Session C14: Extremes of Gravity: From Weak to Strong

Insights into the gravitational wave memory effect

A major breakthrough of General Relativity (GR) happened in 2015 with LIGO's first detection of gravitational waves. Typical sources for gravitational radiation are mergers of binary black holes, binary neutron stars and core-collapse supernovae. In these processes mass and momenta are radiated away in form of gravitational waves. GR predicts that these waves leave a footprint in the spacetime, that is they change the spacetime permanently, which results in a permanent displacement of test masses. This effect is called the memory. In this talk, I will explore the gravitational wave memory. We will see that there are two types of memory, one going back to Ya. B. Zel'dovich and A. G. Polnarev and one to D. Christodoulou. Then I will discuss recent work including my collaboration with D. Garfinkle, S.-T. Yau, P. Chen, focusing on how neutrinos or electromagnetic fields contribute to the memory effect, and work with D. Garfinkle and N. Yunes on cosmological memory.   

Growth of Perturbations near a Rapidly Spinning Black Hole

Aretakis discovered a horizon instability of extremal black holes, wherein transverse derivatives of axisymmetric perturbations grow polynomially in advanced time on the horizon. Since no physical black hole can be precisely extremal, nor any physical perturbation precisely axisymmetric, the physical implications rest on generalization to nonaxisymmetric perturbations of near-extreme black holes. We analytically study the response of a near-extremal Kerr black hole to generic external scalar, electromagnetic, and gravitational field perturbations. We show that the energy density, electromagnetic field strength, and tidal force experienced by infalling observers exhibit transient growth near the horizon. As the black hole spin is increased, the growth lasts arbitrarily long and occurs arbitrarily near the horizon, reproducing the Aretakis instability in a smooth way. We explain these results in terms of near-horizon geometry and discuss potential astrophysical implications.   

Strong Cosmic Censorship

The Hawking-Penrose theorems tell us that solutions of Einstein's equations are generally singular, in the sense of the incompleteness of causal geodesics (the paths of physical observers). These singularities might be marked by the blowup of curvature and therefore crushing tidal forces, or by the breakdown of physical determinism. Penrose has conjectured (in his "Strong Cosmic Censorship Conjecture") that it is generically unbounded curvature that causes singularities, rather than causal breakdown. The verification that “AVTD behavior” (marked by the domination of time derivatives over space derivatives) is generically present in a family of solutions has proven to be a useful tool for studying model versions of Strong Cosmic Censorship in that family. I discuss some of the history of Strong Cosmic Censorship, and then discuss what is known about AVTD behavior and Strong Cosmic Censorship in families of solutions defined by varying degrees of isometry, and discuss recent results which we believe will extend this knowledge and provide new support for Strong Cosmic Censorship. I also comment on some of the recent work on “Weak Null Singularities”, and how this relates to Strong Cosmic Censorship.