| 摘要: |
| 考虑了爱因斯坦真空场方程的慢转近似解,该解是一个稳态轴对称度规.当黑洞的旋转参数a较小时,可用该慢转度规精确地描述a的一阶效应.在该慢转时空中自由粒子的总角动量L2是守恒量.在自由粒子运动的基础上,讨论了一类相对论性的无碰撞气体一Vlasov气体在该慢转时空中的吸积，当Vlasov气体满足一-定的条件时，证明了其在相空间.上的分布可以表示为与位形变量无关的函数.通过分布函数可以定义能流密度、能动张量并计算Vlasov气体在该慢转时空中质量、能量、角动量的吸积率.数值结果表明，能流密度、能动张量等物理量相对与史瓦西时空的偏离量在极角θ方向.上近似地呈现正弦分布，并且在赤道面达到最大值，在两个极点，这些物理量和史瓦西时空一致. |
| 关键词: 慢转时空 Vlasov气体 粒子流密度 能动张量 吸积率 |
| DOI：10.3969/J.ISSN.1000-5137.2023.05.003 |
| 分类号:O 412.1 |
| 基金项目: |
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| Acrcretion of Vlasov gas in slow-rotating spacelime |
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LIU Yongqiang1, LI Ping2, ZHAI Xianghua1
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1.Mathematics and Science College, Shanghai Normal University, Shanghai 200234, China;2.Mathematics and Science College, Hunan University of Arts and Science, Changde 415000, Hunan, China
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| Abstract: |
| We consider a slow-rotation approximation to the solution of the Einstein vacuum field equations, which is a stationary axisymmetric metric. When the rotational parameter $a$ of the black hole is small, the first-order effects of $a$ can be accurately described by this slow-rotation metric. The total angular momentum $L^{2}$ of free particles in the slow-rotation spacetime is a conserved quantity. On the basis of free particle motion, we discuss the accretion of the Vlasov gas, a class of relativistic, collisionless gas, onto the slow-rotation spacetime. When the Vlasov gas satisfies certain conditions, we show that its distribution on the phase space can be expressed as a function independent of the configuration variables. The accretion rates of mass, energy, and angular momentum in this slow-rotating spacetime are further calculated after we select a special distribution function and define the physical quantities of the energy flow density and energy-momentum tensor. The numerical results show that the deviations of the energy flow density, energy-motion tensor, and other physical quantities from the Schwarzschild spacetime are approximately sinusoidally distributed in the direction of the polar angle $\theta$ and reach a maximum in the equatorial plane, and these quantities are consistent with the Schwarzschild spacetime at both poles. |
| Key words: slow-rotation spacetime Vlasov gas particle current density stress energy-momentum tensor accretion rate |
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