Physical Inconsistency of the Corinaldesi–Papapetrou SSC in Schwarzschild Spacetime
Physical Inconsistency of the Corinaldesi–Papapetrou SSC in Schwarzschild Spacetime
In this note, we aim to show that imposing the Corinaldesi–Papapetrou (CP) spin supplementary condition in Schwarzschild spacetime leads to physically unusual and ultimately inconsistent results.
The CP condition was one of the earliest supplementary conditions introduced in the study of spinning particles in gravitational fields and was employed in the pioneering works of Corinaldesi and Papapetrou.
We demonstrate that this choice predicts an electromagnetic-like spectral structure around a Schwarzschild black hole, while arguing that such a prediction arises from the particular choice of supplementary condition rather than representing a realistic physical phenomenon.
Our analysis highlights the crucial role of selecting an appropriate spin supplementary condition in the study of spin–gravity coupling and the motion of spinning particles, and suggests that the Corinaldesi–Papapetrou condition should be regarded primarily as a mathematical construction rather than a physically consistent description of nature.
Physical Inconsistency of the Corinaldesi–Papapetrou SSC in Schwarzschild Spacetime