Non-relativistic and Carrollian limits of Jackiw-Teitelboim gravity

We construct the non-relativistic and Carrollian versions of Jackiw-Teitelboim gravity. In the second order formulation, there are no divergences in the non-relativistic and Carrollian limits. Instead, in the first order formalism, some divergences can be avoided by starting from a relativistic BF theory with (A)dS2 × ℝ gauge algebra. We show how to define the boundary duals of the gravity actions using the method of non-linear realisations and suitable Inverse Higgs constraints. In particular, the non-relativistic version of the Schwarzian action is constructed in this way. We derive the asymptotic symmetries of the theory, as well as the corresponding conserved charges and Newton-Cartan geometric structure. Finally, we show how the same construction applies to the Carrollian case.

Superfluid Dynamics in Neutron Star Crusts: The Iordanskii Force and Chemical Gauge Covariance

We present a geometrical derivation of the relativistic dynamics of the superfluid inner crust of a neutron star. The resulting model is analogous to the Hall-Vinen-Bekarevich-Khalatnikov hydrodynamics for a single-component superfluid at finite temperature, but particular attention should be paid to the fact that some fraction of the neutrons is locked to the motion of the protons in nuclei. This gives rise to an ambiguity in the definition of the two currents (the normal and the superfluid one) on which the model is built, a problem that manifests itself as a chemical gauge freedom of the theory. To ensure chemical gauge covariance of the hydrodynamic model, the phenomenological equation of motion for a quantized vortex should contain an extra transverse force, that is the relativistic version of the Iordanskii force discussed in the context of superfluid Helium. Hence, we extend the mutual friction model of Langlois et al. (1998) to account for the possible presence of this Iordanskii-like force. Furthermore, we propose that a better understanding of the (still not completely settled) controversy around the presence of the Iordanskii force in superfluid Helium, as well as in neutron stars, may be achieved by considering that the different incompatible results present in the literature pertain to two, opposite, dynamical regimes of the fluid system.

Massive Nambu–Goldstone fermions and bosons for non-relativistic superconformal symmetry: Jackiw–Pi vortices in a trap

We discuss a supersymmetric extension of a non-relativistic Chern–Simons matter theory, known as the supersymmetric Jackiw–Pi model, in a harmonic trap. We show that the non-relativistic version of the superconformal symmetry, called the super-Schrödinger symmetry, is not spoiled by an external field including the harmonic potential. It survives as a modified symmetry whose generators have explicit time dependences determined by the strength of the trap, the rotation velocity of the system, and the fermion number chemical potential. We construct 1/3 Bogomol'nyi–Prasad–Sommerfield (BPS) states of trapped Jackiw–Pi vortices preserving part of the modified superconformal symmetry and discuss fluctuations around static BPS configurations. In addition to the bosonic massive Nambu–Goldstone modes, we find that there exist massive Nambu–Goldstone fermions associated with broken generators of the modified super-Schrödinger symmetry. Furthermore, we find that eigenmodes form supermultiplets of a modified supersymmetry preserved by the static BPS backgrounds. As a consequence of the modified supersymmetry, infinite towers of explicit spectra can be found for eigenmodes corresponding to bosonic and fermionic lowest Landau levels.

Causal Heat Conduction Contravening the Fading Memory Paradigm

We propose a causal heat conduction model based on a heat kernel violating the fading memory paradigm. The resulting transport equation produces an equation for the temperature. The model is applied to the discussion of two important issues such as the thermohaline convection and the nuclear burning (in)stability. In both cases, the behaviour of the system appears to be strongly dependent on the transport equation assumed, bringing out the effects of our specific kernel on the final description of these problems. A possible relativistic version of the obtained transport equation is presented.

Analytical solutions of linear and nonlinear Klein-Fock-Gordon equation

In this paper, we deal with some linear and nonlinear Klein-Fock-Gordon (KFG) equations, which is a relativistic version of the Schrödinger equation. The approximate analytical solutions are obtained by using the homotopy analysis method (HAM). The efficiency of the HAM is that it provides a practical way to control the convergence region of series solutions by introducing an auxiliary parameter }. Analytical results presented are in agreement with the existing results in open literature, which confirm the effectiveness of this method.

Hubble constant, lensing, and time delay in Te Ve S

The Hubble constant can be determined from the time delay of gravitationally lensed systems. We adopt Te Ve S as the relativistic version of Modified Newtonian Dynamics to study gravitational lensing phenomena and evaluate the Hubble constant from the derived time-delay formula. We test our method on observed quasar lensing published in the literature. Three candidates are suitable for our study, HE 2149-2745, FBQ J0951+2635, and SBS 0909+532.