Charge and/or spin limits for black holes at a non-commutative scale

Abstract

In the commutative geometrical background, one finds the total charge (Q) and/or the total angular momentum (J) of a generalized black hole of mass M to be bounded by the condition $$Q^2+\left( J{/}M\right) ^2\le M^2$$ , whereas the inclusion of the concept of non-commutativity in geometry leads to a much more richer result. It predicts that the upper limit to Q and/or J is not fixed but depends on the mass/length scale of black holes; it (the upper limit to Q and/or J) goes towards a ‘commutative limit’ when $${M\gg \sqrt{\vartheta }}$$ ( $$\sqrt{\vartheta }$$ characterizes the minimal length scale) and rapidly diminishes towards zero with M decreasing in the strongly non-commutative regime, until approaching a perfect zero value for $${M\simeq 1.904\sqrt{\vartheta }}$$ . We have performed separate calculations for a pure Kerr or a pure Reissner–Nordstrom black hole, and briefly done it for a generalized black hole.