Strong Gravity

I describe recent work with with Stefan Hollands that establishes a new criterion for the dynamical stability of black holes in $D \geq 4$ spacetime dimensions in general relativity with respect to axisymmetric perturbations: Dynamic stability is equivalent to the positivity of the canonical energy, $\mathcal E$, on a subspace of linearized solutions that have vanishing linearized ADM mass, momentum, and angular momentum at infinity and satisfy certain gauge conditions at the horizon.  We further show that $\mathcal E$ is related to the second order variations of mass, angular momentum, and horizon area by $\mathcal E = \delta^2 M - \sum_i \Omega_i \delta^2 J_i - (\kappa/8\pi) \delta^2 A$, thereby establishing a close connection between dynamic stability and thermodynamic stability.

Thermodynamic instability of a family of black holes need not imply dynamic instability because the perturbations towards other members of the family will not, in general, have vanishing linearized ADM mass and/or angular momentum. However, we prove that all black branes corresponding to
thermodynmically unstable black holes are dynamically unstable, as conjectured by Gubser and Mitra. We also prove that positivity of $\mathcal E$ is equivalent to the satisfaction of a ``local Penrose inequality,'' thus showing that satisfaction of this local Penrose inequality is necessary and sufficient for dynamical stability.

Spins play a major role in the strong-field dynamics of
black-hole binaries and their gravitational-wave emission. By detecting spin
effects in the waveforms, existing and future gravitational-wave detectors
therefore provide a natural way to test gravity in strong-field, highly
dynamical regimes.

In the first part of my talk, I will show that the
inclusion of the spins in the gravitational templates for future space-based
detectors will permit testing scenarios for the formation and cosmological
evolution of supermassive black holes, and possibly shed light on models of
galaxy formation. In the second part, I will show that the effective-one-body
(EOB) model provides an efficient way to account for spin effects in both the
dynamics and waveforms, by combining information from post-Newtonian theory,
the self-force formalism, and numerical-relativity simulations.

We discuss well-posed initial-boundary value formulations
in general relativity. These formulations allow us to construct solutions of
Einstein's field equations inside a cylindrical region, given suitable initial
and boundary data. We analyze the restrictions on the boundary data that result
from the requirement of constraint propagation and the minimization of spurious
reflections, and choosing harmonic coordinates we show how to cast the problem
into well-posed form. Then, we consider the particular case where the boundary
represents null infinity of an asymptotically flat spacetime. Here, the rôle of
the boundary conditions is to provide adequate regularity and gauge conditions
at infinity.

As an application of our setup we mention ongoing work on
the computation of quasi-stationary scalar field configurations on a
non-rotating supermassive black hole background.

In this talk I will focus on two topics concerning compact binaries that involve a neutron star companion: a) the fate of and observable signatures from merging white dwarf-neutron star (WDNS) binaries, and b) electromagnetic signals from black hole - neutron star (BHNS) binaries.WDNS systems - the neglected child among compact binaries - generate detectable gravitational waves (GWs) and may also generate observable electromagnetic (EM) signals. One of the most fascinating aspects about these systems is that they are known to exist, but the final fate of massive, merged WDNSs remnants is currently work in progress. Determining the fate of WDNS remnants will be important for interpreting observations from future transient surveys. I will review recent work that provides insight into the physics of WDNSs remnants. Black hole - neutron star systems are among the most promising sources for gravitational waves, and at the same time also possible sources of detectable precursor and aftermath EM signals. I will present recent the results from general relativistic force-free simulations of binary BHNSs and a type of EM precursor signatures expected from these systems.