New tortoise coordinate transformation and Hawking’s radiation in de Sitter space

2012 ◽  
Vol 343 (1) ◽  
pp. 471-479 ◽  
Author(s):  
N. Ibohal ◽  
T. Ibungochouba
Keyword(s):  
Coordinate Transformation ◽  
De Sitter Space ◽  
De Sitter ◽  
Tortoise Coordinate ◽  
Tortoise Coordinate Transformation ◽  
New Tortoise Coordinate Transformation

scholarly journals From Fock’s transformation to de Sitter space

2015 ◽  
Vol 93 (7) ◽  
pp. 734-737 ◽  
Author(s):  
T. Foughali ◽  
A. Bouda
Keyword(s):  
Coordinate Transformation ◽  
Gordon Equation ◽  
De Sitter Space ◽  
Space Time ◽  
Poisson Brackets ◽  
De Sitter ◽  
Deformed Algebra ◽  
Klein Gordon ◽  
The Universe ◽  
Klein Gordon Equation

As with Deformed Special Relativity, we showed recently that the Fock coordinate transformation can be derived from a new deformed Poisson brackets. This approach allowed us to establish the corresponding momentum transformation that keeps invariant the four-dimensional contraction pμxμ. From the resulting deformed algebra, we construct the corresponding first Casimir. After first quantization, we show by using the Klein–Gordon equation that the space-time of the Fock transformation is the de Sitter one. As we will see, the invariant length representing the universe radius in the space-time of Fock’s transformation is exactly the radius of the embedded hypersurface representing the de Sitter space-time.

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