We investigate the nonrotating neutron stars in $f(T)$ gravity with $f(T)=T+alpha T^2$, 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 $alpha$, the modification results in a stronger gravitation exerted on the stellar matter, leading to a smaller stellar mass in comparison to general relativity. Moreover, there seems to be an upper limit for the central density of the neutron stars with $alpha>0$, beyond which the effective $f(T)$ fluid would have a steplike phase transition in density and pressure profiles, collapsing the numerical system. For negative $alpha$, the $f(T)$ modification provides additional support for neutron stars to contain larger amount of matter. 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 BSk19 equation of state, the neutron star model in $f(T)$ gravity can accommodate all the mentioned data when $alphale 3.5 G^2M_odot^2/c^4$. For BSk20, BSk21 and SLy equations of state, the observational data constrain the model parameter $alpha$ to be negative. If one considers the unknown compact object in the event GW190814 not to be a neutron star and hence excludes this dataset, the constraints for BSk20 and BSk21 models can be loosened to $alphale 0.4 G^2M_odot^2/c^4$ and $alphale 1.9 G^2M_odot^2/c^4$, respectively.
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 superradiance instability of the Kerr-like black hole under the perturbation
of a massive scalar field. We find the Lorentz breaking parameter $L$ affects superradiance regime but not the regime of the bound states. 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 superradiance 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 superradiance instability of this black hole depends non-monotonously not only on the rotation speed of the black hole $a$ 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 $L=-0.79637$, $a/M=2.213$ and $Mmu=0.439$, with the maximum growth rate of the field $omega_{I}M=1.676times10^{-6}$, which is about 10 times of that in Kerr black hole.
General relativity can be formulated equivalently with a non-Riemannian geometry that associates with an affine connection of nonzero nonmetricity $Q$ but vanishing curvature $R$ and torsion $T$. Modification based on this description of gravity
generates the $f(Q)$ gravity. In this work we explore the application of $f(Q)$ gravity to the spherically symmetric configurations. We discuss the gauge fixing and connections in this setting. We demonstrate the effects of $f(Q)$ by considering the external and internal solutions of compact stars. The external background solutions for any regular form of $f(Q)$ coincide with the corresponding solutions in general relativity, i.e., the Schwarzschild-de Sitter solution and the Reissner-Nordstrom-de Sitter solution with an electromagnetic field. For internal structure, with a simple model $f(Q)=Q+alpha Q^2$ and a polytropic equation of state, we find that a negative modification ($alpha<0$) provides support to more stellar masses while a positive one ($alpha>0$) reduces the amount of matter of the star.
Conformal invariance can ameliorate or eliminate the singularities residing in the black holes, and may still exist in the strong gravity regimes close to these black holes. In this paper, we try to probe this conformal invariance by looking into t
he wave absorption and scattering by the nonsingular static spherical black holes. The partial and total absorption cross section, as well as the differential scattering cross section, are presented for black holes with different choices of conformal parameters. Although the photon trajectories are unchanged from the Schwarzschild case since the spacetimes are conformally related, the wave optics are affected by the conformal parameters. As a result, the absorption of waves generally increases with the conformal parameters, while the shadow of the black holes remains the same as the Schwarzschild case. Moreover, the peaks in the oscillatory pattern of scattering shift towards smaller observing angles as the conformal parameters grows, while the widths of the glory peaks do not show sensitive dependence. The unique signature of the wave absorption and scattering by the nonsingular static spherical black holes in conformal gravity thus can serve to distinguish themselves from the Schwarzschild in the low frequency regime, and from other spherical black holes of alternative gravities in the high frequency limit and glory peaks.
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 ther
e 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.
Wormholes are hypothetical tunnels that connect remote parts of spacetime. In General Relativity, wormholes are threaded by exotic matter that violates the energy conditions. In this work, we consider wormholes threaded by nonexotic matter in nonmini
mal torsion-matter coupling $f(T)$ gravity. We find that the nonminimal torsion-matter coupling can indeed hold the wormhole open. However, from geometric point of view, for the wormhole to have asymptotic flatness, the coupling matter density must falloff rapidly at large radius, otherwise the physical wormhole must be finite due to either change of metric signature or lack of valid embedding. On the other hand, the matter source supporting the wormhole can satisfy the null energy condition only in the neighborhood of the throat of the wormhole. Therefore, the wormhole in the underlying model has finite sizes and cannot stretch to the entire spacetime.
The currently accelerated expansion of our Universe is unarguably one of the most intriguing problems in todays physics research. Two realistic non-minimal torsion-matter coupling $f(T)$ models have been established and studied in our previous papers
[Phys. Rev. D92, 104038(2015) and Eur. Phys. J. C77, 504(2017)] aiming to explain this dark energy problem. In this paper, we study the generalized power-law torsion-matter coupling $f(T)$ model. Dynamical system analysis shows that the three expansion phases of the Universe, i.e. the radiation dominated era, the matter dominated era and the dark energy dominated era, can all be reproduced in this generalized model. By using the statefinder and $Om$ diagnostics, we find that the different cases of the model can be distinguished from each other and from other dark energy models such as the two models in our previous papers, $Lambda$CDM, quintessence and Chaplygin gas. Furthermore, the analyses also show that all kinds of generalized power-law torsion-matter coupling model are able to cross the $w=-1$ divide from below to above, thus the decrease of the energy density resulting from the crossing of $w$ will make the catastrophic fate of the Universe avoided and a de Sitter expansion fate in the future will be approached.
It is known that the Cardassian universe is successful in describing the accelerated expansion of the universe, but its dynamical equations are hard to get from the action principle. In this paper, we establish the connection between the Cardassian u
niverse and $f(T, mathcal{T})$ gravity, where $T$ is the torsion scalar and $mathcal{T}$ is the trace of the matter energy-momentum tensor. For dust matter, we find that the modified Friedmann equations from $f(T, mathcal{T})$ gravity can correspond to those of Cardassian models, and thus, a possible origin of Cardassian universe is given. We obtain the original Cardassian model, the modified polytropic Cardassian model, and the exponential Cardassian model from the Lagrangians of $f(T,mathcal{T})$ theory. Furthermore, by adding an additional term to the corresponding Lagrangians, we give three generalized Cardassian models from $f(T,mathcal{T})$ theory. Using the observation data of type Ia supernovae, cosmic microwave background radiation, and baryon acoustic oscillations, we get the fitting results of the cosmological parameters and give constraints of model parameters for all of these models.
Using the classical top-hat profile, we study the non-linear growth of spherically symmetric density perturbation and structure formation in $f(T)$ gravities. In particular, three concrete models, which have been tested against the observation of lar
ge-scale evolution and linear perturbation of the universe in the cosmological scenario, are investigated in this framework, covering both minimal and nonminimal coupling cases of $f(T)$ gravities. Moreover, we consider the virialization of the overdense region in the models after they detach from the background expanding universe and turn around to collapse. We find that there are constraints in the magnitude and occurring epoch of the initial perturbation. The existence of these constraints indicates that a perturbation that is too weak or occurs too late will not be able to stop the expanding of the overdense region. The illustration of the evolution of the perturbation shows that in $f(T)$ gravities, the initial perturbation within the constraints can eventually lead to clustering and form structure. The evolution also shows that nonminimal coupling models collapse slower than the minimal coupling one.
In the previous paper, we have constructed two $f(T)$ models with nonminimal 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 $Lambda$CDM. However, the nonminimal coupling between matter and torsion will affect the tests of Solar system. In this paper, we study the effects of Solar system in these models, including the gravitation redshift, geodetic effect and perihelion preccesion. We find that Model I can pass all three of the Solar system tests. For Model II, the parameter is constrained by the measure of the perihelion precession of Mercury.
