Minimal Massive Gravity: Conserved Charges, Excitations and the Chiral Gravity Limit

We find the excitations and construct the conserved charges ( mass and angular momentum) of the recently found Minimal Massive Gravity (MMG) in 2+1 dimensions in asymptotically Anti-de Sitter (AdS) spacetimes. The field equation of the theory does not come from an action and hence lacks the required Bianchi Identity needed to define conserved charges. But the theory, which also provides a healthy extension of the Topologically Massive Gravity in the bulk and boundary of spacetime, does admit conserved charges for metric that are solutions. Our construction is based on background Killing vectors and imperative to provide physical meaning to the integration constants in the black hole type metrics. We also study the chiral gravity limit of MMG.Comment: 9 pages, reference added, typos correcte

Bulk and Boundary Unitary Gravity in 3D: MMG2_2

We construct a massive spin-2 theory in 2+1 dimensions that is immune to the bulk-boundary unitarity conflict in anti-de Sitter space and hence amenable to holography. The theory is an extension of Topologically Massive Gravity, just like the recently found Minimal Massive Gravity (MMG), but it has two massive helicity modes instead of a single one. The theory admits all the solutions of TMG with a redefined topological parameter. We calculate the Shapiro time-delay and show that flat-space (local) causality is not violated. We show that there is an interesting relation between the theory we present here (which we call MMG$_2$), MMG and the earlier New Massive Gravity (NMG): Namely, field equations of these theories are non-trivially related. We study the bulk excitations and boundary charges of the conformal field theory that could be dual to gravity. We also find the chiral gravity limit for which one of the massive modes becomes massless. The virtue of the model is that one does not have to go to the chiral limit to achieve unitarity in the bulk and on the boundary and the log-terms that appear in the chiral limit and cause instability do not exist in the generic theory.Comment: 6 pages, Causality discussion and related references are added, matches the published versio

Stern-Gerlach Experiment with Higher Spins

We analyze idealized sequential Stern-Gerlach experiments with higher spin particles. This analysis serves at least two purposes: The widely discussed spin-1/2 case leads to some misunderstandings which hopefully is removed by the higher spin discussion. Secondly, Wigner rotation matrices for generic spins become conceptually more transparent with this physical example. We also give compact formulas for the probabilities in terms of the angle between the sequential SG apparatuses for generic spins. We work out the spin-$1/2$, spin-$1$ and spin-$2$ cases explicitly. Since there are some confusing issues regarding the actual experiment, we also compile a "facts and fiction" section on the SG experiments.Comment: 10 pages, 5 figures, the published version does not have the section on the spin-2 discussio

Chern-Simons Modified General Relativity: Conserved charges

We construct the conserved charges (mass and angular momentum) of the Chern-Simons modified General Relativity in asymptotically flat and Anti-de Sitter (AdS) spacetimes. Our definition is based on background Killing symmetries and reduces to the known expressions in the proper limits.Comment: 9 pages, References added, version to appear in Phys. Rev.

Particle Content of Quadratic and f(Rμνσρ)f(R_{\mu\nu\sigma \rho}) Theories in (A)dS(A)dS

We perform a complete decoupling of the degrees of freedom of quadratic gravity and the generic $f (R_{\mu\nu\sigma \rho})$ theory about any one of their possible vacua, i.e. maximally symmetric solution, find the masses of the spin-2 and spin-0 modes in explicit forms.Comment: 7 pages, reference added; v3 typos corrected, to appear in PRD Rapid Communicatio

Higgs Mechanism for New Massive Gravity and Weyl Invariant Extensions of Higher Derivative Theories

New Massive Gravity provides a non-linear extension of the Fierz-Pauli mass for gravitons in 2+1 dimensions. Here we construct a Weyl invariant version of this theory. When the Weyl symmetry is broken, the graviton gets a mass in analogy with the Higgs mechanism. In (anti)-de Sitter backgrounds, the symmetry can be broken spontaneously, but in flat backgrounds radiative corrections, at the two loop level, break the Weyl symmetry a la Coleman-Weinberg mechanism. We also construct the Weyl invariant extensions of some other higher derivative models, such as the Gauss-Bonnet theory (which reduces to the Maxwell theory in three dimensions) and the Born-Infeld type gravities.Comment: 9 pages, typos fixed, minor corrections, to appear in Phys. Rev.

Graviton Mass and Memory

Gravitational memory, a residual change, arises after a finite gravitational wave pulse interacts with free masses. We calculate the memory effect in massive gravity as a function of the graviton mass $(m_g)$ and show that it is discretely different from the result of general relativity: the memory is reduced not just via the usual expected Yukawa decay but by a numerical factor which survives even in the massless limit. For the strongest existing bounds on the graviton mass, the memory is essentially wiped out for the sources located at distances above 10 Mpc. On the other hand, for the weaker bounds found in the LIGO observations, the memory is reduced to zero for distances above 0.1 Pc. Hence, we suggest that careful observations of the gravitational wave memory effect can rule out the graviton mass or significantly bound it. We also show that adding higher curvature terms reduces the memory effect.Comment: 6 pages, matches the published versio