Search for quantum spacetime foam

The possibility that quantum fluctuations in the structure of spacetime at the Planck scale might be subject to experimental probes in discussed. The effects of spacetime foam in an approach inspired by string theory, in which solitonic D-brane excitations are taken into account when considering the ground state, are studied. The properties of this medium are described by analyzing the recoil of a D particle which is induced by the scattering of a closed-string state. This recoil causes an energy-dependent perturbation of the background metric, which in turn induces an energy-dependent refractive index in vacuo, and stochastic fluctuations of the light cone. Distant astrophysical sources such as Gamma-Ray Bursters (GRBs) may be used to test this possibility, and an illustrative analysis of GRBs whose redshifts have been measured is presented. The propagation of massive particles through such a quantum spacetime foam is also discussed.     

Probing spacetime foam with extragalactic sources

Because of quantum fluctuations, spacetime is probably "foamy" on very small scales. We propose to detect this texture of spacetime foam by looking for halo structures in the images of distant quasars. We find that the Very Large Telescope interferometer will be on the verge of being able to probe the fabric of spacetime when it reaches its design performance. Our method also allows us to use spacetime foam physics and physics of computation to infer the existence of dark energy or matter, independent of the evidence from recent cosmological observations.     

A class of metric theories of gravitation on Minkowski spacetime

A class of metric theories of gravitation on Minkowski spacetime is considered, which is—provided that certain assumptions (staying close to the original ideas of Einstein) are made—the almost most general one that can be considered. In addition to the Minkowskian metric G a dynamical metric H (called the Einstein metric)is defined by means of a second-rank tensor field S (referred to as gravitational potential).The theory is defined by a Lagrangian , from which the field equations as well as, e.g., the energy-momentum tensor field for the gravitational field follow. The case of weak fields is considered explicitly. The static, spherically and time-inversal symmetric field is calculated, and as a first step to investigate the theory's viability the parameters are fitted to the experimental data of the perihelion advance and the deflection of light at the Sun. Finally the question of gauge freedoms in the gravitational potential is briefly discussed.     

Large N-wormhole approach to spacetime foam

A simple model of spacetime foam, made by N wormholes in a semiclassical approximation, is taken under examination. We show that the qualitative behaviour of the fluctuation of the metric conjectured by Wheeler is here reproduced.     

Rigorous model of classical spacetime foam

If in the gravity quantization process one changes from the smooth manifold category to a more general category, qualitatively new features can appear. To illustrate this, we construct a geometrically precise but physically naive model of a classical “spacetime foam” and discuss the consequences of the principle of general covariance and the equivalence principle in this more general setting. We also show how Einstein's equations can be defined on this “spacetime foam”.     

Fundamental length scale of quantum spacetime foam

It is argued that the fundamental length scale for the quantum dynamics of spacetime need not be equal to the Planck length. Possibly, this new length scale is related to a nonvanishing cosmological constant or vacuum energy density. The text was submitted by the author in English.     

五维时空中度规的计算

在四维R+R2引力理论中给出了Wheeler-Dewitt(W-D)方程,通过分离变量法得到了W-D方程的解.利用Kaluza-Klein理论将Robertson-Walker度规推广到五维时空,结合时空中的场方程得到宇宙项与能量之间的关系.     

Errata: A class of metric theories of gravitation of Minkowski spacetime

A mistake which occurred in the derivation of the field equations from the Lagrangian is corrected. Unfortunately many of the expressions given in the article have to be changed, although the results do not change qualitatively, but only quantitatively.     

Effects related to spacetime foam in particle physics

It is found that the existence of spacetime foam leads to a situation in which the number of fundamental quantum bosonic fields is a variable quantity. The general aspects of an exact theory that allows for a variable number of fields are discussed, and the simplest observable effects generated by the foam are estimated. It is shown that in the absence of processes related to variations in the topology of space, the concept of an effective field can be reintroduced and standard field theory can be restored. However, in the complete theory the ground state is characterized by a nonvanishing particle number density. From the effective-field standpoint, such particles are “dark.” It is assumed that they comprise dark matter of the universe. The properties of this dark matter are discussed, and so is the possibility of measuring the quantum fluctuation in the field potentials. Zh. éksp. Teor. Fiz. 115, 1921–1934 (June 1999)     

de Sitter spacetime: effects of metric perturbations on geodesic motion

Gravitational perturbations of the de Sitter spacetime are investigated using the Regge–Wheeler formalism. The set of perturbation equations is reduced to a single second order differential equation of the Heun-type for both electric and magnetic multipoles. The solution so obtained is used to study the deviation from an initially radial geodesic due to the perturbation. The spectral properties of the perturbed metric are also analyzed. Finally, gauge- and tetrad-invariant first-order massless perturbations of any spin are explored following the approach of Teukolsky. The existence of closed-form, i.e. Liouvillian, solutions to the radial part of the Teukolsky master equation is discussed.     

Quantum corrections to the spacetime metric from geometric phase space quantization

We consider the possibility that the physical spacetime of a quantum particle may be regarded as a four-dimensional hypersurface locally embedded in eightdimensional phase space. We show that, as a consequence, accelerated particles are seen to live in a curved spacetime, and, in the particular case of uniform acceleration, we are led to a generalization of the Rindler metric which implies, for a uniformly accelerated particle, a discrete energy spectrum.     

Dirac equation in curved spacetime with the metric in the Kerr-Schield form

The solution of the Dirac equation in the wave package form in a slightly curved spacetime (compared with the size of the wave package) was studied. For the metric in the Kerr-Schield form, a system of common differential equations describing spin conditions of massive neutral Dirac particles (neutrinos) was obtained. The effect of depolarization of the massive neutrinos in a gravitational field are discussed. This effect allows a considerable similarity between the theoretical and observed solar neutrino flows to be established if $m_{\nu _e } \geqslant 10^{ - 4} $ .     

A NUT-like electrovac spacetime

A solution of the Einstein-Maxwell equations corresponding to source-free electromagnetic field is obtained. The solution is algebraically special. A particular case of the solution is considered which includes Brill’s solution. The details regarding the solution are also discussed.     

A singular conformal spacetime

The infinite cosmological “constant” limit of the de Sitter solutions to Einstein’s equation is studied. The corresponding spacetime is a singular, four-dimensional cone-space, transitive under proper conformal transformations, which constitutes a new example of maximally-symmetric spacetime. Grounded on its geometric and thermodynamic properties, some speculations are made in connection with the primordial universe.