A heavy spinning top launched near a black hole doesn't follow the curve that textbooks draw. Its own rotation and oblateness, like a pumpkin squashed at the poles, make the trajectory wobble. In a new study, this wobbling path has been calculated more precisely than ever before.
Usually, a small body in a black hole's field is treated as a point — without size or spin. But real neutron stars or black hole candidates spin rapidly and become noticeably deformed. Accounting for this deformation (the quadrupole moment) adds an extra bend to the body's path. The authors derived a formula: the correction to the deflection angle grows with the square of the spin and inversely with the cube of the impact parameter — the distance at which the body passes by the black hole.
The formula is derived not for an abstract geodesic but for a real trajectory, including the force that arises from the interaction of spin with spacetime curvature. This could allow future observations of the deflection of light or matter to reveal what lies inside, just as the wobble of a spinning top hints at its contents.
If Earth spun as fast as some neutron stars, its equatorial radius would be noticeably larger than its polar radius, and satellites in low orbits would feel that oblateness.