Interplay between Spacetime Curvature, Speed of Light and Quantum Deformations of Relativistic Symmetries

Recent work showed that κ-deformations can describe the quantum deformation of several relativistic models that have been proposed in the context of quantum gravity phenomenology. Starting from the Poincaré algebra of special-relativistic symmetries, one can toggle the curvature parameter Λ, the Planck scale quantum deformation parameter κ and the speed of light parameter c to move to the well-studied κ-Poincaré algebra, the (quantum) (A)dS algebra, the (quantum) Galilei and Carroll algebras and their curved versions. In this review, we survey the properties and relations of these algebras of relativistic symmetries and their associated noncommutative spacetimes, emphasizing the nontrivial effects of interplay between curvature, quantum deformation and speed of light parameters.

$$ T\overline{T} $$ deformations of non-relativistic models

The light-cone gauge approach to $$ T\overline{T} $$ T T ¯ deformed models is used to derive the $$ T\overline{T} $$ T T ¯ deformed matrix nonlinear Schrödinger equation, the Landau-Lifshitz equation, and the Gardner equation. Properties of one-soliton solutions of the $$ T\overline{T} $$ T T ¯ deformed nonlinear Schrödinger and Korteweg-de Vries equations are discussed in detail. The NLS soliton exhibits the recently discussed phenomenon of widening/narrowing width of particles under the $$ T\overline{T} $$ T T ¯ deformation. However, whether the soliton’s size is increasing or decreasing depends not only on the sign of the deformation parameter but also on soliton and potential parameters. The $$ T\overline{T} $$ T T ¯ deformed KdV equation admits a one-parameter family of one-soliton solutions in addition to the usual velocity parameter. The extra parameter modifies the properties of the soliton, in particular, it appears in the dispersion relation.

Neutron star merger remnants

Binary neutron star mergers observations are a unique way to constrain fundamental physics and astrophysics at the extreme. The interpretation of gravitational-wave events and their electromagnetic counterparts crucially relies on general-relativistic models of the merger remnants. Quantitative models can be obtained only by means of numerical relativity simulations in $$3+1$$ 3 + 1 dimensions including detailed input physics for the nuclear matter, electromagnetic and weak interactions. This review summarizes the current understanding of merger remnants focusing on some of the aspects that are relevant for multimessenger observations.