Induced matter: Curved N-manifolds encapsulated in Riemann-flat N+1 dimensional space

Liko and Wesson have recently introduced a new 5-dimensional induced matter solution of the Einstein equations, a negative curvature Robertson-Walker space embedded in a Riemann flat 5-dimensional manifold. We show that this solution is a special case of a more general theorem prescribing the structure of certain N+1-dimensional Riemann flat spaces which are all solutions of the Einstein equations. These solutions encapsulate N-dimensional curved manifolds. Such spaces are said to "induce matter" in the sub-manifolds by virtue of their geometric structure alone. We prove that the N-manifold can be any maximally symmetric space.Comment: 3 page

A New Formula Describing the Scaffold Structure of Spiral Galaxies

We describe a new formula capable of quantitatively characterizing the Hubble sequence of spiral galaxies including grand design and barred spirals. Special shapes such as ring galaxies with inward and outward arms are also described by the analytic continuation of the same formula. The formula is r() = A/log [B tan (/2N)]. This function intrinsically generates a bar in a continuous, fixed relationship relative to an arm of arbitrary winding sweep. A is simply a scale parameter while B, together with N, determines the spiral pitch. Roughly, greater N results in tighter winding. Greater B results in greater arm sweep and smaller bar/bulge, while smaller B fits larger bar/bulge with a sharper bar/arm junction. Thus B controls the \u27bar/bulge-to-arm\u27 size, while N controls the tightness much like the Hubble scheme. The formula can be recast in a form dependent only on a unique point of turnover angle of pitch - essentially a one-parameter fit, aside from a scalefactor. The recast formula is remarkable and unique in that a single parameter can define a spiral shape with either constant or variable pitch capable of tightly fitting Hubble types from grand design spirals to late-type large barred galaxies. We compare the correlation of our pitch parameter to Hubble type with that of the traditional logarithmic spiral for 21 well-shaped galaxies. The pitch parameter of our formula produces a very tight correlation with ideal Hubble type suggesting it is a good discriminator compared to logarithmic pitch, which shows poor correlation here similar to previous works. Representative examples of fitted galaxies are shown

Photoacoustic Microscopy of Ceramics Using Laser Heterodyne Detection

In recent years a variety of thermoacoustic techniques have been used to image surface and near surface features in ceramics. These include early gas cell methods [1] as well as the Scanning Electron Acoustic Microscopy (SEAM) technique [2] and more recently the Mirage or Optical Beam Deflection (OBD) methods [3,4]. In the gas cell and Mirage methods, the effect of the outgoing thermal wave on the air boundary at the sample surface is sensed, respectively, by a microphone and by a laser beam. In SEAM the specimen vibration or acoustic wave is sensed directly by a contacting transducer. The gas cell and Mirage methods generate pure thermal images but require long times to generate useful images of areas a few millimeters square. SEAM, on the other hand, is a high signal/noise technique due to the exceptional sensitivity of piezoelectrics and thus requires shorter imaging times. However, SEAM is sensitive to both the thermal wave signal and the local mechanical response of the specimen to the thermal wave and convolutes the two responses. The author has recently demonstrated that the entire image can be dominated by the mechanical response alone [5]. Thus SEAM image interpretation is considerably clearer for such cases. This thermomechanical mechanism is now fairly well understood and its analysis will be presented elsewhere. SEAM is thus an excellent method for imaging ceramics. Using Coordinate Modulation (CM) with SEAM 5mm x 5mm areas of ceramics have been imaged for surface and subsurface defects in 2 minutes. CM requires the electron beam to be dithered a small amount instead of being intensity modulated, the usual approach. This increases image contrast and will be described later

Model-Independent Plotting of the Cosmological Scale Factor as a Function of Lookback Time

In the present work we describe a model-independent method of developing a plot of scale factor versus lookback time from the usual Hubble diagram of modulus data against redshift. This is the first plot of this type. We follow the model-independent methodology of Daly and Djorgovski (2004) used for their radio-galaxy data. Once the data plot is completed, any model can be applied and will display accordingly as described in standard literature. We then compile an extensive data set to z = 1.8 by combining SNe Ia data from SNLS3 of Conley et al. (2011), High-z SNe data of Riess et al. (2004) and radio-galaxy data of Daly & Djorgovski (2004) to be used to validate the new plot. We first display these data on a standard Hubble diagram to confirm the best fit for LCDM cosmology and thus validate the joined data set. The scale factor plot is then developed from the data and the LCDM model is again displayed from a least-squares fit. The fit parameters are in agreement with the Hubble diagram fit confirming the validity of the new plot. Of special interest is the transition-time of the universe which in the scale factor plot will appear as an inflection point in the data set. Noise is more visible on this presentation which is particularly sensitive to inflection points of any model displayed on the plot unlike on a modulus-z diagram where there are no inflection points and the transition-z is not at all obvious by inspection. We obtain a lower limit of z >0.6. It is evident from this presentation that there is a dearth of SNe data in the range, z = 1-2, exactly the range necessary to confirm a LCDM transition-z in the neighborhood of z = 0.76.Comment: Accepted Astronomical Journa

Search for Effects of an Electrostatic Potential on Clocks in the Frame of Reference of a Charged Particle

Results of experiments to confirm a theory that links classical electromagnetism with the geometry of spacetime are described. The theory, based on the introduction of a Torsion tensor into Einstein s equations and following the approach of Schroedinger, predicts effects on clocks attached to charged particles, subject to intense electric fields, analogous to the effects on clocks in a gravitational field. We show that in order to interpret this theory, one must re-interpret all clock changes, both gravitational and electromagnetic, as arising from changes in potential energy and not merely potential. The clock is provided naturally by proton spins in hydrogen atoms subject to Nuclear Magnetic Resonance trials. No frequency change of clocks was observed to a resolution of 6310(exp -9). A new "Clock Principle" was postulated to explain the null result. There are two possible implications of the experiments: (a) The Clock Principle is invalid and, in fact, no metric theory incorporating electromagnetism is possible; (b) The Clock Principle is valid and it follows that a negative rest mass cannot exist

Simple Fit of Data Relating Supermassive Black Hole Mass to Galaxy Pitch Angle

Seigar, et al, have recently demonstrated a new, tight correlation between galactic central supermassive black hole (BH) mass and the pitch angle of the spiral arm in disc galaxies which they attribute to other indirect correlations. They fit a double power law, governed by five parameters, to the BH mass as a function of pitch. Noting the features of their fitted curve, we show that a simple linear proportion of the BH mass to the cotangent of the pitch angle can obtain the same fit, within error. Such a direct, elegant fit may help shed light on the nature of the correlation.Comment: 2 pages, 1 fi

On a Bipolar Model of Hyperbolic Geometry and its Relation to Hyperbolic Friedmann-Robertson-Walker Space

Negatively curved regions of space in a Friedmann-Robertson-Walker (FRW) universe are a realistic possibility. These regions would occur in voids in the large-scale structure of the universe where there is no dark matter with only dark energy present. Hyperbolic space is strange from a physical point of view and various models of hyperbolic space have been introduced, each offering a clarifying view. In the present work we develop a new bipolar model of hyperbolic geometry and show that it provides new insights toward an understanding of hyperbolic as well as elliptic FRW space. In particular, using the bipolar model, we show that the circular geodesics of an FRW space can be referenced to two real centers – a Euclidean center and a hyperbolic center. Considering the physics of elliptic FRW space is so well confirmed in the ɅCDM model describing the expansion of the universe with respect to a Euclidean center, it is possible that the hyperbolic center also plays a physical role in regions of hyperbolic space