arXiv subjects

Aharon Davidson

Publications and source records attributed to Aharon Davidson.

50 records · Page 3Linked to original sources

arXiv2003

Brane Variation Dirac Style

Dirac's method for variations of a brane embedded in co-dimension one is demonstrated. The variation in the location of the brane invokes a rest frame formulation of the 'sandwiched' brane action. We first demonstrate the necessity of this method by re-deriving Snell's law. Second, we apply the method to a general $N$-dimensional brane embedded in co-dimension one bulk in the presence of gravity. We re-derive the brane equations: (i) Israel junction condition, (ii) Energy/momentum conservation on the brane, and (iii) Geodetic-type equation for the brane.

hep-th↗

arXiv2002

Geodetic Brane Gravity

Within the framework of geodetic brane gravity, the Universe is described as a 4-dimensional extended object evolving geodetically in a higher dimensional flat background. In this paper, by introducing a new pair of canonical fields {lambda, P_{lambda}}, we derive the quadratic Hamiltonian for such a brane Universe; the inclusion of matter then resembles minimal coupling. Second class constraints enter the game, invoking the Dirac bracket formalism. The algebra of the first class constraints is calculated, and the BRST generator of the brane Universe turns out to be rank-1. At the quantum level, the road is open for canonical and/or functional integral quantization. The main advantages of geodetic brane gravity are: (i) It introduces an intrinsic, geometrically originated, 'dark matter' component, (ii) It offers, owing to the Lorentzian bulk time coordinate, a novel solution to the 'problem of time', and (iii) It enables calculation of meaningful probabilities within quantum cosmology without any auxiliary scalar field. Intriguingly, the general relativity limit is associated with lambda being a vanishing (degenerate) eigenvalue.

gr-qc↗

arXiv2001

Higgs Driven Geodetic Evolution/Nucleation of de-Sitter Brane

Geodetic evolution of a de-Sitter brane is exclusively driven by a Higgs potential, rather than by a plain cosmological constant. The deviation from Einstein gravity, parameterized by the conserved bulk energy, is characterized by a hairy horizon which serves as the locus of unbroken symmetry. The quartic structure of the potential, singled out on finiteness grounds of the total (including the dark component) energy density, chooses the no-boundary proposal.

hep-th↗

arXiv2001

Cold Dark Matter from Dark Energy

Dark energy/matter unification is first demonstrated within the framework of a simplified model. Geodetic evolution of a cosmological constant dominated bubble Universe, free of genuine matter, is translated into a specific FRW cosmology whose effectively induced dark component highly resembles the cold dark matter ansatz. The realistic extension constitutes a dark soliton which bridges past (radiation and/or matter dominated) and future (cosmological constant dominated) Einstein regimes; its experimental signature is a moderate redshift dependent cold dark matter deficiency function.

gr-qc↗

arXiv2000

Dynamical Localization of Gravity

We show that the thin wall limit of the thick domain wall associated with a sine-Gordon soliton in a single non-compactified patch of 5-dimensional spacetime explicitly yields the Randall-Sundrum localized gravity two patch brane, with its discrete $Z_2$ symmetry arising from the discrete symmetry of the potential, and with the thin Minkowski brane $Λ_5+κ^2_5Λ^2_b/6=0$ relation between bulk and brane cosmological constants arising naturally without any need for fine tuning. Additionally we show that for an embedded thin de Sitter brane, localization of gravity is again possible provided the 5-space is compactified, with the now non-zero net cosmological constant $Λ_5+κ^2_5Λ^2_b/6$ on the brane being found to vary inversely with the compactification radius.

hep-th↗

arXiv2000

Fourth Order Theories Without Ghosts

Using the Dirac constraint method we show that the pure fourth-order Pais-Uhlenbeck oscillator model is free of observable negative norm states. Even though such ghosts do appear when the fourth order theory is coupled to a second order one, the limit in which the second order action is switched off is found to be a highly singular one in which these states move off shell. Given this result, construction of a fully unitary, renormalizable, gravitational theory based on a purely fourth order action in 4 dimensions now appears feasible.

hep-th↗

arXiv1999

Λ=0 Cosmology of a Brane-like Universe

We examine the possibility that Friedman-Robertson-Walker evolution is governed by an effective (rather then by the actual) energy density. A concrete example is provided by $Λ=0$ Regge-Teitelboim cosmology, where critical cosmology only requires subcritical matter density $(Ω_{m}<1)$, and the age of a flat matter dominated Universe gets enhanced by a factor of 9/8. Dual to the mature dilute Universe is the embryo Universe, the evolution of both is governed by $P_{eff}=-{1/9}ρ_{eff}$.

gr-qc↗

arXiv1999

Wave Function of a Brane-like Universe

Within the mini-superspace model, brane-like cosmology means performing the variation with respect to the embedding (Minkowski) time $τ$ before fixing the cosmic (Einstein) time $t$. The departure from Einstein limit is parameterized by the 'energy' conjugate to $τ$, and characterized by a classically disconnected Embryonic epoch. In contrast with canonical quantum gravity, the wave-function of the brane-like Universe is (i) $τ$-dependent, and (ii) vanishes at the Big Bang. Hartle-Hawking and Linde proposals dictate discrete 'energy' levels, whereas Vilenkin proposal resembles $α$-particle disintegration.

gr-qc↗

arXiv1999

Cosmic Solenoids: Minimal Cross-Section and Generalized Flux Quantization

A self-consistent general relativistic configuration describing a finite cross-section magnetic flux tube is constructed. The cosmic solenoid is modeled by an elastic superconductive surface which separates the Melvin core from the surrounding flat conic structure. We show that a given amount $Φ$ of magnetic flux cannot be confined within a cosmic solenoid of circumferential radius smaller than $\frac{\sqrt{3G}}{2πc^2}Φ$ without creating a conic singularity. Gauss-Codazzi matching conditions are derived by means of a self-consistent action. The source term, representing the surface currents, is sandwiched between internal and external gravitational surface terms. Surface superconductivity is realized by means of a Higgs scalar minimally coupled to projective electromagnetism. Trading the 'magnetic' London phase for a dual 'electric' surface vector potential, the generalized quantization condition reads: $e/{hc} Φ+ 1/e Q=n$ with $Q$ denoting some dual 'electric' charge, thereby allowing for a non-trivial Aharonov-Bohm effect. Our conclusions persist for dilaton gravity provided the dilaton coupling is sub-critical.

gr-qc↗

arXiv1999

Quantum Gravity of a Brane-like Universe

Quantum gravity of a brane-like Universe is formulated, and its Einstein limit is approached. Regge-Teitelboim embedding of Arnowitt-Deser-Misner formalism is carried out. Invoking a novel Lagrange multiplier, accompanying the lapse function and the shift vector, we derive the quadratic Hamiltonian and the corresponding bifurcated Wheeler-Dewitt-like equation. The inclusion of arbitrary matter resembles minimal coupling.

gr-qc↗

arXiv1998

Linking Geometric Mass Hierarchy with Threefold Family Replication

A link is established between the observed (approximate) geometric mass hierarchy of quarks and leptons and the triangular structure of their tenable flavor representations. This singles out SU(3) as the horizontal flavor group, thereby linking the Fermi mass hierarchy with the threefold family replication. These linkages are exploited within a flavor-chiral SU(3) model, with fermions and Higgs bosons in the 3+6* representation. The model is Left-Right symmetric and utilizes the universal see-saw mechanism with a geometric mass suppression pattern. Given certain assumptions, the model produces successful mass-ratio (rather than square-mass-ratio) mixing angle relations and fixes the light quark mass ratio.

hep-ph↗

arXiv1996

Extensible Black Hole Embeddings for Apparently Forbidden Periodicities

Imposing extendibility on Kasner-Fronsdal black hole local isometric embedding is equivalent to removing conic singularities in Kruskal representation. Allowing for globally non-trivial (living in $M_{5}\times S_{1}$) embeddings, parameterized by $k$, extendibility can be achieved for apparently forbidden frequencies $ω_{1}(k)\leω(k)\le ω_{2}(k)$. The Hawking-Gibbons limit, say $\displaystyle{ω_{1,2}(0)= {1\over{4M}}}$ for Schwarzschild geometry, is respected. The corresponding Kruskal sheets are viewed as slices in some Kaluza-Klein background. Euclidean $k$ discreteness, dictated by imaginary time periodicity, is correlated with twistor flux quantization.

gr-qc↗

arXiv1994

Finite Magnetic Flux Tube as a Black & White Dihole

A finite-length magnetic vortex line solution is derived within the context of (4-dim) dilaton gravity. We approach the Bonnor metric at the Einstein-Maxwell limit, and encounter the "flux tube as (Euclidean) Kerr horizon" at the Kaluza-Klein level. Exclusively for string theory, the magnetic flux tube world-sheet exhibits a 2-dim black & white dihole structure. (The figure has been cut off, and is now available upon request from davidson@bguvms.bgu.ac.il)

gr-qc↗

arXiv1993

Threefold Family of Charged Spin-1/2 Dirac Bubbles

We extend Dirac's `extensible model of the electron' to include spin and family. $U(1)_{e.m.}$ charge conservation on the bubble is translated into a secondary $U(1)_{g}$ world-manifold gauge principle. Reflecting the secondary magnetic monopole configuration on spatial $S^2$, the harmonic excitations may furnish half integer $SU(2)_{spin}\otimes U(1)_{g}$ representations. Our spin--$1/2$ `electron' is described by four world-manifold scalar fields. Its three varieties are associated with different minima of the (6th--order) surface-tension scalar potential.

hep-th↗