Researchers have developed a new Weyl law to quantify the quasinormal modes (QNM) of Schwarzschild black holes. These QNMs are the "fingerprints" of black hole perturbations, analogous to the vibrations of a bell, and their study is crucial for understanding the stability and dynamics of these astrophysical objects. The advance focuses on QNMs with energies near the threshold and high angular momentum, providing a more complete description of their spectral distribution.

To achieve this, a new pseudodifferential operator calculus has been introduced, specifically designed for semiclassical spectral problems near threshold energies. This formalism allows for the combination of elliptic theory with the complex scaling method, leading to uniform resolvent estimates near zero energy. These estimates are applicable to operators that behave, at infinity, like a semiclassical Schrödinger operator with a repulsive inverse-square potential.

Applying these methods to the Regge-Wheeler potential, which describes perturbations of Schwarzschild black holes, the results indicate the absence of high angular momentum QNMs from a disk whose radius grows linearly with angular momentum. Combined with previous asymptotic descriptions of Schwarzschild QNMs, this work shows that the number of QNMs contained in a small sector below the real axis and with modulus bounded by λ grows as Cλ³. Furthermore, the study explored the effect of cutting off the Schwarzschild resolvent away from the event horizon, concluding that such a cutoff does not lead to any pole cancellations.

This theoretical development is fundamental for gravitational wave astrophysics, as a precise understanding of QNMs is essential for interpreting signals from black hole coalescences detected by observatories like LIGO and Virgo. The ability to predict and characterize these modes with greater accuracy enhances our capacity to test general relativity in strong-field environments and to explore the nature of quantum gravity.