arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1908.11058gr-qcastro-ph.COhep-th
收藏

基谢廖夫黑洞既不是完美的流体,也不是精华

The Kiselev black hole is neither perfect fluid, nor is it quintessence

Matt Visser

摘要:

基谢廖夫黑洞时空,\[ ds^2 = - \left(1-{2m\over r} - {K\over r^{1+3w}} \right) dt^2 + {dr^2\over1-{2m\over r} - {K\over r^{1+3w}}} + r^2 \,dΩ_2^2, \]是一个非常受欢迎的玩具模型,截至2019年有超过200个直接和间接引用。不幸的是,尽管一再断言相反,这不是一个完美的流体时空。相对压力各向异性和平均压力很容易计算,以满足\[ Δ= {Δp\over \bar p} = {p_r - p_t \over {1\over3} (p_r+2p_t)} =- {3(1+w)\over 2 w}; \qquad\qquad {\bar p\over ρ} = {{1\over3} (p_r + 2p_t)\over ρ} = w. \]相对压力各向异性$Δ$通常是一个非零常数,(除非$w=-1$,对应于史瓦西-(反)-德西特时空)。基谢廖夫的原始文件是非常小心地指出这一点,在计算,但随后在讨论了一个有点不幸的选择术语已(非常有限的例外)被复制到随后的文献。也许更糟糕的是,基谢廖夫对“精髓”一词的使用与宇宙学界的标准用法不符,导致了另一个不幸和不必要的混乱。很少有后续论文能正确地理解这些观点,因此有必要做一个简短的明确评论。

英文摘要:

The Kiselev black hole spacetime, \[ ds^2 = - \left(1-{2m\over r} - {K\over r^{1+3w}} \right) dt^2 + {dr^2\over1-{2m\over r} - {K\over r^{1+3w}}} + r^2 \,dΩ_2^2, \] is an extremely popular toy model, with over 200 direct and indirect citations as of 2019. Unfortunately, despite repeated assertions to the contrary, this is not a perfect fluid spacetime. The relative pressure anisotropy and average pressure are easily calculated to satisfy \[ Δ= {Δp\over \bar p} = {p_r - p_t \over {1\over3} (p_r+2p_t)} =- {3(1+w)\over 2 w}; \qquad\qquad {\bar p\over ρ} = {{1\over3} (p_r + 2p_t)\over ρ} = w. \] The relative pressure anisotropy $Δ$ is generally a non-zero constant, (unless $w=-1$, corresponding to Schwarzschild-(anti)-de Sitter spacetime). Kiselev's original paper was very careful to point this out in the calculation, but then in the discussion made a somewhat unfortunate choice of terminology which has (with very limited exceptions) been copied into the subsequent literature. Perhaps worse, Kiselev's use of the word "quintessence" does not match the standard usage in the cosmology community, leading to another level of unfortunate and unnecessary confusion. Very few of the subsequent follow-up papers get these points right, so a brief explicit comment is warranted.

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。

↑