Spherical polytropic balls cannot mimic black holes

Hiromi Saida, Atsuhito Fujisawa, Chul Moon Yoo, Yasusada Nambu

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


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 the 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 as black holes, and detection of a shadow image cannot be direct evidence of black hole existence. This paper examines 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 a piecewise polytropic ball. Our result is that the spherical polytropic ball which we have investigated cannot possess UCOP, if the speed of sound at the 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 a shadow image can be regarded as good evidence of black hole existence. As a by-product, we have found the upper bound of the mass-to-radius ratio of a polytropic ball with single index, M/R < 0.281, under the condition of subluminal sound speed.

Original languageEnglish
Article number043E02
JournalProgress of Theoretical and Experimental Physics
Issue number4
Publication statusPublished - Apr 2016
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy


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