Session S04: Developments in Gravitational Theory

Black Holes Cannot be Over-Charged or Over-Spun

The Kerr-Newman solutions are the only stationary black hole solutions of the Einstein-Maxwell equations in 4-dimensions, but they describe black holes only when the inequality $M^2 \geq (J/M)^2 + Q^2$ is satisfied, where $M$, $J$, and $Q$ are the mass, angular momentum, and charge of the black hole. Therefore, if an extremal or nearly extremal black hole can be made to absorb matter with sufficiently large angular momentum or charge as compared with its energy, one would obtain a contradiction with cosmic censorship. Hubeny and others have made proposals as to how this might be done, but a proper analysis of this proposal requires a calculation of all second order effects on energy, including, in particular, effects arising from self-force. We show in this work that when all of the second order effects are taken into account, no over-charging or over-spinning of a black hole can occur, provided only that the non-electromagnetic matter satisfies the null energy condition. The proof is based upon general properties of canonical energy and does not require an explicit calculation of self-force effects.   

Gravitational waves from compact binaries in an effective field theory approach

I review developments and progress using the effective field theory (EFT) approach for modeling compact binary sources of gravitational waves for observations with LIGO. EFT is a powerful paradigm that naturally incorporates the effects from tidal deformation, spin angular momentum, and others that are associated with extended bodies like black holes and neutron stars. In addition, EFT provides a systematic "turn-the-crank" approach for well-organized perturbative calculations based on Feynman diagrams. I review results and progress in modeling astrophysical gravitational wave sources with EFT, including recent work on gravitational radiation reaction and on tail effects from gravitational wave back-scattering among others. I briefly outline how to build an EFT and use Feynman diagrams for practical calculations. In addition, I discuss a crucial development for applying EFT to compact binary inspirals, which leverages work that naturally generalizes Lagrangian and Hamiltonian mechanics to generic systems having nonconservative processes.   

Surprising consequences of a positive cosmological constant

The study of isolated systems has been vastly successful in the context of vanishing cosmological constant, $\Lambda = 0$. However, there is no physically useful notion of asymptotics for the universe we inhabit with $\Lambda > 0$. The full non-linear framework is still under development, but some interesting results at the linearized level have been obtained. I will focus on the conceptual subtleties that arise at the linearized level and discuss the quadrupole formula for gravitational radiation as well as some recent developments.