Real scalar field scattering in the nearly extremal Schwarzschildben de Sitter space

Reasonable approximations are introduced to investigate the real scalar field scattering in the nearly extremal Schwarzschild--de Sitter (SdS) space. The approximations naturally lead to the invertible x(r) and the global replacement of the true potential by a P?shl--Teller one. Meanwhile, the Schr?dinger-like wave equation is transformed into a solvable form. Our numerical solutions to the wave equation show that the wave is characteristically similar to the harmonic under the tortoise coordinate x, while the wave piles up near the two horizons and the wavelength tends to its maximum as the potential approaches to the peak under the radial coordinate r.     

Scalar massless field in de Sitter space

A method for quantizing a scalar massless field in the de Sitter space is demonstrated; the method is based on the conformai invariance of the field equation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 19–24, July, 1972.The author would like to thank Professor N. A. Chernikov for his aid and É. A. Tagirov for helpful criticism.     

Real scalar field scattering in the nearly extremal Schwarzschild de Sitter space

Reasonable approximations are introduced to investigate the real scalar field scattering in the nearly extremal Schwarzschild-de Sitter (SdS) space.The approximations naturally lead to the invertible x(r) and the global replacement of the true potential by a Pshl-Teller one.Meanwhile,the Schrdinger-like wave equation is transformed into a solvable form.Our numerical solutions to the wave equation show that the wave is characteristically similar to the harmonic under the tortoise coordinate x,while the wave piles up near the two horizons and the wavelength tends to its maximum as the potential approaches to the peak under the radial coordinate r.     

de Sitter branes with a bulk scalar

We propose new brane world models arising from a scalar field in the bulk. In these examples, the induced on-brane line element is de Sitter (or anti de Sitter) and the bulk (five dimensional) Einstein equations can be exactly solved to obtain warped spacetimes. The solutions thus derived are single and two-brane models—one with thin branes while the other one of the thick variety. The field profiles and the potentials are obtained and analysed for each case. We note that for the thick brane scenario the field profile resembles a kink, whereas for one or more thin branes, it is finite and bounded in the domain of the extra dimension. We have also addressed the localisation of gravity and other matter fields on the brane for these braneworld models.     

CPT groups for spinor field in de Sitter space

A group structure of the discrete transformations (parity, time reversal and charge conjugation) for spinor field in de Sitter space are studied in terms of extraspecial finite groups. Two CPT groups are introduced, the first group from an analysis of the de Sitter–Dirac wave equation for spinor field, and the second group from a purely algebraic approach based on the automorphism set of Clifford algebras. It is shown that both groups are isomorphic to each other.     

Kink stability of self-similar solutions of scalar field in 2 + 1 gravity

The kink stability of self-similar solutions of a massless scalar field with circular symmetry in 2 + 1 gravity is studied, and found that such solutions are unstable against the kink perturbations along the sonic line (self-similar horizon). However, when perturbations outside the sonic line are considered, and taking the ones along the sonic line as their boundary conditions, we find that non-trivial perturbations do not exist. In other words, the consideration of perturbations in the whole spacetime limits the unstable mode of the perturbations found along the sonic line, and the kink instability rises because of the incomplete treatment of the problem. As a result, the critical solution for the scalar collapse remains critical even after the kink perturbations are taken into account.     

Adiabatic regularization and Green's function of a scalar field in de Sitter space: Positive energy spectrum and no trace anomaly

In the conventional adiabatic regularization the vacuum ultraviolet divergences of a quantum field in curved spacetime are removed by subtracting the k-mode of the stress tensor to the 4 th-order.For a scalar field in de Sitter space,we find that the4 th-order regularized spectral energy density is negative.Moreover,the 2 nd-order regularization for minimal coupling(ξ=0)and the 0 th-order regularization for conformal coupling(ξ=1/6) yield a positive and UV-convergent spectral energy density and power spectrum.The regularized stress tensor in the vacuum is maximally symmetric and can drive inflation,while its k-modes representing the primordial fluctuations are nonuniformly distributed.Conventional regularization of a Green's function in position space is generally plagued by a log IR divergence.Only in the massless case with ξ=0 or 1/6,we can directly regularize the Green's functions and obtain vanishing results that agree with the adiabatic regularization results.In this case,the regularized power spectrum and stress tensor are both zero,and no trace anomaly exists.To overcome the log IR divergence problem in the massive cases with ξ=0 and 1/6,we perform Fourier transformation of the regularized power spectra and obtain the regularized analytical Green's functions which are IR-and UV-convergent.     

Adiabatic invariants and scalar fields in a de Sitter space-time

The method of adiabatic invariants for time dependent Hamiltonians is applied to a massive scalar field in a de Sitter space-time. The scalar field ground state, its Fock space and coherent states are constructed and related to the particle states. Diverse quantities of physical interest are illustrated and compared with previous results.     

On the most general metric of a radiating mass in a de Sitter space

Mallett's generalized form of Vaidya's radiating metric describing a radiating mass in a de Sitter background has been proved to be the most general. Further generalizations by others have turned out to be futile exercises.