Penrose process in rotating black holes with quantum corrections: implications for energy extraction and irreducible mass

Abstract We investigate energy extraction from a rotating black hole spacetime modified by a quantum correction parameter $$ \alpha .$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>α</mml:mi> <mml:mo>.</mml:mo> </mml:mrow> </mml:math> Focusing on the Penrose process, we analyze particle splitting within the ergoregion and evaluate the extraction efficiency $$ \eta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>η</mml:mi> </mml:math> as a function of the spin parameter a and the quantum correction $$ \alpha .$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>α</mml:mi> <mml:mo>.</mml:mo> </mml:mrow> </mml:math> Our analysis shows that quantum effects effectively enlarge the ergoregion by shifting both the static limit and the event horizon toward smaller radii. Numerical results indicate that, within the range of spin values listed in Table 1, an event horizon exists only for the critical value $$ \alpha = 1.1663 ,$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>α</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1.1663</mml:mn> <mml:mo>,</mml:mo> </mml:mrow> </mml:math> beyond which the horizon disappears. A direct comparison with the classical Kerr case reveals that these geometric modifications significantly enhance the efficiency of energy extraction. In particular, the maximum efficiency of the Penrose process reaches approximately $$ 2.85\% $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>2.85</mml:mn> <mml:mo>%</mml:mo> </mml:mrow> </mml:math> for $$ \alpha = 1.1663,$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>α</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1.1663</mml:mn> <mml:mo>,</mml:mo> </mml:mrow> </mml:math> compared to $$ 1.72\% $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>1.72</mml:mn> <mml:mo>%</mml:mo> </mml:mrow> </mml:math> for the Kerr black hole. In addition, we derive an expression for the irreducible mass, emphasizing its role in constraining the extractable rotational energy. Overall, our results demonstrate that quantum corrections have a pronounced impact on black hole energetics, leading to measurable deviations from standard Kerr predictions.