Ripples, Rotations, and the Kerr Black Hole

This chapter begins by examining Einstein’s work on gravitational waves. He initially renounced the unimodular coordinate condition and identified three types of gravitational waves, concluding that only the third type carried energy. This conclusion led him to revisit the unimodular coordinate condition. In response to criticism from his colleagues, Einstein ingeniously redefined the third type as transverse gravitational waves. Einstein served as a guiding figure for young colleagues struggling to solve his field equations. They frequently corresponded with him, sharing the foundations of their derivations, which would later be published. From the surviving correspondence, it is evident that Einstein often assisted them in resolving paradoxes and problems. This is particularly apparent in the case of Hans Thirring, as discussed in this chapter. Einstein’s subtle guidance was instrumental in the discovery of the Lense-Thirring effect during the early development of general relativity, preceding the Kerr solution. Thirring and Lense employed approximate methods to analyze their problem, as the Schwarzschild solution was the only viable option available at the time. Their approach incorporated mathematical techniques drawn from Einstein’s paper on gravitational waves. The chapter concludes with the discovery of the Kerr solution, which relied on mathematical tools developed only after Einstein’s death.