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In space-based gravitational wave detection, gravitational wave signals are detected by measuring the Doppler frequency shift of laser exchange between three satellites. Although the laser is pre-stabilized, the laser phase noise is significantly higher than the gravitational wave signal, approximately 7–8 orders of magnitude higher. To reduce the otherwise-overwhelming laser phase noise, the time delay interferometry (TDI) technique is employed by properly time-shifting and linearly combining raw data. Different TDI combinations have various abilities in suppressing laser phase noise, and the response function of gravitational wave signal as well as the power spectral density of noise floor (including test mass acceleration noise and optical path noise) are also different. In this work, we present a unique class of TDI combinations, denoted as [ZX]116,[ZX]216,[ZX]316,[ZX]416, and [ZX]516, which exhibit a distinct geometric space–time diagrams composed of Michelson interferometers as the fundamental constituents. Specifically, when the detector arm lengths are assumed to be equal, these combinations yield response functions and noise power spectral densities of zero. To evaluate the detection performance of these combinations, we investigate their response functions and noise power spectral densities when the detector arm lengths are unequal, and furthermore, derive the analytical expressions for their sensitivity functions. Through our analysis, we have discovered some intriguing results. When the detector arm lengths are unequal, both the response functions and noise spectral densities of these combinations are correlated with the difference in arm lengths L3−L2. However, the sensitivity functions of these TDI combinations remain unaffected by the specific values of the arm length difference, and are consistent with the sensitivity functions of widely-used TDI combinations. For instance, the sensitivity function of [ZX]116 combination is the same as that of the Michelson combination, while the sensitivity functions of [ZX]216 and [ZX]416 combinations match with that of the Sagnac combination. Furthermore, the [ZX]316 and [ZX]516 combinations share the same sensitivity function as the fully symmetric Sagnac combination, enabling the identification of instrument noise and stochastic gravitational wave backgrounds. The discovery of this class of combinations provides support for the diversity of data processing.

Time-delay interferometry (TDI) is a critical data post-processing technique in space-borne laser interferometer gravitational wave detection, which is developed to suppress the overwhelming laser phase noise below the instrumental noise floor by time-shifting and synthesizing the interferometric data streams. There are virous kinds of TDI combinations, and geometric TDI, as a special means to search TDI combination, has been widely used because of its clear physical significance, i.e. constructing virtual equal-arm interferometer to realize an excellent differential performance of the laser phase noise. To achieve the desired noise level, it is necessary to further suppress the phase fluctuations of the onboard ultra-stable oscillators (USO) used as reference clocks. In this paper, we analyze the characteristics of geometric TDI clock noise residual, and formulate it into a general expression. We find the intrinsic equal-arm length constraint of geometric TDI is a sufficient condition for clock noise reduction, which makes the clock noise terms only appear in differential form. Based on this, we propose a clock noise reduction scheme. Compared with the existing algorithms, our method benefits from the sufficient condition to avoid the problem that the clock noise terms without any time-shift operators cannot be properly handled.

We check the validity of the strong cosmic censorship (SCC) for the massless scalar field on top of a charged black hole in an acceleratingly expanding universe driven by the quintessence fluid with the constant equation of state parameter. As a result, we find that the violation of the SCC occurs as the black hole gets close to the extremal limit. In addition, the critical value of the black hole charge ratio for such a violation is increased with the increase of the energy density amplitude of the quintessence fluid but decreased with the increase of the equation of state parameter. Our result shows that the violation of the SCC occurs not only in asymptotically de Sitter spacetimes, but also ubiquitously in a universe with accelerating expansion.