New Coarse-Grained Models for Loop Quantum Gravity

Researchers have developed a family of effective theories that act as coarse-grained models for canonical loop quantum gravity (LQG). These models are designed to facilitate the study of the continuum limit and the derivation of phenomenological models within the LQG framework. Each effective theory is defined by two key parameters and comprises a Hilbert space of coarse states, along with an effective Hamiltonian operator. This approach seeks to simplify the inherent complexity of LQG, allowing for a more manageable analysis of its fundamental properties. The construction of the coarse Hilbert spaces relies on a systematic coarse-graining procedure applied to spin network states, which are the fundamental structures in LQG representing the quantum geometry of spacetime. The effective Hamiltonians, in turn, are obtained by analyzing the interplay between this coarse-graining procedure and the action of various Hamiltonian operators already defined in loop quantum gravity. This approach allows capturing the essential properties of the system at larger scales, while disregarding fine details at smaller scales. Furthermore, the work presents a detailed prescription for implementing a non-perturbative renormalization framework for these coarse-grained models. The renormalization flow equations have been explicitly derived, which is crucial for understanding how the system's properties change with scale. This renormalization framework is fundamental for addressing the problem of the continuum limit in quantum gravity, where the quantum theory of spacetime is expected to connect with classical general relativity at large distances. The ability to study the emergence of the continuum is a vital step towards validating and understanding LQG as a complete theory of quantum gravity.

Photon Rockets with Cosmological Constant and Gravitational Radiation

Researchers have investigated the existence of asymptotic gravitational radiation in pure-radiation Robinson-Trautman metrics, which describe "photon rockets" with point, string, and sheet sources. The study incorporates a cosmological constant (Λ) of arbitrary sign, extending previous work that focused on the Λ=0 case. The primary goal was to determine the conditions under which these systems emit or do not emit gravitational radiation at infinity, using the asymptotic super-Poynting vector as a criterion. For point sources, it was confirmed that the Kinnersley rocket is the only one without gravitational radiation, a result already known for Λ=0 and which holds for Λ≠0. However, for string and sheet sources, the study reveals new configurations where gravitational radiation can be absent. This distinction between source types is crucial for understanding the dynamics of these systems in a universe with a cosmological constant. The criteria for the absence of gravitational radiation differ depending on the sign of Λ. For Λ>0, the absence of radiation is characterized by the vanishing of the canonical asymptotic super-Poynting vector, computed with respect to the unit normal to scri (null infinity). In contrast, for Λ<0, the appropriate criterion is the vanishing of the components normal to scri of the asymptotic super-Poynting vectors associated with any unit timelike vector tangent to scri, or, equivalently, the proportionality between the Cotton-York tensor and the holographic stress tensor at scri. Explicit examples of metrics have been provided where these tensors commute, but gravitational radiation persists because they are not proportional. Furthermore, the principal null directions of the rescaled Weyl tensor at scri have been determined for both signs of Λ, relating their geometry to the tensorial criteria for gravitational radiation.