CQG+ Insight: More Classical Charges for Black Holes

Written by Geoffrey Compère, a Research Associate at the Université Libre de Bruxelles. He has contributed to the theory of asymptotic symmetries, the techniques of solution generation in supergravity, the Kerr/CFT correspondence and is generally interested in gravity, black hole physics and string theory.

Why mass and angular momentum might not be enough to characterize a stationary black hole

Geoffrey Compère

Geoffrey Compère having family time in the park Le
Cinquantenaire in Brussels.

“Black hole have no hair.” This famous quote originates from John Wheeler in the sixties. In other words, a stationary black hole in general relativity is only characterized by its mass and angular momentum. This is because multipole moments of the gravitational field are sources for gravitational waves which radiate the multipoles away and only the last two conserved quantities, mass and angular momentum, remain. That’s the standard story.

Now, besides gravitational waves, general relativity contains another physical phenomenon which does not exist in Newtonian theory: the memory effect. It was discovered beyond the Iron Curtain by Zeldovich and Polnarev in the seventies and rediscovered in the western world and further extended by Christodoulou in the nineties. While gravitational waves lead to spacetime oscillations, the memory effect leads to a finite permanent displacement of test observers in spacetime. The effect exists for any value of the cosmological constant but in asymptotically flat spacetimes, it can be understood in terms of an asymptotic diffeomorphism known as a BMS supertranslation.

In order to understand that, let’s go back to the sixties where the radiative properties of sources were explored in general relativity; it was found by Bondi, van der Burg, Mezner and Sachs that there is a fundamental ambiguity in the coordinate frame at null infinity. Most expected that Continue reading