Equations of hydrodynamics in general relativity in the slow motion approximation

By means of a formal solution to the Einstein gravitational field equations a slow motion expansion in inverse powers of the speed of light is developed for the metric tensor. The formal solution, which satisfies the deDonder coordinate conditions and the Trautman outgoing radiation condition, is in the form of an integral equation which is solved iteratively. A stress-energy tensor appropriate to a perfect fluid is assumed and all orders of the metric needed to obtain the equations of motion and conserved quantities to the 21/2post-Newtonian approximation are found. The results are compared to those obtained in another gauge by S. Chandrasekhar. In addition, the relation of the fast motion approximation to the slow motion approximation is examined.     

Gravitation and source theory

Schwinger's source theory is applied to the problem of gravitation and its quantization. It is shown that within the framework of a flat-space the source theory implementation leads to a violation of probability. To avoid the difficulty one must introduce a curved space-time hence the source concept may be said to necessitate the transition to a curved-space theory of gravitation. It is further shown that the curved-space theory of gravitation implied by the source theory is not equivalent to the conventional Einstein theory. The source concept leads to a different theory where the gravitational field has a stress-energy tensor t_μ^ν, which contributes to geometric curvatures.     

Axiomatic renormalization of the stress tensor of a conformally invariant field in conformally flat spacetimes

Using only the general properties which the renormalized stress-energy tensor T_μν should satisfy—and not relying on any assumptions associated with specific renormalization techniques—we derive the expression for T_μν for conformally invariant fields in conformally flat spacetimes of two and four dimensions. In two dimensions, these arguments rederive the Davies-Fulling-Unruh expression for the stress tensor of a scalar field; in four dimensions the results agree with those of Brown and Cassidy, except that we exclude the local curvature term depending on fourth-order derivatives of the metric. The dynamics of a k = 0 Robertson-Walker universe filled with radiation of the conformally invariant field is investigated and it is found that the equations cease to admit a solution when the Planck density is reached.     

Wormhole Geometries in f(R,T) Gravity

We study wormhole solutions in the framework of f(R,T) gravity where R is the scalar curvature, and T is the trace of the stress-energy tensor of the matter. We have obtained the shape function of the wormhole by specifying an equation of state for the matter field and imposing the flaring out condition at the throat. We show that in this modified gravity scenario, the matter threading the wormhole may satisfy the energy conditions, so it is the effective stress-energy that is responsible for violation of the null energy condition.     

The renormalized stress-energy tensor and its associated operators for photons in curved four-dimensional space–time

We establish expressions for the renormalized stress-energy (or energy-momentum) tensor and its associated operators relative to photons as a Klein–Gordon field of non-zero rest-mass particles (with gravitational interaction) in curved four-dimensional space–time.     

Behavior of the Lorenz number in the light heavy-fermion system YbInCu4

The electrical resistivity and thermal conductivity of two polycrystalline YbInCu₄ samples prepared by different techniques at the Ioffe Physicotechnical Institute, RAS (St. Petersburg, Russia), and the Goethe University (Frankfurt-am-Main, Germany) are studied within the temperature range 4.2–300 K. At T _v～75–78 K, these samples exhibited an isostructural phase transition from a state with an integer valence (at T>T _v) to a state with an intermediate valence (at T<T _v) of the Yb ions. It is shown that at T<T _v; i.e., in the temperature range where YbInCu₄ is assumed to be a light heavy-fermion compound, the Lorenz number behaves as it should in a classical heavy-fermion system. At T>T _v, where YbInCu₄ is a semimetal, the Lorenz number has a value characteristic of standard metals.     

具有广义协变的包含重力场贡献的重力场方程

利用半度规λ^(α)_μ表象的数学工具定义一个对广义坐标具有协变形式的重力场矢势函数ω^(α)_μ≡-cλ^(α)_μ，给出一个具有广义协变的包含重力场贡献的重力场方程R_μν-g_μνR/2+Λg_μν=8πG(T^(Ⅰ)_μν+T^(Ⅱ)_μν) 关键词： 重力场方程 协变形式 能量-动量张量 量子化     

Quantum gravity,the origin of time and time's arrow

The local Lorentz and diffeomorphism symmetries of Einstein's gravitational theory are spontaneously broken by a Higgs mechanism by invoking a phase transition in the early universe, at a critical temperature T_c below which the symmetry is restored. The spontaneous breakdown of the vacuum state generates an external time, and the wave function of the universe satisfies a time-dependent Schrödinger equation, which reduces to the Wheeler-deWitt equation in the classical regime for T<T_c, allowing a semiclassical WKB approximation to the wave function. The conservation of energy is spontaneously violated for T>T_c, and matter is created fractions of seconds after the big bang, generating the matter in the Universe. The time direction of the vacuum expectation value of the scalar Higgs field generates a time asymmetry, which defines the cosmological arrow of time and the direction of increasing entropy as the Lorentz symmetry is restored at low temperatures.     

Born Reciprocity and the Granularity of Spacetime

The Schrödinger-Robertson inequality for relativistic position and momentum operators X ^μ, P _ν, μ, ν = 0, 1, 2, 3, is interpreted in terms of Born reciprocity and ‘non-commutative’ relativistic position-momentum space geometry. For states which saturate the Schrödinger-Robertson inequality, a typology of semiclassical limits is pointed out, characterised by the orbit structure within its unitary irreducible representations, of the full invariance group of Born reciprocity, the so-called ‘quaplectic’ group U(3, 1) #x2297;_s H(3, 1) (the semi-direct product of the unitary relativistic dynamical symmetry U(3, 1) with the Weyl-Heisenberg group H(3, 1)). The example of the ‘scalar’ case, namely the relativistic oscillator, and associated multimode squeezed states, is treated in detail. In this case, it is suggested that the semiclassical limit corresponds to the separate emergence of spacetime and matter, in the form of the stress-energy tensor, and the quadrupole tensor, which are in general reciprocally equivalent.     

Some structural features induced by the space-time metrical fluctuation in the theory of gravitational fields

Under the assumption that the so-called space-time fluctuationy(x) in a classical sense, attached to each point of the gravitational field at some microscopic stage, is summarized as the metrical fluctuation in the formg _λκ (x)=g_λκ (x)·exp2σ(y(x)), some new physical aspects induced by the conformal scalarσ(x) (≡σ(y(x))) are found: By introducing the torsionT _κ ^λμ (x) from a general standpoint, the resulting micro-gravitational field is made to have a conformally non-Riemannian structure, where a special form ofT _κ ^λμ (i.e.,T _κ ^λμ =δ _κ ^λ σ_μ?δ _κ ^μ σ_λ(σ_μ=?σ/?x ^μ)) shows some peculiar features. An averaging process with respect toy is taken into account, by which the spatial structure of the corresponding macro-field is shown, in general, to have a somewhat “non”-Riemannian structure due to the contributions of the torsionT _κ ^λμ .     

Application of the contact transformation method to torsional problems in methyl silane

The effect of the torsional degree of freedom on redundancies in the Hamiltonian and on the dipole operator has been investigated for methyl silane-like molecules. By applying a rotational contact transformation to the torsion-rotation Hamiltonian H_TR for the ground vibrational state, a systematic method is demonstrated for treating the redundancies that relate different terms in H_TR. In general, with this method, the experimentally accessible molecular parameters in the reduced Hamiltonian can be related to the physically significant molecular parameters in the untransformed Hamiltonian. It is shown that H_TR contains a new term which has matrix elements with selection rules (ΔK = ±3), (Δσ = 0), and Δv_T arbitrary, where v_T and σ label the torsional levels and sublevels, respectively. As a result of this term, the distortion dipole constant μ_D which characterizes (ΔK = ±3) matrix elements in C_3v molecules cannot, in systems like CH₃SiH₃, be ascribed entirely to centrifugal distortion but can contain a significant contribution from torsional effects. Furthermore, new transitions can appear in the pure torsional bands which may be strong enough to observe in low barrier molecules. By applying a vibrational contact transformation, the form is derived of the leading torsional terms in the dipole moment expansion. The four dipole distortion constants μ₀^T, μ₂^T, μ_|;^T, and μ_Λ^T which characterize these terms are related to the molecular parameters that enter the Coriolis, centrifugal distortion, and anharmonicity contributions to the vibration-torsion-rotation Hamiltonian.     

Cosmological perturbations: a new gauge-invariant approach

A new gauge-invariant approach for describing cosmological perturbations is developed. It is based on a physically motivated splitting of the stress-energy tensor of the perturbation into two parts—the bare perturbation and the complementary perturbation associated with stresses in the background gravitational field induced by the introduction of the bare perturbation. The complementary perturbation of the stress-energy tensor is explicitly singled out and taken to the left side of the perturbed Einstein equations so that the bare stress-energy tensor is the sole source for the perturbation of the metric tensor and both sides of these equations are gauge invariant with respect to infinitesimal coordinate transformations. For simplicity we analyze the perturbations of the spatially-flat Friedmann–Lemaı̂tre–Robertson–Walker (FLRW) dust model. A cosmological gauge can be chosen such that the equations for the perturbations of the metric tensor are completely decoupled for the h₀₀, h_0i, and h_ij metric components and explicitly solvable in terms of retarded integrals.     

Letter: Trace Anomaly and Backreaction of the Dynamical Casimir Effect

The Casimir energy for massless scalar field which satisfies periodic boundary conditions in two-dimensional domain wall background is calculated by making use of general properties of renormalized stress-tensor. The line element of domain wall is time dependent, the trace anomaly which is the nonvanishing T for a conformally invariant field after renormalization, represent the back reaction of the dynamical Casimir effect.     

A model for the structure of point-like fermions: Qualitative features and physical description

A model for the structure of point-like fermions as tightly bound composite states is described. The model is based upon the premise that electromagnetism is the only fundamental interaction. The fundamental entity of the model is an object called the vorton. Vortons are semiclassical monopole configurations of electromagnetic charge and field, constructed to satisfy Maxwell's equations. Vortons carry topological charge and one unit each of two different kinds of angular momenta, and are placed in magnetically bound pair states having angular momentum l=1/2. The topological charge prevents the mutual annihilation of the vorton pair. The helicity eigenstates of the vortons' intrinsic angular momenta form the basis for a set of internal quantum numbers for the pair which distinguish the different (point-like) pair states. Sixteen fourcomponent spinor states, eight leptonic and eight hadronic, are obtained. Eleven of these are identified with the quantum numbers of the experimentally known particles: e, v_e, μ, v_μ, τ, v_τ; p, n, Λ, Λ_c, and b. Thus one new heavy lepton with its neutrino and three new quark states are predicted. Some possibilities for the extension of this model are discussed.     

Generalised Kerr-Schild space-times

If V is a space-time with metric tensor g_μν admitting a null, geodesic shear free vector field l_μ, then one may determine a function H so that the spacetime $\text{V}\text{?}$ with metric g_μν = g_μν + 2Hl_μl_ν satisfies the Einstein field equations for various material sources, and for no sources. When V is Minkowski space, $\text{V}\text{?}$ is a Kerr-Schild space-time. In case V is a vacuum space-time, one may choose H so that the source is a null fluid with no pressure. In case V is a Robertson-Walker universe H may be chosen so that the source has a stress-energy tensor with one timelike proper vector and three spacelike ones. There are two equal proper values associated with the latter vectors and one which differs from these. The stress-energy tensor describing this source may be interpreted as representing a perfect fluid with anisotropic pressures or as one describing the sum of a perfect fluid with isotropic pressures and a presureless null fluid. Vaidya's Kerr metric in a cosmological background [Pramana8 (1977) 512–517] is discussed as is the metric representing an accelerating point mass in an expanding universe.     

Semiclassical Cosmological Perturbations Generated During Inflation

Interaction with the environment may induce stochastic semiclassical dynamicsin open quantum systems. In the gravitational context, stress-energy fluctuationsof quantum matter fields give rise to a stochastic behavior in the spacetimegeometry. The Einstein—Langevin equation is a suitable tool to take these effectsinto account when addressing the backreaction problem in semiclassical gravity.We analyze within this framework the generation of gravitational fluctuationsduring inflation, which are of great interest for large-scale structure formationin cosmology.     

Geometric study of the connection between the Lagrangian and Hamiltonian constraints

The second order differential equation character of the solutions of the dynamical equation i(Γ)ω_L = dE_L for a singular Lagrangian L, as well as the conditions for the existence of such a solution, are studied. We also introduce a couple of maps R (L)_v : T _FL(v)(T¹Q) → T_v(TQ) and T(L)_v : T_FL(v)(T¹Q) → T_FL(v)(T¹Q), with v ϵ TQ, which are shown to be very useful for establishing the connection between the constraints arising in the Lagrangian and Hamiltonian formulations.