One-loop quantum gravity repulsion in the early Universe

Perturbative quantum gravity formalism is applied to compute the lowest order corrections to the classical spatially flat cosmological Friedmann-Lema?tre-Robertson-Walker solution (for the radiation). The presented approach is analogous to the approach applied to compute quantum corrections to the Coulomb potential in electrodynamics, or rather to the approach applied to compute quantum corrections to the Schwarzschild solution in gravity. In the framework of the standard perturbative quantum gravity, it is shown that the corrections to the classical deceleration, coming from the one-loop graviton vacuum polarization (self-energy), have (UV cutoff free) opposite to the classical repulsive properties which are not negligible in the very early Universe. The repulsive "quantum forces" resemble those known from loop quantum cosmology.     

One-loop counterterms for dimensionally reduced quantum gravity

The technique of regularization by dimensional reduction is applied to source-free quantum gravity. The one-loop counterterms for the effective gravity-matter system are calculated in the background field formalism. The ersatz matter fields which arise in this regularization scheme are found to have no effect on the renormalizability of the theory.     

One-loop counterterms in 2d dilaton-Maxwell quantum gravity

The renormalization structure of two-dimensional quantum gravity is investigated in a covariant gauge. One-loop divergences of the effective action are calculated. All the surface divergent terms are taken into account thus completing previous one-loop calculations of the theory. It is shown that the on-shell effective action contains only surface divergences. The off-shell renormalizability of the theory is discussed and classes of renormalizable dilaton and Maxwell potentials are found.     

Analytical time-like geodesics in Schwarzschild space-time

Time-like orbits in Schwarzschild space-time are presented and classified in a very transparent and straightforward way into four types. The analytical solutions to orbit, time, and proper time equations are given for all orbit types in the form r = r(λ), t = t(χ), and τ= τ (χ), where λ is the true anomaly and χ is a parameter along the orbit. A very simple relation between λ and χ is also shown. These solutions are very useful for modelling temporal evolution of transient phenomena near black holes since they are expressed with Jacobi elliptic functions and elliptic integrals, which can be calculated very efficiently and accurately.     

One-loop scalar field contributions to graviton-graviton scattering and helicity non-conservation in quantum gravity

We present and discuss the helicity amplitudes for graviton-graviton scattering via a loop of massless scalars. The amplitudes have the expected analytic structure but do not conserve helicity. We prove that as a consequence helicity is not conserved in pure quantum gravity either and the helicity flip amplitudes are given by two times the scalar loop contributions. Implications for the higher-loop renormalizability of quantum gravity are discussed.     

Black holes in loop quantum gravity: the complete space-time

We consider the quantization of the complete extension of the Schwarzschild space-time using spherically symmetric loop quantum gravity. We find an exact solution corresponding to the semiclassical theory. The singularity is eliminated but the space-time still contains a horizon. Although the solution is known partially numerically and therefore a proper global analysis is not possible, a global structure akin to a singularity-free Reissner-Nordstr?m space-time including a Cauchy horizon is suggested.     

Third-order Killing tensors in the Schwarzschild space-time

The general solution for the third-order Killing tensor equation in the Schwarzschild space-time is written down. It follows that the Schwarzschild metric admits only redundant Killing tensors of order 3.This work was carried out under the auspices of the National Group for Mathematical Physics of C. N. R.     

Tachyon trajectories in Schwarzschild’s space-time

The motion of a tachyon in the empty Schwarzschild solution outside a massm is discussed. It is shown that a tachyon falling radially inwards never reaches the space-time singularity at the origin. Instead, it is bounced back at a point inside the Schwarzschild radius. The causal and non-causal aspects of such a bounce are considered. It is shown that a tachyon dropped from a radial co-ordinate <2.56m always airives before it went in whereas a tachyon dropped from a radial co-ordinate >3.27m always arrives later than its starting time. The more general case of a tachyon with a finite angular momentum is also analyzed. The possible astrophysical consequences of the presence of tachyons near condensed or collapsing objects and black holes are qualitatively discussed.     

Circular orbits and relative strains in Schwarzschild space-time

The equation of the relative strain is analyzed in tetrad form with respect to a family of observers moving on spatially circular orbits, in the Schwarzschild space-time. We select a field of tetrads, which we term phase locking frames, and explicitly calculate how, in the equatorial plane, the orbital acceleration, its gradient and the Fermi drag add together to compensate the curvature and assure equilibrium among a set of comoving neighbouring particles. While equilibrium is achieved in the radial and azimuthal directions, in the direction orthogonal to the equatorial plane there is a residue of acceleration which pulls a particle towards that plane leading to a harmonic oscillation with a frequency equal to the proper frequency of the orbital revolution. This measurement, combined with those of the frequency shift of an incoming photon and the frequency of precession of the local compass of inertia, enables one to determine the relativistic ratio 2M/r, whereM is the gravitational mass of the source andr the coordinate radius of the circular orbits.     

Curved space-time formulation of the conformal sector for 4D quantum gravity

Developing the approach by Antoniadis and mottola to 4D quantum gravity, we investigate the dynamics of the conformal factor of 4D induced gravity in arbitrary curved background. The one-loop -functions are calculated in infrared stable fixed point where the effective scalar theory is multiplicatively renormalized.     

Self-interaction and massive vector field in the Schwarzschild space-time

Using a multipole expansion, we determine formally the massive vector field generated by a point source held fixed in the Schwarzschild space-time. We prove that its limit, when the mass of the Proca field goes to zero, does not tend to the corresponding massless vector field. In this limit we evaluate the expression of the self-force acting on the particle. The result is in accordance with that of Vilenkin, without the assumption that the point source is at a large distance from the horizon, that we extend to the case of a Reissner-Nordström space-time. We also investigate a further case: a point source within a spherical shell of matter for which the Proca field tends to the corresponding massless vector field.     

One-loop divergences of linear gravity with torsion terms

We investigate the role of the torsion field at the quantum level. One-loop counterterms are calculated in the theory with terms quadratic in the torsion field. We have shown that the theory is finite at the one-loop level.     

史瓦西时空中自由粒子的运动方程

直接求解史瓦西时空中自由粒子的测地线方程,得出粒子运动方程的一般常见形式.此方法与一般教材中根据史瓦西度规的静态球对称性以及四速归一条件得出的运动方程完全相同.此方法物理意义更清晰、明确,同时对理解弯曲时空中的测地线方程具有重要意义.