On September 14, 2015 at 09:50:45 UTC the two detectors of the Laser Interferometer Gravitational-Wave Observatory simultaneously observed a transient gravitational-wave signal. The signal sweeps upwards in frequency from 35 to 250 Hz with a peak gravitational-wave strain of 1.0×10(-21). It matches the waveform predicted by general relativity for the inspiral and merger of a pair of black holes and the ringdown of the resulting single black hole. The signal was observed with a matched-filter signal-to-noise ratio of 24 and a false alarm rate estimated to be less than 1 event per 203,000 years, equivalent to a significance greater than 5.1σ. The source lies at a luminosity distance of 410(-180)(+160)  Mpc corresponding to a redshift z=0.09(-0.04)(+0.03). In the source frame, the initial black hole masses are 36(-4)(+5)M⊙ and 29(-4)(+4)M⊙, and the final black hole mass is 62(-4)(+4)M⊙, with 3.0(-0.5)(+0.5)M⊙c(2) radiated in gravitational waves. All uncertainties define 90% credible intervals. These observations demonstrate the existence of binary stellar-mass black hole systems. This is the first direct detection of gravitational waves and the first observation of a binary black hole merger.

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The Observation of Gravitational Waves from a Binary Black Hole Merger

Massive gravity has seen a resurgence of interest due to recent progress which has overcome its traditional problems, yielding an avenue for addressing important open questions such as the cosmological constant naturalness problem. The possibility of a massive graviton has been studied on and off for the past 70 years. During this time, curiosities such as the van Dam, Veltman, and Zakharov (vDVZ) discontinuity and the Boulware-Deser ghost were uncovered. These results are rederived in a pedagogical manner and the St\"uckelberg formalism to discuss them from the modern effective field theory viewpoint is developed. Recent progress of the last decade is reviewed, including the dissolution of the vDVZ discontinuity via the Vainshtein screening mechanism, the existence of a consistent effective field theory with a stable hierarchy between the graviton mass and the cutoff, and the existence of particular interactions which raise the maximal effective field theory cutoff and remove the ghosts. In addition, some peculiarities of massive gravitons on curved space, novel theories in three dimensions, and examples of the emergence of a massive graviton from extra dimensions and brane worlds are reviewed.

Theoretical Aspects of Massive Gravity

Treating the cosmological constant as a thermodynamic pressure and its conjugate quantity as a thermodynamic volume, we reconsider the critical behaviour of charged AdS black holes. We complete the analogy of this system with the liquid-gas system and study its critical point, which occurs at the point of divergence of specific heat at constant pressure. We calculate the critical exponents and show that they coincide with those of the Van der Waals system.

P − V criticality of charged AdS black holes

We review the problem of dark energy, including a survey of theoretical models and some aspects of numerical studies

Dark Energy

Conformal field theories have been long known to describe the fascinating universal physics of scale invariant critical points. They describe continuous phase transitions in fluids, magnets, and numerous other materials, while at the same time sit at the heart of our modern understanding of quantum field theory. For decades it has been a dream to study these intricate strongly coupled theories nonperturbatively using symmetries and other consistency conditions. This idea, called the conformal bootstrap, saw some successes in two dimensions but it is only in the last ten years that it has been fully realized in three, four, and other dimensions of interest. This renaissance has been possible both due to significant analytical progress in understanding how to set up the bootstrap equations and the development of numerical techniques for finding or constraining their solutions. These developments have led to a number of groundbreaking results, including world record determinations of critical exponents and correlation function coefficients in the Ising and $O(N)$ models in three dimensions. This article will review these exciting developments for newcomers to the bootstrap, giving an introduction to conformal field theories and the theory of conformal blocks, describing numerical techniques for the bootstrap based on convex optimization, and summarizing in detail their applications to fixed points in three and four dimensions with no or minimal supersymmetry.

The Conformal Bootstrap: Theory, Numerical Techniques, and Applications

Horndeski gravity as D → 4 limit of Gauss-Bonnet

We study black hole solutions in extended gravities with higher-order curvature terms, including conformal and Einstein-Weyl gravities. In addition to the usual anti-de Sitter (AdS) vacuum, the theories admit Lifshitz and Schr\"odinger vacua. The AdS black hole in conformal gravity contains an additional parameter over and above the mass, which may be interpreted as a massive spin-2 hair. By considering the first law of thermodynamics, we find that it is necessary to introduce an associated additional intensive/extensive pair of thermodynamic quantities. We also obtain new Lifshitz black holes in conformal gravity and study their thermodynamics. We use a numerical approach to demonstrate that AdS black holes beyond the Schwarzschild-AdS solution exist in Einstein-Weyl gravity. We also demonstrate the existence of asymptotically Lifshitz black holes in Einstein-Weyl gravity. The Lifshitz black holes arise at the boundary of the parameter ranges for the AdS black holes. Outside the range, the solutions develop naked singularities. The asymptotically AdS and Lifshitz black holes provide an interesting phase transition, in the corresponding boundary field theory, from a relativistic Lorentzian system to a nonrelativistic Lifshitz system.

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AdS and Lifshitz black holes in conformal and Einstein-Weyl gravities

We study the structure of the phase space in Horava-Lifshitz theory. With the constraints derived from the action, the phase space is described by five fields, thus there is a lack of canonical structure. The Poisson brackets of the Hamiltonian density do not form a closed structure, resulting in many new constraints. Taking these new constraints into account, it appears that there is no degree of freedom left, or the phase space is reduced to one with an odd number of fields.

A trouble with Hořava-Lifshitz gravity

We obtain spherically-symmetric and $ {{\mathbb{R}}^2} $
 -symmetric dyonic black holes that are asymptotic to anti-de Sitter space-time (AdS), which are solutions in maximal gauged four-dimensional supergravity, with just one of the U(1) fields carrying both the electric and magnetic charges (Q, P). We study the thermodynamics, and find that the usually-expected first law does not hold unless P = 0, Q = 0 or P = Q. For general values of the charges, we find that the first law requires a modification with a new pair of thermodynamic conjugate variables. We show that they describe the scalar hair that breaks some of the asymptotic AdS symmetries.

AdS dyonic black hole and its thermodynamics

Higher-order curvature corrections involving the conformally invariant Weyl-squared action have played a role in two recent investigations of four-dimensional gravity: in critical gravity, where they are added to the standard cosmological Einstein-Hilbert action with a coefficient tuned to make the massive ghostlike spin-2 excitations massless, and in a pure Weyl-squared action considered by Maldacena, where the massive spin-2 modes are removed by the imposition of boundary conditions. We exhibit the connections between the two approaches, and we also generalize critical gravity to a wider class of Weyl-squared modifications to cosmological Einstein gravity where one can eliminate the massive ghostlike spin-2 modes by means of boundary conditions. The cosmological constant plays a crucial role in the discussion, since there is then a "window'' of negative mass-squared spin-2 modes around AdS(4) that are not tachyonic. We also construct analogous conformal and nonconformal gravities in six dimensions.

Yi Pang

Papers

Horndeski gravity as D → 4 limit of Gauss-Bonnet

AdS and Lifshitz black holes in conformal and Einstein-Weyl gravities

A trouble with Hořava-Lifshitz gravity

AdS dyonic black hole and its thermodynamics

Conformal gravity and extensions of critical gravity