球形多变球不能模仿黑洞
Spherical polytropic balls cannot mimic black holes
摘要：
所谓黑洞阴影，是在光学观测黑洞的精细图像中，预计会出现的暗区。它实质上是一个黑洞的吸收截面，阴影的边界由不稳定的光子圆轨道（UCOP）决定。如果存在一个具有UCOP但没有黑洞视界的致密天体，它可以提供与黑洞相同的阴影像，而阴影像的探测不能作为黑洞存在的直接证据。然后，本文研究了在适当的条件下，这种紧对象是否存在。本文对具有单一多变指数的理想流体的静态球形多变球进行了深入的研究，并对一个典型的分段多变球进行了研究。我们的结果是，我们所研究的球形多变球，如果中心的声速是亚光速（慢于光速），则不具有UCOP。这意味着，如果本文所处理的多面体是致密天体中恒星物质的一个好模型，那么阴影像的探测就被认为是黑洞存在的一个好证据。作为副产品，我们在亚光速条件下，找到了单折射率多变球的质径比（M/R）的上界，M/R < 0.281。
英文摘要：
The so-called black hole shadow is a dark region which is expected to appear in a fine image of optical observation of black holes. It is essentially an absorption cross section of black hole, and the boundary of shadow is determined by unstable circular orbits of photons (UCOP). If there exists a compact object possessing UCOP but no black hole horizon, it can provide us with the same shadow image with black holes, and a detection of shadow image cannot be a direct evidence of black hole existence. Then, this paper examine whether or not such compact objects can exist under some suitable conditions. We investigate thoroughly the static spherical polytropic ball of perfect fluid with single polytrope index, and then investigate a representative example of the piecewise polytropic ball. Our result is that the spherical polytropic ball which we have investigated cannot possess UCOP, if the sound speed at center is subluminal (slower-than-light). This means that, if the polytrope treated in this paper is a good model of stellar matter in compact objects, the detection of shadow image is regarded as a good evidence of black hole existence. As a by-product, we have found the upper bound of the mass-to-radius radio (M/R) of polytropic ball with single index, M/R < 0.281, under the subluminal-sound-speed condition.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
