In this paper, we review modified <i>f(R)</i> theories of gravity in Palatini formalism. In this framework, we use the Raychaudhuri’s equation along with the requirement that the gravity is attractive, wh...In this paper, we review modified <i>f(R)</i> theories of gravity in Palatini formalism. In this framework, we use the Raychaudhuri’s equation along with the requirement that the gravity is attractive, which holds for any geometrical theory of gravity to discuss the energy conditions. Then, to derive these conditions, we obtain an expression for effective pressure and energy density by considering FLRW metric. To simply express the energy conditions, we write the Ricci scalar and its derivatives in terms of the deceleration (<i>q</i>), jerk (<i>j</i>) and snap (<i>s</i>) parameters. Energy conditions derived in Palatini version of <i>f(R)</i> Gravity differ from those derived in GR. We will see that the WEC (weak energy condition) derived in Palatini formalism has exactly the same expression in its metric approach.展开更多
A perfect fluid with self-similarity of the second kind is studied within the framework of the teleparallel equivalent of general relativity （TEGR）. A spacetime which is not asymptotically fiat is derived. The energ...A perfect fluid with self-similarity of the second kind is studied within the framework of the teleparallel equivalent of general relativity （TEGR）. A spacetime which is not asymptotically fiat is derived. The energy conditions of this spacetime are studied. It is shown that after some time the strong energy condition is not enough to satisfy showing a transition from standard matter to dark energy. The singularities of this solution are discussed.展开更多
We consider f(R,T) theory of gravity, where R is the curvature scalar and T is the trace of the energy momentum tensor. Attention is attached to the special case, f(R,T)=R+2f(T) and two expressions are assumed for the...We consider f(R,T) theory of gravity, where R is the curvature scalar and T is the trace of the energy momentum tensor. Attention is attached to the special case, f(R,T)=R+2f(T) and two expressions are assumed for the function f(T),(a1Tn+b1)/(a2Tn+b2) and a3Inq(b3Tm), where a1,a2 ,b1,b2,n,a3 ,b3,q and m are input parameters. We observe that by adjusting suitably these input parameters, energy conditions can be satisfied. Moreover, an analysis of the perturbations and stabilities of de Sitter solutions and power-law solutions is performed with the use of the two models. The results show that for some values of the input parameters, for which energy conditions are satisfied, de Sitter solutions and power-law solutions may be stables.展开更多
Squeezed quantum vacua seems to violate the averaged null energy conditions (ANEC’s), because they have a negative energy density. When treated as a perfect fluid, rapidly rotating Casimir plates will create vorticit...Squeezed quantum vacua seems to violate the averaged null energy conditions (ANEC’s), because they have a negative energy density. When treated as a perfect fluid, rapidly rotating Casimir plates will create vorticity in the vacuum bounded by them. The geometry resulting from an arbitrarily extended Casimir plates along their axis of rotation is similar to van Stockum spacetime. We observe closed timelike curves (CTC’s) forming in the exterior of the system resulting from frame dragging. The exterior geometry of this system is similar to Kerr geometry, but because of violation of ANEC, the Cauchy horizon lies outside the system unlike Kerr blackholes, giving more emphasis on whether spacetime is multiply connected at the microscopic level.展开更多
The association between biodiversity and belowground biomass(BGB) remains a central debate in ecology.In this study, we compared the variations in species richness(SR) and BGB as well as their interaction in the top(0...The association between biodiversity and belowground biomass(BGB) remains a central debate in ecology.In this study, we compared the variations in species richness(SR) and BGB as well as their interaction in the top(0–20 cm), middle(20–50 cm) and deep(50–100 cm) soil depths among 8 grassland types(lowland meadow, temperate desert, temperate desert steppe, temperate steppe desert, temperate steppe, temperate meadow steppe, mountain meadow and alpine steppe) and along environmental gradients(elevation, energy condition(annual mean temperature(AMT) and potential evapotranspiration(PET)), and mean annual precipitation(MAP)) based on a 2011–2013 survey of 379 sites in Xinjiang, Northwest China.The SR and BGB varied among the grassland types.The alpine steppe had a medium level of SR but the highest BGB in the top soil depth, whereas the lowland meadow had the lowest SR but the highest BGB in the middle and deep soil depths.The SR and BGB in the different soil depths were tightly associated with elevation, MAP and energy condition;however, the particular forms of trends in SR and BGB depended on environmental factors and soil depths.The relationship between SR and BGB was unimodal in the top soil depth, but SR was positively related with BGB in the middle soil depth.Although elevation, MAP, energy condition and SR had significant effects on BGB, the variations in BGB in the top soil depth were mostly determined by elevation, and those in the middle and deep soil depths were mainly affected by energy condition.These findings highlight the importance of environmental factors in the regulations of SR and BGB as well as their interaction in the grasslands in Xinjiang.展开更多
文摘In this paper, we review modified <i>f(R)</i> theories of gravity in Palatini formalism. In this framework, we use the Raychaudhuri’s equation along with the requirement that the gravity is attractive, which holds for any geometrical theory of gravity to discuss the energy conditions. Then, to derive these conditions, we obtain an expression for effective pressure and energy density by considering FLRW metric. To simply express the energy conditions, we write the Ricci scalar and its derivatives in terms of the deceleration (<i>q</i>), jerk (<i>j</i>) and snap (<i>s</i>) parameters. Energy conditions derived in Palatini version of <i>f(R)</i> Gravity differ from those derived in GR. We will see that the WEC (weak energy condition) derived in Palatini formalism has exactly the same expression in its metric approach.
文摘A perfect fluid with self-similarity of the second kind is studied within the framework of the teleparallel equivalent of general relativity （TEGR）. A spacetime which is not asymptotically fiat is derived. The energy conditions of this spacetime are studied. It is shown that after some time the strong energy condition is not enough to satisfy showing a transition from standard matter to dark energy. The singularities of this solution are discussed.
文摘We consider f(R,T) theory of gravity, where R is the curvature scalar and T is the trace of the energy momentum tensor. Attention is attached to the special case, f(R,T)=R+2f(T) and two expressions are assumed for the function f(T),(a1Tn+b1)/(a2Tn+b2) and a3Inq(b3Tm), where a1,a2 ,b1,b2,n,a3 ,b3,q and m are input parameters. We observe that by adjusting suitably these input parameters, energy conditions can be satisfied. Moreover, an analysis of the perturbations and stabilities of de Sitter solutions and power-law solutions is performed with the use of the two models. The results show that for some values of the input parameters, for which energy conditions are satisfied, de Sitter solutions and power-law solutions may be stables.
文摘Squeezed quantum vacua seems to violate the averaged null energy conditions (ANEC’s), because they have a negative energy density. When treated as a perfect fluid, rapidly rotating Casimir plates will create vorticity in the vacuum bounded by them. The geometry resulting from an arbitrarily extended Casimir plates along their axis of rotation is similar to van Stockum spacetime. We observe closed timelike curves (CTC’s) forming in the exterior of the system resulting from frame dragging. The exterior geometry of this system is similar to Kerr geometry, but because of violation of ANEC, the Cauchy horizon lies outside the system unlike Kerr blackholes, giving more emphasis on whether spacetime is multiply connected at the microscopic level.
基金supported by the National Natural Science Foundation of China (U1603235, 31660127)the Tianshan Innovation Team Plan of Xinjiang (2017D14009)
文摘The association between biodiversity and belowground biomass(BGB) remains a central debate in ecology.In this study, we compared the variations in species richness(SR) and BGB as well as their interaction in the top(0–20 cm), middle(20–50 cm) and deep(50–100 cm) soil depths among 8 grassland types(lowland meadow, temperate desert, temperate desert steppe, temperate steppe desert, temperate steppe, temperate meadow steppe, mountain meadow and alpine steppe) and along environmental gradients(elevation, energy condition(annual mean temperature(AMT) and potential evapotranspiration(PET)), and mean annual precipitation(MAP)) based on a 2011–2013 survey of 379 sites in Xinjiang, Northwest China.The SR and BGB varied among the grassland types.The alpine steppe had a medium level of SR but the highest BGB in the top soil depth, whereas the lowland meadow had the lowest SR but the highest BGB in the middle and deep soil depths.The SR and BGB in the different soil depths were tightly associated with elevation, MAP and energy condition;however, the particular forms of trends in SR and BGB depended on environmental factors and soil depths.The relationship between SR and BGB was unimodal in the top soil depth, but SR was positively related with BGB in the middle soil depth.Although elevation, MAP, energy condition and SR had significant effects on BGB, the variations in BGB in the top soil depth were mostly determined by elevation, and those in the middle and deep soil depths were mainly affected by energy condition.These findings highlight the importance of environmental factors in the regulations of SR and BGB as well as their interaction in the grasslands in Xinjiang.
