Abstract
We discuss a possible link between the deformation parameter Theta ^{mu nu } arising in the framework of noncommutative geometry and the parameter beta of the generalized uncertainty principle (GUP). We compute the shift of the Hawking temperature induced by the Theta ^{mu nu }-deformed Schwarzschild geometry, and then we relate it to one obtained by GUP. Results suggest a granular structure of specetime at the Planck scales. The current bounds on beta allow to constraint the noncommutative parameter Theta ^{mu nu }.
Highlights
The possibility to describe spacetime in noncommutive frameworks was noted long time ago [1], and its interest renewed recently owing to the discovery of SeibergWitten map [2], which relates noncommutative to commutative gauge theories
By comparing the temperature (3.11) with the generalized uncertainty principle (GUP)-deformed Hawking temperature given by Eq (2.3), one obtains β
In this paper we have derived an upper bound on the deformation parameter Υ of the noncommutative geometry, by relating Υ to the coefficients β of GUP
Summary
The possibility to describe spacetime in noncommutive frameworks was noted long time ago [1], and its interest renewed recently owing to the discovery of SeibergWitten map [2], which relates noncommutative to commutative gauge theories. The general idea is to define the fields over phase space by replacing the ordinary product of fields with the GronewaldMoyal product and map (via the Seiberg-Witten) this theory in the equivalent commutative theory with expansion of the fields in terms of the noncommutative parameter This approach has been extensively used to study many gauge theories [22,23,24,25,26,27,28] (see [29,30,31,32]), and since gravity can be considered as a gauge theory, the commutative equivalent approach appears to be a promising formulation2 [33,48,62,63,64,65,66,67,68,69,70,71,72].
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
