We compare Newtonian and general relativistic descriptions of the stationary accretion of self-gravitating fluids onto compact bodies. Spherical symmetry and thin gas approximation are assumed. Luminosity depends, amongst other factors, on the temperature and the contribution of gas to the total mass, in both -- general relativistic ($L_{GR}$) and Newtonian ($L_N$) -- models. We discover a remarkable universal behaviour for transonic flows: the ratio of respective luminosities $L_{GR}/L_N$ is independent of the fractional mass of the gas and depends on asymptotic temperature. It is close to 1 in the regime of low asymptotic temperatures and can grow by one order of magnitude for high temperatures. These conclusions are valid for a wide range of polytropic equations of state.
我们引入了一个腔封闭源质量$M$来定义温度力。从定态时空中的托尔曼温度出发，我们找到了一个非相对论温度$T_{non}= T_\infty(1-Φ/c^2)$，它具有牛顿势$Φ$。该温度也可以从Tolman-Ehrfest效应导出，满足$T=T_{\infty}e^{-Φ/c^2}$与局部温度$T$的关系。最后，在不引入全息原理定义的全息屏和熵力均分定律的情况下，导出了温度力$\vec{F}_{tem}=mc^2(\vec{\nabla} \ln T )$，从而导出牛顿力定律。
Universality in Relativistic Spinning Particle Models
Walter Burke Institute for Theoretical Physics, California Institute of Technology（加州理工学院沃尔特·伯克理论物理研究所）；School of Physics, Korea Institute for Advanced Study（韩国高等科学研究院物理学院）
