Prof. Aharon Davidson - Recent Papers

Selected Publications can be found here
The complete List of Publications (links included) is available here

 Ricci linear Weyl/Maxwell mutual sourcing * Aharon Davidson and Tomer Ygael          Universe 6, 151 (2020)          arXiv:2003.08088 [gr-qc]      Abstract: We elevate the field theoretical similarities between Maxwell and Weyl vector fields into a full local scale/gauge invariant Weyl/Maxwell mutual sourcing theory. In its simplest form, and exclusively in 4-dimensions, the associated Lagrangian is scalar field free, hosts no fermion matter fields, and Holdom kinetic mixing can be switched off. The theory is then characterized by the following distinctive features: (i) The Weyl/Maxwell mutual sourcing term is necessarily spacetime curvature (not just metric) dependent, implying that (ii) A non-vanishing spacetime curvature can induce an electric current. (iii) In line with Weyl-Dirac (and Einstein-Hilbert) action, the mutual sourcing term is inevitably Ricci linear, and comes thus with the bonus that (iv) The co-divergence of the Maxwell vector field plays the role of a dilaton. * Honorable mentioned, Gravity Research Foundation (2020) Local Scale Invariant Kaluza-Klein Reduction Tomer Ygael and Aharon Davidson 024010 (2020)          arXiv:2005.02065 [gr-qc]      Abstract: We perform the 4-dimensional Kaluza-Klein (KK) reduction of the 5-dimensional locally scale invariant Weyl-Dirac gravity. While compactification unavoidably introduces anexplicit length scale into the theory, it does it in such a way that the  KK radius can be integrated out from the low energy regime, leaving the KK vacuum to still enjoy local scale invariance at the classical level. Imitating a $U(1)\times\tilde{U}(1)$ gauge theory, the emerging 4D theory is characterized by a kinetic Maxwell-Weyl mixing whose diagonalization procedure is carried out in detail. In particular, we identify the unique linear combination which defines the 4D Weyl vector, and fully classify the 4D scalar sector. The later consists of (using Weyl language) a co-scalar and two in-scalars. The analysis is performed for a general KK $m$-ansatz, parametrized by the power $m$ of the scalar field which factorizes the 4D metric. The no-ghost requirement, for example, is met provided $-\frac{1}{2}\leq m \leq 0$. An $m$-dependent dictionary is then established between the original 5D Brans-Dicke parameter $\omega_5$ and the resulting 4D $\omega_4$. The critical $\omega_5=-\frac{4}{3}$ is consistently mapped into critical $\omega_4 = -\frac{3}{2}$. The KK reduced Maxwell-Weyl kinetic mixing cannot be scaled away as it is mediated by a 4D in-scalar (residing within the 5D Weyl vector). The mixing is explicitly demonstrated within the Einstein frame for the special physically motivated choice of $m=-\frac{1}{3}$. For instance, a super critical Brans-Dicke parameter induces a tiny positive contribution to the original (if introduced via the 5-dimensional scalar potential) cosmological constant. Finally, some no-scale quantum cosmological aspects are studied at the universal mini-superspace level. Mini-Superspace Universality and No-Scale Quantum Cosmology Tomer Ygael and Aharon Davidson                 arXiv:1908.02959 [gr-qc]    Abstract: We prove that, at the mini superspace level, and for an arbitrary Brans-Dicke parameter, one cannot tell traditional Einstein-Hilbert gravity from local scale invariant Weyl-Dirac gravity. Both quantum mechanical cosmologies are governed by the one and the same time-independent single-variable Hartle-Hawking wave function. It is only that its original argument, the cosmic scale factor $a$, is replaced by $a\phi$ ($\phi$ being the dilaton field) to form a Dirac in-scalar. The Weyl vector enters quantum cosmology only in the presence of an extra dimension, where its fifth component, serving as a 4-dim Kaluza-Klein in-scalar, governs the near Big Bang behavior of the wave function. The case of a constant Kaluza-Klein in-radius is discussed in some detail. From Planck Area to Graph Theory: Topologically Distinct Black Hole Microstates Aharon Davidson        arXiv:1907.03090 [gr-qc]    Abstract: We postulate a Planck scale horizon unit area, with no bits of information locally attached to it, connected but otherwise of free form, and let n such geometric units compactly tile the black hole horizon. Associated with each such topologically distinct tiling configuration is the a simple, connected, undirected, unlabeled, planar, chordal graph. The asymptotic enumeration of the corresponding integer sequence gives rise to the Bekenstein-Hawking area entropy formula, automatically accompanied by a proper logarithmic term, and fixes the size of the horizon unit area, thereby constituting a global realization of Wheeler's "it from bit" phrase. Invoking Polya's theorem, an exact number theoretical entropy spectrum is offered for the 2+1-dimensional quantum black hole. Hydrogen-like Spectrum of Spontaneously Created Brane Universes with de-Sitter Ground State Aharon Davidson        arXiv:1708.00987 [gr-qc]    Abstract: Unification of Randall-Sundrum and Regge-Teitelboim brane cosmologies gives birth to a serendipitous Higgs-deSitter interplay. A localized Dvali-Gabadadze-Porrati scalar field, governed by a particular (analytically derived) double-well quartic potential, becomes a mandatory ingredient for supporting a deSitter brane universe. When upgraded to a general Higgs potential, the brane surface tension gets quantized, resembling a Hydrogen atom spectrum, with deSitter universe serving as the ground state. This reflects the local/global structure of the Euclidean manifold: From finite energy density no-boundary initial conditions, via a novel acceleration divide filter, to exact matching conditions at the exclusive nucleation point. Imaginary time periodicity comes as a bonus, with the associated Hawking temperature vanishing at the continuum limit. Upon spontaneous creation, while a finite number of levels describe universes dominated by a residual dark energy combined with damped matter oscillations, an infinite tower of excited levels undergo a Big Crunch. Frozen up Dilaton and the GUT/Planck Mass Ratio Aharon Davidson and Tomer Ygael       arXiv:1706.00368 [gr-qc]    Abstract: By treating modulus and phase on equal footing, as pointed out by Dirac, local scale invariance can consistently accompany any Brans-Dicke ω-theory. We show that in the presence of a soft scale symmetry breaking term, the classical solution, when it exists, cannot be anything else but general relativistic. The dilaton modulus gets frozen up by the Weyl-Proca vector field, thereby constituting a gravitational quasi-Higgs mechanism. Assuming all grand unifying scalars are dilatons, they enjoy Weyl universality, and upon symmetry breaking, the Planck (mass)2 becomes the sum of all their individual (VEV)2. The emerging GUT/Planck (mass)2 ratio is thus ∼ωg2GUT/4π

Selected Publications
can be found here
The complete List of Publications