent PLANCK and BICEP2 data.