Abstract: Axion stars, gravitationally bound states of low-energy axions, described by a field theory with potential energy f^2 m^2(1-Cos (A/f)) have a maximum mass allowed by gravitational stability. Weakly bound states obtaining this maximum mass have sufficiently large radii such that they are dilute, and as a result, they are well described by a leading-order expansion of the axion potential. Heavier states are susceptible to gravitational collapse. Inclusion of higher-order interactions, present in the full potential, can give qualitatively different results in the analysis of collapsing heavy states, as compared to the leading-order expansion. In this work, we find that collapsing axion stars are stabilized by repulsive interactions present in the full potential, providing evidence that such objects do not form black holes. These dense configurations, which are the endpoints of collapse, have extremely high binding energy, and as a result, quickly decay through number changing interactions.

On September 14, 2015, LIGO detectors picked up a gravitational wave signal coming from the merger of a binary black hole. This is the first direct detection of gravitational waves and the first observation of binary black hole and its merger. In this talk we will go over the key aspects of the discovery, and highlight some its implications for fundamental physics and astrophysics.

Recently, unexpected relations between unrelated physical quantities such as Hall viscosity, conductivity and angular momentum have been proposed for certain condensed matter systems with broken parity. We derive the quantum field theory Ward identities originated from area preserving as well as conformal transformations for relativistic as well as non-relativistic systems. The relations among these physical quantities depend on the symmetries of the system. A special cases yields the well known relation: Hall viscosity is half the angular momentum.

We introduce a new 2+1 dimensional topological current that is identically conserved and whose charge is equal to the Euler character of the two dimensional spacelike foliations. The existence of this current allows us to introduce new Chern-Simons-type terms in the effective field theories describing relativistic quantum Hall states and (2+1) dimensional superfluids. In the quantum Hall case, this current provides the natural relativistic generalization of the Wen-Zee term, required to characterize the shift and Hall viscosity in quantum Hall systems. For the superfluid case this term is required to have nonzero Hall viscosity and to describe superfluids with non s-wave pairing.