# 托尔曼－奥本海默－沃尔科夫方程

## 方程形式

$\frac{dP(r)}{dr}=-\frac{G(\rho(r)+P(r)/c^2)(M(r)+4\pi P(r) r^3/c^2)}{r^2(1-2GM(r)/rc^2)}.$

$\frac{dM(r)}{dr}=4 \pi \rho(r) r^2.$

$ds^2=e^{\nu(r)} c^2 dt^2 - (1-2GM(r)/rc^2)^{-1} dr^2 - r^2(d\theta^2 + sin^2 \theta d\phi^2),$

$\frac{d\nu(r)}{dr}=-\frac{2}{P(r)+\rho(r)c^2} \frac{dP(r)}{dr}.$

$ds^2=(1-2GM_0/rc^2) c^2 dt^2 - (1-2GM_0/rc^2)^{-1} dr^2 - r^2(d\theta^2 + sin^2 \theta d\phi^2)\,$

$M_0=M(r_B)=\int_0^{r_B} 4\pi \rho(r) r^2\, dr.$

$M_1=\int_0^{r_B} \frac{4\pi \rho(r) r^2}{\sqrt{1-2GM(r)/rc^2}} \, dr.$

$\delta M=\int_0^{r_B} 4\pi \rho(r) r^2((1-2GM(r)/rc^2)^{-1/2}-1)\, dr,$

## 参考资料

1. ^ 1.0 1.1 1.2 1.3 1.4 On Massive Neutron Cores, J. R. Oppenheimer and G. M. Volkoff, Physical Review '55', #374 (February 15, 1939), pp. 374–381.
2. '^ Effect of Inhomogeneity on Cosmological Models, Richard C. Tolman, Proceedings of the National Academy of Sciences '20, #3 (March 15, 1934), pp. 169–176.
3. '^ Static Solutions of Einstein's Field Equations for Spheres of Fluid, Richard C. Tolman, Physical Review '55, #374 (February 15, 1939), pp. 364–373.
4. '^ The maximum mass of a neutron star, I. Bombaci, Astronomy and Astrophysics '305 (January 1996), pp. 871–877.
5. ^ Bombaci, I. The maximum mass of a neutron star. Astronomy and Astrophysics. 1996, 305: 871–877.
6. ^ The evolution and explosion of massive stars, S. E. Woosley, A. Heger, and T. A. Weaver, Reviews of Modern Physics 74, #4 (October 2002), pp. 1015–1071.
7. ^ Black Hole Binaries, Jeffrey E. McClintock and Ronald A. Remillard, arXiv:astro-ph/0306213v4.
8. ^ Observational evidence for stellar-mass black holes, Jorge Casares, arXiv:astro-ph/0612312v1.