Self-interactions can stabilize excited boson stars

We study the time evolution of spherical, excited (i.e. nodeful) boson star models. We consider a model including quartic self-interactions, controlled by a coupling Λ. Performing non-linear simulations of the Einstein-(complex)-Klein-Gordon system, using as initial data equilibrium boson stars solutions of that system, we assess the impact of Λ in the stability properties of the boson stars. In the absence of self-interactions (Λ = 0), we observe the known behaviour that the excited stars in the (candidate) stable branch decay to a non-excited star without a node; however, we show that for large enough values of the self-interactions coupling, these excited stars do not decay (up to timescales of about t ∼104). The stabilization of the excited states for large enough self-interactions is further supported by evidence that the nodeful states dynamically form through the gravitational cooling mechanism, starting from dilute initial data. Our results support the healing power (against dynamical instabilities) of self-interactions, recently unveiled in the context of the non-axisymmetric instabilities of spinning boson stars.

Numerical Scheme Based on the Implicit Runge-Kutta Method and Spectral Method for Calculating Nonlinear Hyperbolic Evolution Equations

A numerical scheme for nonlinear hyperbolic evolution equations is made based on the implicit Runge-Kutta method and the Fourier spectral method. The detailed discretization processes are discussed in the case of one-dimensional Klein-Gordon equations. In conclusion, a numerical scheme with third-order accuracy is presented. The order of total calculation cost is O(Nlog2N). As a benchmark, the relations between numerical accuracy and discretization unit size and that between the stability of calculation and discretization unit size are demonstrated for both linear and nonlinear cases.

Central potential effects induced by Lorentz symmetry violation on modified quantum oscillator field

In this paper, effects of Lorentz symmetry violation determined by a tensor field [Formula: see text] out of the Standard Model Extension on a modified quantum oscillator field in the presence of Cornell-type scalar potential are analyzed. We first introduced a scalar potential [Formula: see text] by modifying the mass square term via transformation [Formula: see text] in the Klein–Gordon equation, and then replace the momentum operator [Formula: see text], where [Formula: see text] is an arbitrary function other than [Formula: see text] to study the modified Klein–Gordon oscillator. We solve the wave equation and obtain the analytical bound-states solutions and see the dependence of oscillator frequency [Formula: see text] on the quantum numbers [Formula: see text] as well as on Lorentz-violating parameters with the potential which shows a quantum effect.

Symmetries and Covariant Poisson Brackets on Presymplectic Manifolds

As the space of solutions of the first-order Hamiltonian field theory has a presymplectic structure, we describe a class of conserved charges associated with the momentum map, determined by a symmetry group of transformations. A gauge theory is dealt with by using a symplectic regularization based on an application of Gotay’s coisotropic embedding theorem. An analysis of electrodynamics and of the Klein–Gordon theory illustrate the main results of the theory as well as the emergence of the energy–momentum tensor algebra of conserved currents.

Gravitational decoupling of generalized Horndeski hybrid stars

Gravitational decoupled compact polytropic hybrid stars are here addressed in generalized Horndeski scalar-tensor gravity. Additional physical properties of hybrid stars are scrutinized and discussed in the gravitational decoupling setup. The asymptotic value of the mass function, the compactness, and the effective radius of gravitational decoupled hybrid stars are studied for both cases of a bosonic and a fermionic prevalent core. These quantities are presented and discussed as functions of Horndeski parameters, the decoupling parameter, the adiabatic index, and the polytropic constant. Important corrections to general relativity and generalized Horndeski scalar-tensor gravity, induced by the gravitational decoupling, comply with available observational data. Particular cases involving white dwarfs, boson stellar configurations, neutron stars, and Einstein–Klein–Gordon solutions, formulated in the gravitational decoupling context, are also scrutinized.