In this study, we propose a new toothed gear for mechanical transmissions built from a satellite wheel with two toothed conical crowns, one of which conjugates with a fixed central conical wheel mounted in the transmission housing and the other with a movable conical wheel installed on the flange of the driven shaft. The satellite wheel is mounted on the inclined portion of the crankshaft and performs spherospatial motion around a fixed point. When the crankshaft rotates, the teeth of the wheels engage with spherospatial interaction in two lateral gearings of the satellite wheel, yielding kinematic ratios dependent on the correlation of the number of teeth. The teeth of the satellite wheel are used with circular arc profiles, and the teeth of the central wheel have flank profiles with variable curvatures increasing continuously from the root to the tip, so that, in meshing, the teeth form multipair contacts with convex–concave geometry with a small difference in flank curvatures. The flank profile geometry and pairs of teeth simultaneously engage depending on the configurational parameters of the gearing and can use up to 100% of pairs of simultaneously conjugated teeth.
We address the concerns raised by the author of "Comment: Some exact quasinormal frequencies of a massless scalar field in Schwarzschild spacetime" appeared in arXiv:1807.05940. In particular, we explain why the analysis in our paper [Phys. Rev. D{\bf{98}}, 024017 (2018)] is relevant and correct.
We show that Friedmann-Robertson-Walker (FRW) geometry with flat spatial section in quantized (Wheeler deWitt quantization) Brans Dicke (BD) theory reveals a rich phase structure owing to anomalous breaking of a classical symmetry, which maps the scale factor $a\mapstoλa$ for some constant $λ$. In the weak coupling ($ω$) limit, the theory goes from a symmetry preserving phase to a broken phase. The existence of phase boundary is an obstruction to another classical symmetry [arXiv:gr-qc/9902083] (which relates two BD theory with different coupling) admitted by BD theory with scale invariant matter content i.e $T^μ{}_μ=0$. Classically, this prohibits the BD theory to reduce to General Relativity (GR) for scale invariant matter content. We show that strong coupling limit of BD and GR both preserves the symmetry involving scale factor. We also show that with a scale invariant matter content (radiation i.e $P=\frac{1}{3}ρ$), the quantized BD theory does reduce to GR as $ω\rightarrow\infty$, which is in sharp contrast to classical behavior. This is a first known illustration of a scenario, where quantized BD theory provides example of anomalous symmetry breaking and resulting binary phase structure. We make a conjecture regarding strong coupling limit of BD theory in generic scenario.
Nicola Bartolo, Daniele Bertacca, Marco Bruni
et al.
In General Relativity, the constraint equation relating metric and density perturbations is inherently nonlinear, leading to an effective non-Gaussianity in the dark matter density field on large scales - even if the primordial metric perturbation is Gaussian. Intrinsic non-Gaussianity in the large-scale dark matter overdensity in GR is real and physical. However, the variance smoothed on a local physical scale is not correlated with the large-scale curvature perturbation, so that there is no relativistic signature in the galaxy bias when using the simplest model of bias. It is an open question whether the observable mass proxies such as luminosity or weak lensing correspond directly to the physical mass in the simple halo bias model. If not, there may be observables that encode this relativistic signature.
Reformulating our recent result (arXiv:1007.1246 [hep-th]) in coordinate space we point out that no matter how regular is short-distance behavior of Green's function the entanglement entropy in the corresponding quantum field theory is always UV divergent. In particular, we discuss a recent example by Padmanabhan (arXiv:1007.5066 [gr-qc]) of a regular Green's function and show that provided this function arises in a field theory the entanglement entropy in this theory is UV divergent and calculate the leading divergent term.
The authors of the paper ''On Anisotropic Dark Energy Stars'', arXiv:0803.2508 [gr-qc], consider the equations of state $p_r=\omega \rho$ and $p_t=\omega \rho$, ignoring the fact that this implies an isotropic pressure, which places strict restrictions on the values of $\omega$. The authors then argue for an anisotropic pressure fluid throughout their work, and apply these equations of state to the energy conditions, consequently obtaining incorrect intervals for the parameter $\omega$. This procedure invalidates their criticisms on the following paper: Class.Quant.Grav. 23, 1525 (2006).
All known stationary black hole solutions in higher dimensions possess additional rotational symmetries in addition to the stationary Killing field. Also, for all known stationary solutions, the event horizon is a Killing horizon, and the surface gravity is constant. In the case of non-degenerate horizons (non-extremal black holes), a general theorem was previously established [gr-qc/0605106] proving that these statements are in fact generally true under the assumption that the spacetime is analytic, and that the metric satisfies Einstein's equation. Here, we extend the analysis to the case of degenerate (extremal) black holes. It is shown that the theorem still holds true if the vector of angular velocities of the horizon satisfies a certain "diophantine condition," which holds except for a set of measure zero.
We calculate the amount of primordial matter density contrast and the size of the very early universe in the recent Quantum Big Bang theory [arXiv:0705.4549 [gr-qc](2007)] of the cosmological constant. We obtain $(\delta\rho/\rho)_M = 1.75 \times 10^{-5}$, {\it without} the introduction of an adjustable free parameter. Harrison-Zel'dovich $k$-dependence with $A = 64/9\pi^2 = 0.72$ and $n = 1$ in $|\delta_k|^2 = Ak^n$ arises inherently. The size of the universe with which it enters the classical Friedmann-Robertson-Walker (FRW) phase comes out to be 0.2 cm. We conclude that the hypothesis of classical inflation at an early stage of cosmic evolution is {\bf not} needed.
We work on the uniqueness, gr-qc/0504147, of representations of the holonomy-flux algebra in loop quantum gravity. We argue that for analytic diffeomorphisms, the flux operators can be only constants as functions on the configuration space in representations with no anomaly, which are zero in the standard representation.
We look at the covariant techniques and the ideas on constraints and gauge-invariance, which were recently employed in [gr-qc/0702104] to support earlier work by the same authors. That work was criticised in [gr-qc/0503042]. Using very simple and well known examples we show that, when adopted, the methods and views of [gr-qc/0702104] lead to basic-level mathematical problems, with analogous consequences for the physics. We provide a few simple rules that should help to avoid similar problems in the future.
Our investigation of differential conservation laws in Lagrangian field theory is based on the first variational formula which provides the canonical decomposition of the Lie derivative of a Lagrangian density by a projectable vector field on a bundle (Part 1: gr-qc/9510061). If a Lagrangian density is invariant under a certain class of bundle isomorphisms, its Lie derivative by the associated vector fields vanishes and the corresponding differential conservation laws take place. If these vector fields depend on derivatives of parameters of bundle transformations, the conserved current reduces to a superpotential. This Part of the work is devoted to gravitational superpotentials. The invariance of a gravitational Lagrangian density under general covariant transformations leads to the stress-energy-momentum conservation law where the energy-momentum flow of gravity reduces to the corresponding generalized Komar superpotential. The associated energy-momentum (pseudo) tensor can be defined and calculated on solutions of metric and affine-metric gravitational models.
Recently E. E. Donets, D. V. Galtsov, and the author reported the results of numerical and analytical investigation of the SU(2) Einstein-Yang-Mills black hole interior solutions (gr-qc/9612067). It was shown that a generic interior solution develops a new type of an infinitely oscillating behavior with exponentially growing amplitude. Numerical data for three sequential oscillations were presented. The numerical integration technique was not discussed. Later P. Breitenlohner, G. Lavrelashvili, and D. Maison confirmed our main results (gr-qc/9703047). But they have made some misleading statements. In particular, they claimed, discussing the oscillations, that ``as one performs the numerical integration one quickly runs into serious problems...'' so that ``it is practically impossible to follow more than one or two of them numerically'' because ``the numerical integration procedure breaks down''. It is shown here that trivial logarithmic substitutions and integration along the integral curve solve these ``serious problems'' easily.
A standard and reasonable definition of asymptotic velocity term dominance (AVTD) shows that the numerical study by Hern and Stewart (gr-qc/9708038) confirms previous results that generic Gowdy cosmologies on $T^3 \times R$ have an AVTD singularity.