Using Energy Conditions to Distinguish Brane Models and Study Brane Matter

Current universe （assumed here to be normal matter on the brahe） is pressureless from observations. In this case the energy condition is po ≥ 0 and po =O. By using this condition, brahe models can be distinguished. Then, assuming arbitrary component of matter in DGP model, we use four known energy conditions to study the matter on the brahe. If there is nonnormal matter or energy （for example dark energy with w 〈-1/3） on the brane, the universe is accelerated.

Energy Conditions and Constraints on the Generalized Non-Local Gravity Model

We study and derive the energy conditions in generalized non-local gravity, which is the modified theory of general relativity obtained by adding a term m2n-2R□-nRto the Einstein-Hilbert action. Moreover, to obtain some insight on the meaning of the energy conditions, we illustrate the evolutions of four energy conditions with the model parameter ε for different n. By analysis we give the constraints on the model parameters ε.

Energy Conditions in Palatini Approach to Modified <i>f(R)</i>Gravity

In this paper, we review modified f(R) 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 (q), jerk (j) and snap (s) parameters. Energy conditions derived in Palatini version of f(R) 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.

New black-to-white hole solutions with improved geometry and energy conditions

We construct new black-to-white hole solutions which connect the geometry of spacetime at some gluing surface inside the horizon.The continuity of the metric can be guaranteed up to the arbitrary order which is controlled by the power factor n.This sort of black-to-white holes is characterized by the sub-Planckian scalar curvature,independent of the mass of black-to-white holes.More importantly,we show that the energy condition is only violated within a small region near the gluing surface.The geodesics of particles within the region from black hole to white hole is also analyzed.It turns out that the matter falling into the black hole may pass through the center without singularity and come out from the white hole.This scenario provides novel ideas for understanding the information loss paradox in traditional black hole physics.

Energy conditions of the f(T,B) gravity dark energy model with the validity of thermodynamics

In this article, the analysis of Tsallis holographic dark energy(which turns into holographic dark energy for a particular choice of positive non-additivity parameter δ) in modified f(T, B) gravity with the validity of thermodynamics and energy conditions for a homogeneous and isotropic FLRW Universe has been studied. The enlightenment of the field equation towards f(T,B)=αT^m+βB^n, made possible by the fact that the model is purely accelerating,corresponds to q=-0.54(Mamon and Das 2017 Eur. Phys.J.C 77 49). The generalized second law of thermodynamics is valid not only for the same temperature inside the horizon, but also for the apparent horizon for a change in temperature. The essential inspiration driving this article is to exhibit the applicability that the holographic dark energy achieved from standard Tsallis holographic dark energy and the components acquired from f(T, B) gravity are identical for the specific bounty of constants. The analysis of energy conditions confirms that the weak energy condition and the null energy condition are fulfilled throughout the expansion, while violation of the strong energy condition validates the accelerated expansion of the Universe.With the expansion, the model becomes a quintessence dominated model. The dominant energy condition is not observed initially when the model is filled with genuine baryonic matter,whereas it appears when the model is in the quintessence dominated era.

f(R,L(X))-gravity in the context of dark energy with power law expansion and energy conditions

The objective of this work is to generate a general formalism of f(R,L(X))-gravity in the context of dark energy under the framework of K-essence emergent geometry with the Dirac-Born-Infeld(DBI) variety of action,where R is the familiar Ricci scalar,L(X) is the DBI type non-canonical Lagrangian with X=1/2g^(μν)▽_(μ)φ▽_(ν)φ,and φ is the K-essence scalar field.The emergent gravity metric(G_(μν)) and the well known gravitational metric(g^(μν))are not conformally equivalent.We have constructed a modified field equation using the metric formalism in f(R,L(X))-gravity incorporating the corresponding Friedmann equations into the framework of the background gravitational metric,which is of Friedmann-Lemaitre-Robertson-Walker(FLRW) type.The solution of the modified Friedmann equations have been deduced for the specific choice of f(R,L(X)),which is of Starobinsky-type,using the power law expansion method.The consistency of the model with the accelerating phase of the universe has been shown when we restrict ourselves to consider the value of the dark energy density as φ^(2)=8/9=0.888 <1,which indicates that the present universe is dark-energy dominated.Graphical plots for the energy density(ρ),pressure(p),and equation of state parameter(ω) with respect to(w.r.t.) time(t) based on parametric values are interestingly consistent with the dark energy domination theory,and hence the accelerating features.We also highlight the corresponding energy conditions and constraints of the f(R,L(X)) theory with a basic example.

Wormhole solutions and energy conditions in f(R,G)gravity

In this manuscript,the traversable wormhole solutions have been explored in modified f(R,G)gravity by taking into consideration the model f(R,G)=R+rG2,where R is the Ricci curvature scalar and G is the Gauss–Bonnet term.An acceptable form of the redshift function has been incorporated which is a non-constant in nature along with the implementation of those already defined in literature,the two shape functions namely b(r)=r/exp(r-r0)and b(r)=r0log(r+1)/log(r0+1).It is shown by studying the energy condition and through the graphical analysis that the null energy bounds for the effective energy-momentum tensor are generally violated for the presence of the ordinary matter in modified f(R,G)gravity.Energy conditions associated with the matter content threading the wormhole geometries are evaluated and in general are found to favor the null energy conditions in the vicinity of the wormhole throat,the existence of the nonexotic wormhole geometries threaded by the matter has been confirmed under this gravity.

Energy Conditions and Conservation Laws in LRS Bianchi Type Ⅰ Spacetimes via Noether Symmetries

In this paper, we have completely classified the locally rotationally symmetric(LRS) Bianchi Type Ⅰ spacetimes via Noether symmetries(NS). The usual Lagrangian corresponding to LRS Bianchi Type Ⅰ metric is used to find the set of determining equations. To achieve a complete classification, these determining equations are generally integrated to find the components of NS vector field and the metric coefficients. During this procedure, several cases arise which give different Noether algebras of dimension 5,..., 9, 11, and 17. A comparison is established between the obtained NS and the Killing and homothetic vectors. Corresponding to all NS generators, the conservation laws are stated by using Noether's theorem. The metrics which we have obtained as a result of our classification are shown to be anisotropic or perfect fluids which satisfy certain energy conditions.

Regular black holes with improved energy conditions and their analogues in fluids

On the premise of the importance of energy conditions for regular black holes,we propose a method to remedy those models that break the dominant energy condition,e.g.,the Bardeen and Hayward black holes.We modify the metrics but ensure their regularity at the same time,so that the weak,null,and dominant energy conditions are satisfied,with the exception of the strong energy condition.Likewise,we prove a no-go theorem for conformally related regular black holes,which states that the four energy conditions can never be met in this class of black holes.In order to seek evidences for distinguishing regular black holes from singular black holes,we resort to analogue gravity and regard it as a tool to mimic realistic regular black holes in a fluid.The equations of state for the fluid are solved via an asymptotic analysis associated with a numerical method,which provides a modus operandi for experimental observations,in particular,the conditions under which one can simulate realistic regular black holes in the fluid.

Energy conditions in the new model of loop quantum cosmology

Recently,a de-Sitter epoch has been found in the new model of loop quantum cosmology,which is governed by the scalar constraint with both Euclidean and Lorentz terms.The singularity free bounce in the new LQC model and the emergent cosmology constant strongly suggest that the effective stress-energy tensor induced by quantum corrections must violate the standard energy conditions.In this study,we perform an explicit calculation to analyze the behaviors of specific representative energy conditions,i.e.,average null,strong,and dominant energy conditions.We reveal that the average null energy condition is violated at all times,while the dominant energy condition is violated only at a period around the bounce point.The strong energy condition is violated not only at a period around the bounce point but also in the whole period from the bounce point to the classical phase corresponding to the de Sitter period.Our results will shed some light on the construction of a wormhole and time machine,which usually require exotic matter to violate energy conditions.

Gravitational collapse with standard and dark energy in the teleparallel equivalent of general relativity

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.

Energy-Efficient Transceiver Design for Multi-Pair Two-Way Relay Systems

In this paper, we focus on energy-efficient transceiver and relay beamforming design for multi-pair two-way relay system. The multi-antenna users and the multi-antenna relay are considered in this work. Different from the existing works, the proposed algorithm is energy-efficient which is more applicable to the future green network. It considers both the sum-MSE problem and the power consumption problem for the users under the relay power constraint. Based on the optimal condition decomposition(OCD) method, the energy-efficient precoders at the users can be designed separately with limited information exchanged. The proposed relay beamforming algorithm is based on the alternative direction method of multipliers(ADMM) which has simpler iterative solution and enjoys good convergence. Simulation results demonstrate the performance of the proposed algorithms in terms of power consumption and MSE performance.

Optimal Scheduling of Air Conditioners for Energy Efficiency

Energy saving is one of the most important research hotspots, by which operational expenditure and CO2 emission can be reduced. Optimal cooling capacity scheduling in addition to temperature control can improve energy efficiency. The main contribution of this work is modeling the telecommunication building for the fabric cooling load to schedule the operation of air conditioners. The time series data of the fabric cooling load of the building envelope is taken by simulation by using Energy Plus, Building Control Virtual Test Bed （BCVTB）, and Matlab. This pre-computed data and other internal thermal loads are used for scheduling in air conditioners. Energy savings obtained for the whole year are about 4% to 6% by simulation and the field study, respectively.

Time-Machine Solutions of Einstein's Equations with Electromagnetic Field

In this paper we investigate the time-machine problem in the electromagnetic field. Based on a metric which is a more general form of Ori＇s, we solve the Einstein＇s equations with the energy-momentum tensors for electromagnetic field, and construct the time-machine solutions, which solve the time machine problem in electromagnetic field.

Rotating Squeezed Vacua as Time Machines

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.

Theoretical analysis on capillary adhesion of microsized plates with a substrate

The stiction of a thin plate induced by the capillary force has attracted much attention in the broad range of applications. A novel method is presented to calculate the capillary adhesion problem of the plate through analytical method. The expressions of the surface energy, the strain energy and the total potential energy of the plate-substrate system have been analyzed and delineated. By means of continuum mechanics and the principle of minimum potential energy, the governing equation of the plate with an arbitrary shape and the corresponding transversality boundary condition due to the moving bound have been derived. Then the critical adhesion radius of the circular plate has been solved according to the supplementary transversality condition. Thus the deflections of the plates are analytically calculated with different critical adhesion radii. The results may be beneficial to the engineering application and the micro/nanomeasurement.

Changes in the relationship between species richness and belowground biomass among grassland types and along environmental gradients in Xinjiang, Northwest China

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.

Describing failure in geomaterials using second-order work approach

Geomaterials are known to be non-associated materials. Granular soils therefore exhibit a variety of failure modes, with diffuse or localized kinematical patterns. In fact, the notion of failure itself can be confusing with regard to granular soils, because it is not associated with an obvious phenomenology. In this study, we built a proper framework, using the second-order work theory, to describe some failure modes in geomaterials based on energy conservation. The occurrence of failure is defined by an abrupt increase in kinetic energy. The increase in kinetic energy from an equilibrium state, under incremental loading, is shown to be equal to the difference between the external second-order work,involving the external loading parameters, and the internal second-order work, involving the constitutive properties of the material. When a stress limit state is reached, a certain stress component passes through a maximum value and then may decrease. Under such a condition, if a certain additional external loading is applied, the system fails, sharply increasing the strain rate. The internal stress is no longer able to balance the external stress, leading to a dynamic response of the specimen. As an illustration, the theoretical framework was applied to the well-known undrained triaxial test for loose soils. The influence of the loading control mode was clearly highlighted. It is shown that the plastic limit theory appears to be a particular case of this more general second-order work theory. When the plastic limit condition is met, the internal second-order work is nil. A class of incremental external loadings causes the kinetic energy to increase dramatically, leading to the sudden collapse of the specimen, as observed in laboratory.

When null energy condition meets ADM mass

We give a conjecture on the lower bound of the ADM mass M by using the null energy condition.The conjecture includes a Penrose-like inequality 3M≥_(k)A/(4π)+√A/4πand the Penrose inequality 2M≥√A/4πwith A the event horizon area andκthe surface gravity.Both the conjecture in the static spherically symmetric case and the Penrose inequality for a dynamical spacetime with spherical symmetry are proved by imposing the null energy condition.We then generalize the conjecture to a general dynamical spacetime.Our results raise a new challenge for the famous unsettled question in general relativity:in what general case can the null energy condition replace other energy conditions to ensure the Penrose inequality?

Hyperbolic positive mass theorem under modified energy condition

We provide two new positive mass theorems under respective modified energy conditions allowing T00 negative on some compact set for certain modified asymptotically hyperbolic manifolds. This work is analogous to Zhang’s previous result for modified asymptotically flat initial data sets.