scholarly journals Effects of mathematical locality and number scaling on coordinate chart use

2014 ◽  
Author(s):  
Paul Benioff
Keyword(s):  
Coordinate Chart

scholarly journals The Gravitational Magnetoelectric Effect

Universe ◽  
2019 ◽  
Vol 5 (4) ◽  
pp. 88 ◽  
Author(s):  
Gary Gibbons ◽  
Marcus Werner
Keyword(s):  
Gravitational Waves ◽  
Electromagnetic Fields ◽  
Magnetoelectric Effect ◽  
Dielectric Medium ◽  
Multiferroic Materials ◽  
Schwarzschild Spacetime ◽  
Coordinate Chart

Electromagnetism in spacetime can be treated in terms of an analogue linear dielectric medium. In this paper, we discuss the gravitational analogue of the linear magnetoelectric effect, which can be found in multiferroic materials. While this is known to occur for metrics with non-zero mixed components, we show how it depends on the choice of spatial formalism for the electromagnetic fields, including differences in tensor weight, and also on the choice of coordinate chart. This is illustrated for Langevin–Minkowski, four charts of Schwarzschild spacetime, and two charts of pp gravitational waves.

scholarly journals NEW SPHERICAL SCALAR MODES ON THE DE SITTER EXPANDING UNIVERSE

2012 ◽  
Vol 27 (23) ◽  
pp. 1250124 ◽  
Author(s):  
GABRIEL PASCU
Keyword(s):  
Plane Wave ◽  
Time Evolution ◽  
Gordon Equation ◽  
Expanding Universe ◽  
De Sitter ◽  
Coordinate Chart ◽  
Sitter Spacetime ◽  
Klein Gordon ◽  
Klein Gordon Equation ◽  
Wave Modes

New spherical scalar modes on the expanding part of Sitter spacetime, eigenfunctions of a conserved Hamiltonian-like operator are found by solving the Klein–Gordon equation in the appropriate coordinate chart, with the help of a time evolution picture technique specially developed for spatially flat Friedmann–Lemaître–Robertson–Walker (FLRW) charts. Transition coefficients are computed between these modes and the rest of the scalar spherical and plane wave modes, either momentum or energy eigenfunctions on the spatially flat FLRW chart.

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