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The bumblebee model is an extension of the Einstein–Maxwell theory that allows for the spontaneous breaking of the Lorentz symmetry of the spacetime. In this paper, we study the quasinormal modes of the spherical black holes in this model that are characterized by a global monopole. We analyze the two cases with a vanishing cosmological constant or a negative one (the anti-de Sitter case). We find that the black holes are stable under the perturbation of a massless scalar field. However, both the Lorentz symmetry breaking and the global monopole have notable impacts on the evolution of the perturbation. The Lorentz symmetry breaking may prolong or shorten the decay of the perturbation according to the sign of the breaking parameter. The global monopole, on the other hand, has different effects depending on whether a nonzero cosmological constant presences: it reduces the damping of the perturbations for the case with a vanishing cosmological constant, but has little influence for the anti-de Sitter case.

We investigate the nonrotating neutron stars in f(T) gravity with f(T)=T+αT2, where T is the torsion scalar in the teleparallel formalism of gravity. In particular, we utilize the SLy and BSk family of equations of state for perfect fluid to describe the neutron stellar matter and search for the effects of the f(T) modification on the models of neutron stars. For positive α, the modification results in a smaller stellar mass in comparison to general relativity, while the neutron stars will contain larger amount of matter for negative α. Moreover, there seems to be an upper limit for the central density of the neutron stars with α>0, beyond which the effective f(T) fluid would have a steplike phase transition in density and pressure profiles, collapsing the numerical system. We obtain the mass–radius relations of the realistic models of neutron stars and subject them to the joint constraints from the observed massive pulsars PSR J0030+0451, PSR J0740+6620, and PSR J2215+5135, and gravitational wave events GW170817 and GW190814. For the neutron star model in f(T) gravity to be able to accommodate all the mentioned data, the model parameter α needs to be smaller than -4.295, -6.476, -4.4, and -2.12 (in the unit of G2M⊙2/c4) for SLy, BSk19, BSk20, and BSk21 equations of state, respectively. If one considers the unknown compact object in the event GW190814 not to be a neutron star and hence excludes this dataset, the constraints can be loosened to α<-0.594, -3.5, 0.4 and 1.9 (in the unit of G2M⊙2/c4), respectively.

We propose a new model for the viscosity of cosmic matters, which can be applied to different epochs of the universe. Using this model, we include the bulk viscosities as practical corrections to the perfect fluid models of the baryonic and dark matters since the material fluids in the real world may have viscosities due to thermodynamics. Such inclusion is put to the test within the framework of f(T) gravity that is proved to be successful in describing the cosmic acceleration, where T denotes the torsion scalar. We perform an observational fit to our model and constrain the cosmological and model parameters by using various latest cosmological datasets. Based on the fitting result, we discuss several cosmological implications including the dissipation of matters, the evolutionary history of the universe, f(T) modification as an effective dark energy, and the Hubble tension problem. The corresponding findings are (i) The late time dissipation will make the density parameters of the matters vanish in the finite future. Moreover, the density ratio between the baryonic and dark matters will change over time. (ii) The radiation dominating era, matter dominating era and the accelerating era can be recovered and the model can successfully describe the known history of the universe. (iii) The f(T) modification is the main drive of the acceleration expansion and currently mimics a phantom-like dark energy. But the universe will eventually enter a de Sitter expansion phase. (iv) The Hubble tension between local and global observations can be significantly alleviated in our model.

In the previous paper, we have constructed two f ( T ) models with non-minimal torsion–matter coupling extension, which are successful in describing the evolution history of the Universe including the radiation-dominated era, the matter-dominated era, and the present accelerating expansion. Meantime, the significant advantage of these models is that they could avoid the cosmological constant problem of Λ CDM. However, the non-minimal coupling between matter and torsion will affect the tests of the Solar system. In this paper, we study the effects of the Solar system in these models, including the gravitation redshift, geodetic effect and perihelion precession. We find that Model I can pass all three of the Solar system tests. For Model II, the parameter is constrained by the uncertainties of the planets’ estimated perihelion precessions.

We investigate the cosmological implications of a phantom dark energy model with bulk viscosity. We explore this model as a possible way to resolve the big rip singularity problem that plagues the phantom models. We use the latest type Ia supernova and Hubble parameter data to constrain the model parameters and find that the data favor a significant bulk viscosity over a non-constant potential term for the phantom field. We perform a dynamical analysis of the model and show that the only stable and physical attractor corresponds to a phantom-dominated era with a total equation of state that can be greater than - 1 due to the viscosity. We also study the general effect of viscosity on the phantom field and the late time evolution of the universe. We apply the statefinder diagnostic to the model and find that it approaches a nearby fixed point asymptotically, indicating that the universe can escape the big rip singularity with the presence of bulk viscosity. We conclude that bulk viscosity can play an important role in affecting the late-time behavior as well as alleviating the singularity problem of the phantom universe.

In this paper we analyze the traversability of static and evolving Schwarzschild-Anti-de Sitter wormholes. The wormhole metric under consideration is not asymptotically flat. Hence one can only embed this metric into the Euclidean space for a limited radius r max . For r > r max , an exterior vacuum spacetime should be matched to the wormhole spacetime. In the framework of f ( T ) gravities, we discuss the null energy condition that the matter supporting the wormhole should satisfy and find that the nontrivial form of f ( T ) is necessary. For the wormholes to be suitable for human to traverse, we consider the tidal force that a traveler would have felt during his trip. This leads to an upper bound of the traveler’s velocity. Utilizing the velocity allowed, we will estimate the travel time through the wormhole. In the evolving cases, the wormhole should not be expanding too fast, otherwise the traveler may not be able to arrive at the other side of the wormhole. Besides this, for static wormholes, we briefly discuss the geodesics in the plane θ = π / 2 .

The bumblebee model is an extension of the Einstein-Maxwell theory that allows for the spontaneous breaking of the Lorentz symmetry of the spacetime. In this paper, we study the quasinormal modes of the spherical black holes in this model that are characterized by a global monopole. We analyze the two cases with a vanishing cosmological constant or a negative one (the anti-de Sitter case). We find that the black holes are stable under the perturbation of a massless scalar field. However, both the Lorentz symmetry breaking and the global monopole have notable impacts on the evolution of the perturbation. The Lorentz symmetry breaking may prolong or shorten the decay of the perturbation according to the sign of the breaking parameter. The global monopole, on the other hand, has different effects depending on whether a nonzero cosmological constant presences: it reduces the damping of the perturbations for the case with a vanishing cosmological constant, but has little influence for the anti-de Sitter case.

We investigate the cosmological implications of a phantom dark energy model with bulk viscosity. We explore this model as a possible way to resolve the big rip singularity problem that plagues the phantom models. We use the latest type Ia supernova and Hubble parameter data to constrain the model parameters and find that the data favor a significant bulk viscosity over a non-constant potential term for the phantom field. We perform a dynamical analysis of the model and show that the only stable and physical attractor corresponds to a phantom-dominated era with a total equation of state that can be greater than \\(-1\\) due to the viscosity. We also study the general effect of viscosity on the phantom field and the late time evolution of the universe. We apply the statefinder diagnostic to the model and find that it approaches a nearby fixed point asymptotically, indicating that the universe can escape the big rip singularity with the presence of bulk viscosity. We conclude that bulk viscosity can play an important role in affecting the late-time behavior as well as alleviating the singularity problem of the phantom universe.

An exact Kerr-like solution has been obtained recently in Einstein-bumblebee gravity model where Lorentz symmetry is spontaneously broken. In this paper, we investigate the superradiant instability of the Kerr-like black hole under the perturbation of a massive scalar field. We find the Lorentz breaking parameter \\(L\\) does not affect the superradiance regime or the regime of the bound states. However, since \\(L\\) appears in the metric and its effect cannot be erased by redefining the rotation parameter \\(\\tilde{a}=\\sqrt{1+L}a\\), it indeed affects the bound state spectrum and the superradiance. We calculate the bound state spectrum via the continued-fraction method and show the influence of \\(L\\) on the maximum binding energy and the damping rate. The superradiant instability could occur since the superradiance condition and the bound state condition could be both satisfied. Compared with Kerr black hole, the nature of the superradiant instability of this black hole depends non-monotonously not only on the rotation parameter of the black hole \\(\\tilde{a}\\) and the product of the black hole mass \\(M\\) and the field mass \\(\\mu\\), but also on the Lorentz breaking parameter \\(L\\). Through the Monte Carlo method, we find that for \\(l=m=1\\) state the most unstable mode occurs at \\(L=-0.79637\\), \\(\\tilde{a}/M=0.99884\\) and \\(M\\mu=0.43920\\), with the maximum growth rate of the field \\(\\omega_{I}M=1.676\\times10^{-6}\\), which is about 10 times of that in Kerr black hole.

The restoration of spin connection clarifies the long known local Lorentz invariance problem in telelparallel gravities. It is considered now that any tetrad together with the associated spin connection can be equally utilized. Among the tetrads there is a particular one, namely proper tetrad, in which all the spurious inertial effects are removed and the spin connection vanishes. A specific tetrad was proposed in the literature for spherically symmetric cases, which has been used in regularizing the action, as well as in searching solutions in various scenarios. We show in this paper that the this tetrad is not the unique choice for the proper tetrad. We construct a new tetrad that can be considered as the proper one, and it will lead to different behaviors of the field equation and results in different solutions. With this proper tetrad, it is possible to find solutions to teleparallel gravities in the strong field regime, which may have physical applications. In the flat spacetime limit, the new tetrad coincides with the aforementioned one.