Dynamics of Einstein's equation modified by a higher-order derivative term
Dynamics of Einstein's equation modified by a higher-order derivative term
复制标题
由高阶导数项修正的爱因斯坦方程的动力学
DOI：
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发表时间：
1978
期刊：
影响因子：
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通讯作者：
R. Wald
中科院分区：
文献类型：
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作者：
G. Horowitz;R. Wald
在弯曲时空中寻找量子场的重整化应力-能量算符提出了一个问题，即是否可以在爱因斯坦方程中加入包含度规四阶导数的项，并且仍然保持合理的理论。我们调查这个问题，考虑一个简单的情况下，共形不变的字段在共形平坦的时空，其中一个有一个明确的预测的真空应力能量的字段。我们发现，如果一个特定的四阶项（与D/sup 7/AlembertianR迹异常）进入一个符号，平坦的时空是不稳定的共形平坦的扰动，指数增长的普朗克时间尺度。如果这个项以另一个符号进入，共形平坦微扰可能导致时空以普朗克频率振荡，导致带电测试粒子的高能辐射。
The search for a renormalized stress-energy operator of a quantum field in curved spacetime has raised the question of whether one can add terms to Einstein's equation containing fourth-order derivatives of the metric, and still maintain a reasonable theory. We investigate this question by considering the simple case of a conformally invariant field in a conformally flat spacetime, where one has a well-defined prediction for the vacuum stress energy of the field. We find that if a certain fourth-order term (associated with the D/sup 7/AlembertianR trace anomaly) enters with one sign, flat spacetime is unstable to conformally flat perturbations that grow exponentially on the Planck time scale. If this term enters with the other sign, conformally flat perturbations could cause spacetime to oscillate at the Planck frequency, resulting in high-energy radiation by charged test particles.