Upper bound on the GUP parameter using the black hole shadow
Juliano C. S. Neves
Abstract
Abstract An upper bound on the parameter that provides a generalized uncertainty principle (GUP) is obtained from the black hole shadow. With the aid of a recent constraint between regular black holes and the GUP parameter, it is indicated a relation between this parameter and the deviation from circularity of the black hole shadow. In the case of the recent announcement of the M87* results from the Event Horizon Telescope collaboration, a deviation from circularity $$\lesssim 10\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>≲</mml:mo><mml:mn>10</mml:mn><mml:mo>%</mml:mo></mml:mrow></mml:math> imposes a GUP parameter $$\beta _0 <10^{90}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>β</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mo><</mml:mo><mml:msup><mml:mn>10</mml:mn><mml:mn>90</mml:mn></mml:msup></mml:mrow></mml:math> .