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The behavior of a massive charged test Dirac field in the background of a Reissner-Nordstr\"om black hole is investigated. Especially, we obtain the frequencies of quasibound states by solving the Dirac equation numerically both in time and frequency domain. Our results suggest that although the absence of superradiance excludes the existence of stationary solutions for massive Dirac fields, it is still possible to find arbitrarily long-lived solutions., Comment: 9 pages, 5 figures, accepted for publication in PRD

In this paper, the behaviour of a charged massive scalar test field in the background of a Kerr-Sen black hole is investigated. A kind of stationary solutions, dubbed scalar clouds, are obtained numerically and expressed by the existence lines in the parameter space. We show that for fixed background and a given set of harmonic indices, the mass and charge of the scalar clouds are limited in a finite region in the parameter space of the scalar field. Particularly, the maximum values of the mass and charge of the clouds around extremal Kerr-Sen black holes are independent of the angular velocity of the black hole, whereas those in the extremal Kerr-Newman background depend on the angular velocity. In addition, it is demonstrated that, as the static limit of Kerr-Sen black hole, Gibbons-Maeda-Garfinkle-Horowitz-Strominger black hole can not support scalar cloud., Comment: 15 pages, 7 figures, accepted for publication in Class. Quantum Grav

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 universe 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., Comment: 7 pages, 3 figures

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 large-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., Comment: 19 pages,5 figures

We present a detailed study of the Vaidya solution and its generalization in de Rham-Gabadadze-Tolley (dRGT) theory. Since the diffeomorphism invariance can be restored with the St\"{u}ckelberg fields $\phi^a$ introduced, there is a new invariant $I^{ab}=g^{\mu \nu}\partial_\mu \phi^a\partial_\nu \phi^b$ in the massive gravity, which adds to the ones usually encountered in general relativity. There is no conventional Vaidya solution if we choose unitary gauge. In this paper, we obtain three types of self-consistent ansatz with some nonunitary gauge, and find accordingly the Vaidya, generalized Vaidya and furry Vaidya solution. As by-products, we obtain a series of furry black hole. The Vaidya solution and its generalization in dRGT massive gravity describe the black holes with a variable horizon., Comment: 9 pages, to be published in Phys. Rev. D. arXiv admin note: substantial text overlap with arXiv:1603.06039

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., Comment: 10 pages

Using the observation data of SNeIa, CMB and BAO, we establish two concrete $f(T)$ models with nonminimal torsion-matter coupling extension. We study in detail the cosmological implication of our models and find they are successful in describing the observation of the Universe, its large scale structure and evolution. In other words, these models do not change the successful aspects of $\Lambda$CDM scenario under the error band of fitting values as describing the evolution history of the Universe including radiation-dominated era, matter-dominated era and the present accelerating expansion. Meanwhile, the significant advantage of these models is that they could avoid the cosmological constant problem of $\Lambda$CDM. A joint analysis is performed by using the data of CMB+BAO+JLA, which leads to $\Omega_{m0}=0.255\pm 0.010, \Omega_{b0}h^2=0.0221\pm 0.0003$ and $H_0=68.54\pm 1.27$ for model I and $\Omega_{m0}=0.306\pm 0.010, \Omega_{b0}h^2=0.0225\pm 0.0003$ and $H_0=60.97\pm 0.44$ for model II at 1$\sigma$ confidence level. The evolution of the decelaration parameter $q(a)$ and the effective equation of state $w_{DE}(a)$ are displayed. Furthermore, The resulted age of the Universe from our models is consistent with the ages of the oldest globular clusters. As for the fate of the Universe, model I results in a de Sitter accelerating phase while model II appears a power-law one, even though $w_{DE0}< -1$ makes model I look like a phantom at present time., Comment: 12 pages, 5 figures

The Casimir effect for rectangular boxes has been studied for several decades. But there are still some points unclear. Recently, there are new developments related to this topic, including the demonstration of the equivalence of the regularization methods and the clarification of the ambiguity in the regularization of the temperature-dependent free energy. Also, the interesting quantum spring was raised stemming from the topological Casimir effect of the helix boundary conditions. We review these developments together with the general derivation of the Casimir energy of the $p$-dimensional cavity in ($D+1$)-dimensional spacetime, paying special attention to the sign of the Casimir force in a cavity with unequal edges. In addition, we also review the Casimir piston, which is a configuration related to rectangular cavity., Comment: 49 pages, review article

Zeta function regularization is an effective method to extract physical significant quantities from infinite ones. It is regarded as mathematically simple and elegant but the isolation of the physical divergency is hidden in its analytic continuation. By contrast, Abel-Plana formula method permits explicit separation of divergent terms. In regularizing the Casimir energy for a massless scalar field in a $D$-dimensional rectangular box, we give the rigorous proof of the equivalence of the two methods by deriving the reflection formula of Epstein zeta function from repeatedly application of Abel-plana formula and giving the physical interpretation of the infinite integrals. Our study may help with the confidence of choosing any regularization method at convenience among the frequently used ones, especially the zeta function method, without the doubts of physical meanings or mathematical consistency., Comment: 14 pages

Magnetic fields are believed to play an essential role in astrophysical jets with observations suggesting the presence of helical magnetic fields. Here, we present three-dimensional (3D) ideal MHD simulationsof the Caltech plasma jet experiment using a magnetic tower scenario as the baseline model. Magnetic fields consist of an initially localized dipole-like poloidal component and a toroidal component that is continuously being injected into the domain. This flux injection mimics the poloidal currents driven by the anode-cathode voltage drop in the experiment. The injected toroidal field stretches the poloidal fields to large distances, while forming a collimated jet along with several other key features. Detailed comparisons between 3D MHD simulations and experimental measurements provide a comprehensive description of the interplay among magnetic force, pressure and flow effects. In particular, we delineate both the jet structure and the transition process that converts the injected magnetic energy to other forms. With suitably chosen parameters that are derived from experiments, the jet in the simulation agrees quantitatively with the experimental jet in terms of magnetic/kinetic/inertial energy, total poloidal current, voltage, jet radius, and jet propagation velocity. Specifically, the jet velocity in the simulation is proportional to the poloidal current divided by the square root of the jet density, in agreement with both the experiment and analytical theory. This work provides a new and quantitative method for relating experiments, numerical simulations and astrophysical observation, and demonstrates the possibility of using terrestrial laboratory experiments to study astrophysical jets., Comment: accepted by ApJ 37 pages, 15 figures, 2 tables

We reconsider the thermal scalar Casimir effect for $p$-dimensional rectangular cavity inside $D+1$-dimensional Minkowski space-time. We derive rigorously the regularization of the temperature-dependent part of the free energy by making use of the Abel-Plana formula repeatedly and get the explicit expression of the terms to be subtracted. In the cases of $D$=3, $p$=1 and $D$=3, $p$=3, we precisely recover the results of parallel plates and three-dimensional box in the literature. Furthermore, for $D>p$ and $D=p$ cases with periodic, Dirichlet and Neumann boundary conditions, we give the explicit expressions of the Casimir free energy in both low temperature (small separations) and high temperature (large separations) regimes, through which the asymptotic behavior of the free energy changing with temperature and the side length is easy to see. We find that for $D>p$, with the side length going to infinity, the Casimir free energy tends to positive or negative constants or zero, depending on the boundary conditions. But for $D=p$, the leading term of the Casimir free energy for all three boundary conditions is a logarithmic function of the side length. We also discuss the thermal Casimir force changing with temperature and the side length in different cases and find with the side length going to infinity the force always tends to zero for different boundary conditions regardless of $D>p$ or $D=p$. The Casimir free energy and force at high temperature limit behave asymptotically alike in that they are proportional to the temperature, be they positive (repulsive) or negative (attractive) in different cases. Our study may be helpful in providing a comprehensive and complete understanding of this old problem., Comment: 25 pages, 8 figures, accepted by Int. J. Mod. Phys. A

When one studies the Casimir effect, the periodic (anti-periodic) boundary condition is usually taken to mimic a periodic (anti-periodic) structure for a scalar field living in a flat space with a non-Euclidean topology. However, there could be an arbitrary phase difference between the value of the scalar field on one endpoint of the unit structure and that on the other endpoint, such as the structure of nanotubes. Then, in this paper, a periodic condition on the ends of the system with an additional phase factor, which is called the ``quasi-periodic" condition, is imposed to investigate the corresponding Casimir effect. And an attractive or repulsive Casimir force is found, whose properties depend on the phase angle value. Especially, the Casimir effect disappears when the phase angle takes a particular value. High dimensional space-time case is also investigated., Comment: 8 pages, 1 figure, accepted by MPLA

We obtain the Schwarzschild solution from thermodynamic considerations using the assumptions of a quasi local mass form (the Misner-Sharp mass) and geometric surface gravity in a spherically symmetric spacetime. The deduction is extended to other cases such as the de Sitter, anti-de Sitter, Reissner-Nordstr\"om and higher dimensional spacetimes. This paper demonstrates the simple hypotheses to obtain these known spherically symmetric solutions via thermodynamics, where essentially the Misner-Sharp mass is the mass for an adiabatic system., Comment: two new authors joined, 5pages, no figure, PRD in press

Depending on the choice of its potential, the scalar phantom field $\phi$ (the equation of state parameter $w<-1$) leads to various catastrophic fates of the universe including big rip, little rip and other future singularity. For example, big rip results from the evolution of the phantom field with an exponential potential and little rip stems from a quadratic potential in general relativity (GR). By choosing the same potential as in GR, we suggest a new mechanism to avoid these unexpected fates (big and little rip) in the inverse-\textit{R} gravity. As a pedagogical illustration, we give an exact solution where phantom field leads to a power-law evolution of the scale factor in an exponential type potential. We also find the sufficient condition for a universe in which the equation of state parameter crosses $w=-1$ divide. The phantom field with different potentials, including quadratic, cubic, quantic, exponential and logarithmic potentials are studied via numerical calculation in the inverse-\textit{R} gravity with $R^{2}$ correction. The singularity is avoidable under all these potentials. Hence, we conclude that the avoidance of big or little rip is hardly dependent on special potential., Comment: 9 pages,6 figures

We use the generalized Chowla-Selberg formula to consider the Casimir effect of a scalar field with a helix torus boundary condition in the flat ($D+1$)-dimensional spacetime. We obtain the exact results of the Casimir energy density and pressure for any $D$ for both massless and massive scalar fields. The numerical calculation indicates that once the topology of spacetime is fixed, the ratio of the sizes of the helix will be a decisive factor. There is a critical value $r_{crit}$ of the ratio $r$ of the lengths at which the pressure vanishes. The pressure changes from negative to positive as the ratio $r$ passes through $r_{crit}$ increasingly. In the massive case, we find the pressure tends to the result of massless field when the mass approaches zero. Furthermore, there is another critical ratio of the lengths $r_{crit}^{\prime}$ and the pressure is independent of the mass at $r=r_{crit}^{\prime}$ in the D=3 case., Comment: 11 pages, 3 figures, to be published in Mod. Phys. Lett. A

In this paper, we consider the fermionic Casimir effect under a new type of space-time topology using the concept of quotient topology. The relation between the new topology and that in Ref. \cite{Feng,Zhai3} is something like that between a M\"obius strip and a cylindric. We obtain the exact results of the Casimir energy and force for the massless and massive Dirac fields in the ($D+1$)-dimensional space-time. For both massless and massive cases, there is a $Z_2$ symmetry for the Casimir energy. To see the effect of the mass, we compare the result with that of the massless one and we found that the Casimir force approaches the result of the force in the massless case when the mass tends to zero and vanishes when the mass tends to infinity., Comment: 7 pages, 4 figures, published in Eur. Phys. J. C

The Casimir effect for a massless scalar field on the helix boundary condition which is named as quantum spring is studied in our recent paper\cite{Feng}. In this paper, the Casimir effect of the quantum spring is investigated in $(D+1)$-dimensional spacetime for the massless and massive scalar fields by using the zeta function techniques. We obtain the exact results of the Casimir energy and Casimir force for any $D$, which indicate a $Z_2$ symmetry of the two space dimensions. The Casimir energy and Casimir force have different expressions for odd and even dimensional space in the massless case but in both cases the force is attractive. In the case of odd-dimensional space, the Casimir energy density can be expressed by the Bernoulli numbers, while in the even case it can be expressed by the $\zeta$-function. And we also show that the Casimir force has a maximum value which depends on the spacetime dimensions. In particular, for a massive scalar field, we found that the Casimir force varies as the mass of the field changes., Comment: 9 pages, 5 figures, v2, massive case added, refs. added

We present theoretical results of a piecewise isothermal shock wind model devised for predicting the luminosity and surface brightness profile of diffuse X-ray emissions primarily from the inner shocked downstream wind zone of a planetary nebula (PN) surrounded by self-similar shocked dense shell and outer slow AGB wind envelope involving self-gravity and compare/fit our computational model results with available observations of a few grossly spherical X-ray emitting PNe. Matching shocked piecewise isothermal self-similar void (ISSV) solutions with self-gravity of Lou & Zhai (LZ) for the outer zone and a stationary isothermal fast tenuous wind with a reverse shock for the inner zone across an expanding contact discontinuity, we can consistently construct dynamic evolution models of PNe with diffuse X-ray emissions. On the basis of such a chosen dynamic wind interaction model, both X-ray luminosity and radial X-ray brightness profile are determined by three key parameters, namely the so-called X-ray parameter $X$, two radii $R_{rs}$ and $R_c$ of the reverse shock and the contact discontinuity. We find that morphologies of X-ray emissions would appear in the forms of either a central luminous sphere or a bright ring embedded within optically bright shells. In contrast to previous adiabatic models, the X-ray brightness peaks around the reverse shock, instead of the contact discontinuity surface just inside the outer shocked dense shell. Diffuse X-ray emissions of a few observed PNe appear to support this wind-wind dynamic interaction scenario., Comment: 13 pages, 8 figures, accepted by Mon. Not. R. Astron. Soc. Accepted 2010 June 2. Received 2010 May 28; in original form 2010 May 4

We explore self-similar hydrodynamic evolution of central voids embedded in an isothermal gas of spherical symmetry under the self-gravity. More specifically, we study voids expanding at constant radial speeds in an isothermal gas and construct all types of possible void solutions without or with shocks in surrounding envelopes. We examine properties of void boundaries and outer envelopes. Voids without shocks are all bounded by overdense shells and either inflows or outflows in the outer envelope may occur. These solutions, referred to as type $\mathcal{X}$ void solutions, are further divided into subtypes $\mathcal{X}_{\rm I}$ and $\mathcal{X}_{\rm II}$ according to their characteristic behaviours across the sonic critical line (SCL). Void solutions with shocks in envelopes are referred to as type $\mathcal{Z}$ voids and can have both dense and quasi-smooth edges. Asymptotically, outflows, breezes, inflows, accretions and static outer envelopes may all surround such type $\mathcal{Z}$ voids. Both cases of constant and varying temperatures across isothermal shock fronts are analyzed; they are referred to as types $\mathcal{Z}_{\rm I}$ and $\mathcal{Z}_{\rm II}$ void shock solutions. We apply the `phase net matching procedure' to construct various self-similar void solutions. We also present analysis on void generation mechanisms and describe several astrophysical applications. By including self-gravity, gas pressure and shocks, our isothermal self-similar void (ISSV) model is adaptable to various astrophysical systems such as planetary nebulae, hot bubbles and superbubbles in the interstellar medium as well as supernova remnants., Comment: 24 pages, 13 figuers, accepted by ApSS

The Casimir force on two-dimensional pistons for massive scalar fields with both Dirichlet and hybrid boundary conditions is computed. The physical result is obtained by making use of generalized $\zeta$-function regularization technique. The influence of the mass and the position of the piston in the force is studied graphically. The Casimir force for massive scalar field is compared to that for massless scalar field., Comment: 6 pages, 7 figures, in press version of Mod. Phys. Lett. A