Noncommutative gravity is a natural method of quantizing spacetime by promoting the spacetime coordinates themselves to operators which do not commute. This approach is motivated from a quantum gravity perspective, as well as from other theoretical considerations.} Noncommutative gravity has been tested against the binary black hole merger event GW150914. Here, we extend and improve upon such a previous analysis by (i) relaxing an assumption made on the preferred direction due to noncommutativity, (ii) using posterior samples produced by the LIGO/Virgo Collaborations, (iii) consider other gravitational wave events, namely GW151226, GW170608, GW170814 and GW170817, and (iv) consider binary pulsar observations. Using Kepler’s law that contains the noncommutative effect at second post-Newtonian order, we derive corrections to the gravitational waveform phase and the pericenter precession. Using the gravitational wave and double pulsar binary observations, we find bounds on a space-time noncommutative tensor ${\theta }^{0i}$ in terms of the preferred frame direction with respect to the orientation of each binary. We find that the gravitational wave bounds are stronger than the binary pulsar one by an order of magnitude and the noncommutative tensor normalized by the Planck length and time is constrained to be of order unity.

中文翻译：

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利用引力波和二元脉冲星观测探测非对流重力

非交换重力是通过将时空坐标自身提升为不上下班的算子来量化时空的自然方法。从量子引力的角度以及其他理论考虑出发，采用了这种方法。}已针对二元黑洞合并事件GW150914对非交换重力进行了测试。在这里，我们通过（i）放宽对由于非可交换性而在首选方向上做出的假设，（ii）使用LIGO /处女座合作社产生的后验样本，（iii）考虑其他引力波事件，来扩展和改进此类分析。 GW151226，GW170608，GW170814和GW170817，以及（iv）考虑二进制脉冲星观测。使用开普勒定律，该定律包含牛顿二阶后阶的非交换效应，我们得出对重力波形相位和中心点进动的校正。利用引力波和双脉冲星二元观测，我们发现了时空非交换张量的界${\theta }^{0\mathrm{一世}}$相对于每个二进制文件的方向的首选帧方向而言。我们发现，引力波边界比二元脉冲星的边界强一个数量级，并且通过普朗克长度和时间归一化的非交换张量被约束为一阶。