scholarly journals Kodama-Schwarzschild versus Gaussian Normal Coordinates Picture of Thin Shells

2016 ◽  
Vol 2016 ◽  
pp. 1-6 ◽  
Author(s):  
Mikhail Z. Iofa
Keyword(s):  
Spherical Shell ◽  
Coordinate Transformation ◽  
Time Dependent ◽  
Thin Shells ◽  
Junction Conditions ◽  
Coordinate Systems ◽  
Normal Coordinate ◽  
Normal Coordinates

Geometry of the spacetime with a spherical shell embedded in it is studied in two coordinate systems: Kodama-Schwarzschild coordinates and Gaussian normal coordinates. We find explicit coordinate transformation between the Kodama-Schwarzschild and Gaussian normal coordinate systems. We show that projections of the metrics on the surface swept by the shell in the 4D spacetime in both cases are identical. In the general case of time-dependent metrics we calculate extrinsic curvatures of the shell in both coordinate systems and show that the results are identical. Applications to the Israel junction conditions are discussed.

scholarly journals CONNECTION BETWEEN TWO FORMS OF EXTRA DIMENSIONAL METRIC REVISITED

2012 ◽  
Vol 27 (22) ◽  
pp. 1250121 ◽  
Author(s):  
MIKHAIL Z. IOFA
Keyword(s):  
Cosmological Model ◽  
Coordinate Transformation ◽  
Time Dependent ◽  
Coordinate Systems ◽  
Fixed Position

5D cosmological model with 3-brane with matter is considered. The brane divides the bulk in two AdS half-spaces. Geometry of the model can be described by two types of coordinate systems: in the first setting the metric is static and the brane is moving in the bulk, in the second approach the metric is time-dependent and the brane is located at a fixed position in the bulk. Coordinate transformation connecting two coordinate systems is constructed.

scholarly journals Rotating thin shells in (2 + 1)-dimensional asymptotically AdS spacetimes: Mechanical properties, machian effects, and energy conditions

2015 ◽  
Vol 24 (09) ◽  
pp. 1542022 ◽  
Author(s):  
José P. S. Lemos ◽  
Francisco J. Lopes ◽  
Masato Minamitsuji
Keyword(s):  
Energy Momentum Tensor ◽  
Energy Condition ◽  
Momentum Tensor ◽  
Energy Conditions ◽  
Thin Shells ◽  
Dominant Energy Condition ◽  
Junction Conditions ◽  
Rest Energy ◽  
Inertial Frames ◽  
Ads Spacetime

In this paper, a rotating thin shell in a (2 + 1)-dimensional asymptotically AdS spacetime is studied. The spacetime exterior to the shell is the rotating BTZ spacetime and the interior is the empty spacetime with a cosmological constant. Through the Einstein equation in (2 + 1) dimensions and the corresponding junction conditions we calculate the dynamical relevant quantities, namely, the rest energy–density, the pressure, and the angular momentum flux density. We also analyze the matter in a frame where its energy–momentum tensor has a perfect fluid form. In addition, we show that Machian effects, such as the dragging of inertial frames, also occur in rotating (2 + 1)-dimensional spacetimes. The weak and the dominant energy condition for these shells are discussed.

Spherically Symmetric Vibration of an Elastic Spherical Shell Subject to a Radial and Time-Dependent Body-Force Field

1971 ◽  
Vol 38 (3) ◽  
pp. 702-705 ◽  
Author(s):  
J. M. McKinney
Keyword(s):  
Continuous Function ◽  
Spherical Shell ◽  
Force Field ◽  
Body Force ◽  
Time Dependent ◽  
Symmetric Body ◽  
Spherically Symmetric ◽  
Symmetric Vibration ◽  
Elastic Spherical Shell

A solution, exact within the framework of linear elastokinetics, is obtained for a vibrating, elastic, arbitrarily thick spherical shell subject only to a spherically symmetric body force field of the form FR(r, τ) = Fr(r)Ft(τ). Fr(r) is taken in the form of a polynomial whereas Ft(τ) is restricted only to being a sectionally continuous function of time.

Discontinuities in spherically symmetric gravitational fields and shells of radiation

1958 ◽  
Vol 248 (1254) ◽  
pp. 404-414 ◽  
Keyword(s):  
Boundary Conditions ◽  
Spherical Shell ◽  
Previous Treatment ◽  
Empty Space ◽  
Point Of View ◽  
Spherically Symmetric ◽  
Junction Conditions ◽  
Metric Tensor ◽  
Gravitational Fields

Boundary conditions at a 3-space of discontinuity ∑ are considered from the point of view of Lichnerowicz. The validity of the O’Brien—Synge junction conditions is established for co-ordinates derivable from Lichnerowicz’s ‘admissible co-ordinates’ by a transformation which is uniformly differentiable across ∑. The co-ordinates r , θ , ϕ , t , used by Schwarzschild and most later authors when dealing with spherically symmetric fields, are shown to be of this type. In Schwarzschild’s co-ordinates, the components of the metric tensor can always be made continuous across Ʃ, and simple relations are derived connecting the jumps in their first derivatives. A spherical shell of radiation expanding in empty space is examined in the light of the above ideas, and difficulties encountered by Raychaudhuri in a previous treatment of this problem are cleared up. A particular model is then discussed in some detail.

Vibration Frequencies and Normal Coordinates of Benzo(c)phenanthrene

2001 ◽  
Vol 56 (6-7) ◽  
pp. 499-504
Author(s):  
Rehab M. Kubba ◽  
Muthana Shanshal
Keyword(s):  
Spectroscopic Data ◽  
Normal Coordinate Analysis ◽  
Quantum Mechanical ◽  
Ir Absorption ◽  
Quantum Mechanical Calculations ◽  
Vibration Frequencies ◽  
Normal Coordinate ◽  
Normal Coordinates ◽  
Comparative Relations

Abstract MINDO/3-FORCES quantum mechanical calculations yielded non-planar (C2) geometry of Ben-zo(c)phenanthrene. The result agrees with the majority of published results but disagrees with others in which a planar (C2 V) structure was accepted in order to simplify the analysis of certain spectroscopic data. Vibration frequencies and IR absorption intensities were calculated then, applying the non-planar (C2) structure. A complete normal coordinate analysis for the molecule is reported. Inspection of these coordinates allowed the discovery of some useful comparative relations between them, which are re­ ported in the paper.

scholarly journals ALL ORDER COVARIANT TUBULAR EXPANSION

2014 ◽  
Vol 26 (01) ◽  
pp. 1350019 ◽  
Author(s):  
PARTHA MUKHOPADHYAY
Keyword(s):  
Riemannian Manifold ◽  
Closed Form ◽  
Tubular Neighborhood ◽  
Normal Coordinate ◽  
Integral Theorem ◽  
Normal Coordinates ◽  
Expansion Coefficients

We consider tubular neighborhood of an arbitrary submanifold embedded in a (pseudo-) Riemannian manifold. This can be described by Fermi normal coordinates (FNC) satisfying certain conditions as described by Florides and Synge in [15]. By generalizing the work of Muller et al. in [54] on Riemann normal coordinate expansion, we derive all order FNC expansion of vielbein in this neighborhood with closed form expressions for the curvature expansion coefficients. Our result is shown to be consistent with certain integral theorem for the metric proved in [15].

Scaling laws for time-dependent stagnant lid convection in a spherical shell

2005 ◽  
Vol 149 (3-4) ◽  
pp. 361-370 ◽  
Author(s):  
C.C. Reese ◽  
V.S. Solomatov ◽  
J.R. Baumgardner
Keyword(s):  
Spherical Shell ◽  
Scaling Laws ◽  
Time Dependent
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