Speaker
Description
In this talk I will discuss the displacement memory effect of gravitational wave firstly. Then the local Carroll symmetry of gravitational waves formulated in Baldwin-Jeffery-Rosen coordinates is extended to a globally well-defined symmetry via a coordinate transformation to Brinkmann coordinates. Two independent global solutions to the Sturm-Liouville equation are derived to characterize the corresponding symmetries—including translations and Carroll boosts—and geodesic motions of the system. Specifically, one solution satisfies specialized initial conditions with zero initial momentum, whereas the other solution possesses nonvanishing initial momentum. Pure displacement occurs when the nonvanishing momentum solution is suppressed and the wave parameters adopt specific values corresponding to integer half-wave numbers. At last, the general theoretical conclusions are verified and demonstrated using the Pöschl-Teller profile as a typical example.
