The energy of Einstein-Maxwell dilation-axion black hole in the teleparallel geometry

The energy of the stationary axisymmetric Einstein-Maxwell dilation-axion （EMDA） black hole is studied in the context of the Hamiltonian formulation of the teleparallel equivalence of general relativity （TEGR）. The energy expression for the finite and arbitrary space-like two spheres is exactly computed by means of the integral form of the constraint equations of the formalism naturally without any restriction on the metric parameters. We also show that our results give the same values obtained by other methods for some special cases.     

Covariant energy–momentum and an uncertainty principle for general relativity

We introduce a naturally-defined totally invariant spacetime energy expression for general relativity incorporating the contribution from gravity. The extension links seamlessly to the action integral for the gravitational field. The demand that the general expression for arbitrary systems reduces to the Tolman integral in the case of stationary bounded distributions, leads to the matter-localized Ricci integral for energy–momentum in support of the energy localization hypothesis. The role of the observer is addressed and as an extension of the special relativistic case, the field of observers comoving with the matter is seen to compute the intrinsic global energy of a system. The new localized energy supports the Bonnor claim that the Szekeres collapsing dust solutions are energy-conserving. It is suggested that in the extreme of strong gravity, the Heisenberg Uncertainty Principle be generalized in terms of spacetime energy–momentum.     

Local and nonlocal space-like fields in the relativistic description of nucleon-nucleus scattering

It is shown that a local complex space-like nucleon-nucleus potential does not influence the observables associated with the elastic scattering, in contrast to a nonlocal space-like potential obtained from nuclear matter via a local density approximation. In order to eliminate the nonlocal space-like field, new scalar and time-like local components are defined. The energy dependence of the ratio of the strengths of the real parts of these two quantities is investigated.     

Integrability of Nonlinear Equations of Motion on Two-Dimensional World Sheet Space-Time

The integrability character of nonlinear equations of motion of two-dimensional gravity with dynamical torsion and bosonic string coupling is studied in this paper. The space-like and time-like first integrals of equations of motion are also found.     

Integrability of Nonlinear Equations of Motion on Two-Dimensional World Sheet Space-Time

The integrability character of nonlinear equations of motion of two-dimensional gravity with dynamical torsion and bosonic string coupling is studied in this paper. The space-like and time-like first integrals of equations of motion are also found.     

Isometric Embeddings into the Minkowski Space and New Quasi-Local Mass

The definition of quasi-local mass for a bounded space-like region Ω in space-time is essential in several major unsettled problems in general relativity. The quasi-local mass is expected to be a type of flux integral on the boundary two-surface \({\Sigma=\partial \Omega}\) and should be independent of whichever space-like region \({\Sigma}\) bounds. An important idea which is related to the Hamiltonian formulation of general relativity is to consider a reference surface in a flat ambient space with the same first fundamental form and derive the quasi-local mass from the difference of the extrinsic geometries. This approach has been taken by Brown-York [4,5] and Liu-Yau [16,17] (see also related works [3,6,9,12,14,15,28,32]) to define such notions using the isometric embedding theorem into the Euclidean three space. However, there exist surfaces in the Minkowski space whose quasilocal mass is strictly positive [19]. It appears that the momentum information needs to be accounted for to reconcile the difference. In order to fully capture this information, we use isometric embeddings into the Minkowski space as references. In this article, we first prove an existence and uniqueness theorem for such isometric embeddings. We then solve the boundary value problem for Jang’s [13] equation as a procedure to recognize such a surface in the Minkowski space. In doing so, we discover a new expression of quasi-local mass for a large class of “admissible” surfaces (see Theorem A and Remark 1.1). The new mass is positive when the ambient space-time satisfies the dominant energy condition and vanishes on surfaces in the Minkowski space. It also has the nice asymptotic behavior at spatial infinity and null infinity. Some of these results were announced in [29].     

Quintessential inflation from a variable cosmological constant in a 5D vacuum

We explore an effective 4D cosmological model for the universe where the variable cosmological constant governs its evolution and the pressure remains negative along all the expansion. This model is introduced from a 5D vacuum state where the (space-like) extra coordinate is considered as noncompact. The expansion is produced by the inflaton field, which is considered as nonminimally coupled to gravity. We conclude from experimental data that the coupling of the inflaton with gravity should be weak, but variable in different epochs of the evolution of the universe.     

Analysis of the pion form factor in the space-like and time-like region

We discuss an analytic parametrization of the pion form factor which is only weakly model dependent. Its model dependence comes from a preference of those analytic functions that are smooth in a certain well-defined sense. Different solutions for different values ofχ ² corresponding to different degrees of smoothness can be constructed. All available space-like and time-like data are taken into account simultaneously. Our approach allows conclusions on an incompatibility of space-like with time-like data sets and on the significance of the occurrence of higher coupled resonances. We discuss the asymptotic behaviour which is consistent with QCD and give the relevant low energy and resonance parameters.     

关于层子模型中的电磁形式因子与结构波函数的积分表示

虽然从B-S方程出发,用谐振子位势来讨论介子的质谱,可以得到较好的结果,但是当用这样得到的近似波函数来计算电磁形式因子时,却给出形式因子对类空的q²为复数。本文指出,出现上述不合理结果的原因,在于所得的近似波函数不具有正确的对P₀的解析性。为了保证这种解析性同时又使波函数保持协变形式,比较适当的方法是,利用戴逊证明的定理将波函数写成积分表示。另外,根据波函数在x=0点为有限的物理要求,我们还给出了积分表示中的谱函数所应满足的一些求和条件。     

Friedmann-Like Equations for High Energy Area of Universe

In this paper, evolution of the high energy area of universe, through the scenario of 5 dimensional (5D) universe, has been studied. For this purpose, we solve Einstein equations for 5D metric and 5D perfect fluid to derive Friedmann-like equations. Then we obtain the evolution of scale factor and energy density with respect to both space-like and time-like extra dimensions. We obtain the novel equations for the space-like extra dimension and show that the matter with zero pressure cannot exist in the bulk. Also, for dark energy fluid and vacuum fluid, we have both accelerated expansion and contraction in the bulk.     

Path integrals and the indefiniteness of the gravitational action

The Euclidean action for gravity is not positive definite unlike those of scalar and Yang-Mills fields. Indefiniteness arises because conformal transformations can make the action arbitrarily negative. In order to make the path integral converge one has to take the contour of integration for the conformal factor to be parallel to the imaginary axis. The path integral will then converge at least in the one-loop approximation if a certain positive action conjecture holds. We perform a zeta function regularization of the one-loop term for gravity and obtain a non-trivial scaling behaviour in cases in which the background metric has non-zero curvature tensor, and hence non-trivial topologies.     

Quaternion-Loop Quantum Gravity

It is shown that the Riemannian curvature of the 3-dimensional hypersurfaces in space-time, described by the Wilson loop integral, can be represented by a quaternion quantum operator induced by the SU(2) gauge potential, thus providing a justification for quaternion quantum gravity at the Tev energy scale.     

Fluid models of single-particle kinematics

A family of trajectories of a single particle, parameterized by initial velocities on some space-like hypersurface, is somewhat analogous to streamline fluid flow. This model is applied to electromagnetism and gravity by introducing velocity and displacement fields. The resulting kinetic field equations are of simpler form than the original equations of motion, and have certain advantages for solution. The gravitational kinetic field equation is, in fact, linear. Some simple solutions are given for illustration.     

Space-time geometry and symmetry breaking

We look for solutions of the Einstein-Yang-Mills equations in a 4 + D dimensional space-time. We find solutions where the first 4 dimensions are a flat Minkowskian space-time, while the D others are a compact, space-like manifold of small size. Such solutions can be obtained for an arbitrary compact gauge group K and are invariant under a sub-group G of K related to the space-time geometry. This shows that 4 + D dimensional gravity can give a mechanism for the super-strong symmetry breaking needed in grand unified field theories without introducing Higgs scalars.     

Apparent horizons of time-symmetric initial value for three black holes

The apparent horizon of three black holes on a time-symmetric space-like hypersurface is examined. The area is computed for various values of separation parameters. Using Hawking's mass formula, we found that the maximum possible efficiency of energy release is no more than 8.44 × 10^-3 when the initial apparent horizon encloses three black holes.     

Space-like Penguin effects in B_c decays

The space-like penguin contributions to branching ratios and CP asymmetries in charmless decays of to two pseudoscalar mesons are studied using the next-to-leading order low energy effective Hamiltonian and factorization approximation. Both the gluonic penguin and the electroweak penguin diagrams are considered. In addition the annihilation diagram contributions are also taken in account. We find that the space-like penguin effects are significant. Received: 15 December 1997 / Published online: 23 June 1998     

Measurement of the space–time interval between two events using the retarded and advanced times of each event with respect to a time-like world-line

Several recent studies have been devoted to investigating the limitations that standard quantum mechanics and/or quantum gravity might impose on the measurability of space–time observables. These analyses are often confined to the simplified context of 2D flat space–time and rely on a simple procedure for the measurement of space-like distances based on the exchange of light signals. We present a generalization of this measurement procedure applicable to all three types of space–time intervals between two events in space–times of any number of dimensions. We also present a preliminary account of an alternative measurement procedure that can be applied taking into account the gravitational field of the macroscopic measuring apparatus.     

Volume dependence of the energy spectrum in massive quantum field theories

The low-lying energy values associated to energy eigenstates describing two stable particles enclosed in a (space-like) box of sizeL are shown to be expandable in an asymptotic power series of 1/L. The coefficients in these expansions are related to the appropriate elastic scattering amplitude in a simple and apparently universal manner. At low energies, the scattering amplitude can thus be determined, if an accurate calculation of two-particle energy values is possible (by numerical simulation, for example).     

Covariant description of Hamiltonian form for field dynamics

Hamiltonian form of field dynamics is developed on a space-like hypersurface in space-time. A covariant Poisson bracket on the space-like hypersurface is defined and it plays a key role to describe every algebraic relation into a covariant form. It is shown that the Poisson bracket has the same symplectic structure that was brought in the covariant symplectic approach. An identity invariant under the canonical transformations is obtained. The identity follows a canonical equation in which the interaction Hamiltonian density generates a deformation of the space-like hypersurface. The equation just corresponds to the Yang-Feldman equation in the Heisenberg pictures in quantum field theory. By converting the covariant Poisson bracket on the space-like hypersurface to four-dimensional commutator, we can pass over to quantum field theory in the Heisenberg picture without spoiling the explicit relativistic covariance. As an example the canonical QCD is displayed in a covariant way on a space-like hypersurface.     

Energy and Angular Momentum of Systems in General Relativity

Stemming from our energy localization hypothesis that energy in general relativity is localized in the regions of the energy-momentum tensor, we had devised a test with the classic Eddington spinning rod. Consistent with the localization hypothesis, we found that the Tolman energy integral did not change in the course of the motion. This implied that gravitational waves do not carry energy in vacuum, bringing into question the demand for the quantization of gravity. Also if information is conveyed by the waves, the traditional view that information transfer demands energy is challenged. Later, we showed that the body angular momentum changed at a rate indicating that the moment of inertia increased to higher order, contrary to traditional expectations. We consider the challenges facing the development of a localized expression for the total angular momentum of the body including the contribution from gravity. We find that Komar's expression does not lead to an adequate formulation of localized angular momentum.