Energy-Momentum Pseudo-Tensor of Relic Gravitational Wave of Both the Polarized States

Unlike usual celestial gravitational waves, the relic gravitational waves （RGWs） form random signals in curved spacetime background. We calculate the energy-momentum pseudo-tensor of a certain component of the RGWs propagating along arbitrary directions in Cartesian coordinates. It is found that the energy density of RGWs is positive definitely, and the momentum density components have reasonable behaviour. Such results may provide a theoretical basis for the detection of RGWs.     

高频引力波与现代宇宙学

文章简要综述了由典型现代宇宙学模型和膜振荡模型预期的微波频带的高频引力波的特性和可能的观测方案，以及研究这一课题的重要科学意义和所面临的挑战和机遇．     

POSITIVE DEFINITE PROBLEM OF ENERGY DENSITY AND RADIATIVE ENERGY FLUX FOR PULSE CYLINDRICAL GRAVITATIONAL WAVE

By using the general expressions of energy momentum pseudo-tensor of the cylin-drical gravitational waves (GW) given by Rosen and Virbhadra in Cartesian coor-dinates, the concrete forms of energy density and radiative energy flux of the pulse cylindrical GW are obtained. Their physical properties, suitable range and asymp-totic behaviour are considered. It is found that: For the region in which space radial coordinates to origin are greater than the pulse width of the pulse cylindrical GW, the energy density and radiative energy flux of the outward travelling pulse cylindrical GW propagating along at light-cone are positive definite. However, for the region in which the space radial coordinates are less than the pulse width, there is no guarantee for the positive definite property of the radiative energy flux of the outward travelling wave. Moreover, we show that the asymptotic behaviour of the energy and energy flux densities of the pulse cylindrical GW and that of the Riemann curvature tensor have good self-consistancy in space like, time like and null infinity regions.     

Phase and Polarization State of High-Frequency Relic Gravitational Waves

The displaying condition of strength, phase and polarization states of high-frequency relic gravitational waves （HFRGWs） in electromagnetic （EM） detecting systems is studied. It is shown that the displaying condition depends not only on the sensitivity of EM detecting systems and the amplitudes of HFRGWs, but also on the phase, the polarization states of HFRGWs and their matching to the EM detecting systems. In order to display simultaneously the strength, phase and polarization states of the resonant ＂monochromatic component＂ of HFRGWs, an important necessary condition is the utilization of two or more different EM detectors.     

A special form of electrodynamical response to a gravitational wave：outgoing and imploding photon fluxes

We have investigated the interaction of an electromagnetic (EM) wave with a standing gravitational wave (GW) in an external static magnetic field,and obtained concrete forms of first-order perturbative EM energy fluxes.Unlike the propagating properties of the “left-circular” and “right-circular” waves of the tangential perturbative energy fluxes around the symmetrical axis,the radial perturbative energy fluxes are expressed as the outgoing and imploding waves to the symmetrical axis.We also examine several physical examples and show that this effect can produce very small but nonvanishing radial perturbative photon fluxes.This may be useful for EM detection of the high-frequency relic GWs of the GHz region in quintessential inflationary models.     

狭窄波束型高频引力辐射与电磁场的作用效应

从弱引力场的Einstein-Maxwell方程出发,讨论了晶体空间阵列的狭窄波束型高频引力辐射与电磁场的作用效应,并给出了扰动解。计算表明,在TT(Transvese Traceless)坐标系中,最优辐射方向的引力波束是纯十型极化的,并可使同频的电磁波产生倍频的扰动效应,使静态电磁场产生与时间成线性关系的累积扰动效应。对于任意方向上的引力辐射波束,在垂直于引力波矢的平面内仍然是纯十型极化的。在高频辐射和实验室典型尺度条件下,TT坐标系与Fermi坐标系的差异是可以忽略的。 关键词：     

Energy—Momentum Pseudo—tensor of Cylindrical Gravitational Waves of Both the Polarized States

According to the Einstein-Tolman expression of the energy-momentum pseudo-tensor(EMPT),we calculate the EMPT of cylindrical gravitational waves (CGW) of both the polarized states (BPS) in cylindrical polar coordinates and Cartesian coordinates.We find that Cartesian coordinates are the more suitable coordinates to describe the CGW of BPS.     

静磁场中双极化态弱平面引力波对高斯束的扰动能量

讨论了处于静磁场中双极化态弱平面引力波对高斯束的一阶和二阶扰动能量，数值计算表明，引力波对整个电磁体系的能量扰动很小.换言之，背景电磁场在引力波作用下其总能量不会发生明显改变，但在局部区域中产生的扰动能流则可能引起可供观测的效应. 关键词： 双极化态弱平面引力波 高斯束 电磁响应 扰动能量     

Utilization of Electromagnetic Detector for Selection and Detection of High-Frequency Relic Gravitational Waves

It is shown that the coupling system between fractal membranes and a Gaussian beam passing through a static magnetic field has strong selection capability for the stochastic relic gravitational wave （GW） background. The relic GW components propagating along the positive direction of the symmetrical axis of the Gaussian beam might generate an optimal electromagnetic perturbation, while the perturbation produced by the relic GW components propagating along the negative and perpendicular directions to the symmetrical axis will be much less than the former, and the influence of the random fluctuation of the relic GWs to such effect can be neglected. The high-frequency relic GWs satisfying the parameters requirement （h - 10^-31 or larger）, frequency resonance and “direction coupling”, in principle, would be selectable and measurable in seconds.     

High-frequency gravitational waves having large spectral densities and their electromagnetic response

Various cosmology models, brane oscillation scenarios, interaction of interstellar plasma with intense electromagnetic radiation, and even high-energy physics experiments （e.g., Large Hadron Collider （LHC）） all predict high frequency gravitational waves （HFGWs, i.e., high-energy gravitons） in the microwave band and higher frequency region, and some of them have large energy densities. Electromagnetic （EM） detection to such HFGWs would be suitable due to very high frequencies and large energy densities of the HFGWs. We review several typical EM detection schemes, i.e., inverse Gertsenshtein effect （G-effect）, coupling of the inverse G effect with a coherent EM wave, coupling of planar superconducting open cavity with a static magnetic field, cylindrical superconducting closed cavity, and the EM sychro-resonance system, and discuss related minimal detectable amplitudes and sensitivities. Furthermore, we give some new ideas and improvement ways enhancing the possibility of measuring the HFGWs. It is shown that there is still a large room for improvement for those schemes to approach and even reach up the requirement of detection of HFGWs expected by the cosmological models and high-energy astrophysical process.