The New Fundamental Plane of 4FGL Blazars Based on the Black Hole Spin-mass Energy

The fundamental plane is a key scaling relation connecting jet power, accretion, and black hole mass in active galactic nuclei. In this work, we construct a sample of 73 Fermi-Large Area Telescope-detected 4FGL blazars and explore an extended version of the fundamental plane that incorporates γ -ray luminosity ( L γ ), which directly traces the highly beamed jet emission. We find that γ -ray luminosity serves as an effective proxy for jet power in blazars. The traditional radio fundamental plane shows a strong correlation both before and after beaming correction ( R ≈ 0.88 and 0.69, respectively), confirming that blazars generally follow the same relation found in other black hole systems. The newly proposed γ -ray version of the plane also exhibits strong correlations ( R ≈ 0.85 before correction and 0.78 after correction), indicating that radio and γ -ray jet emission are linked to the same underlying accretion–jet mechanism despite different radiation processes. Furthermore, including an estimate of black hole spin energy ( M spin ) instead of only dynamical mass slightly improves the correlation strength in both radio and γ -ray planes, suggesting that black hole spin may play an important role in powering jets in blazars. These results provide additional support for the Blandford–Znajek mechanism and offer a potential pathway to refine the fundamental plane relation for jetted active galactic nuclei.