By Schmidt B.G. (ed.)
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G. [18,76,91]). For example for 3M < r < 6M unstable circular particle orbits exist which are energetically unbound, and thus perturbed particles may escape to infinity; at r = 3M circular photon orbits occur and there are no circular orbits for r < 3M . Particles are trapped by a Schwarzschild black hole if they reach the region r < 3M . g. [92,93], 30 Jiˇr´ı Biˇca ´k and many references therein). One would like to have a split of a covariantly defined quantity (like an acceleration) into non-covariant parts, the physical meaning of which would increase our intuition of relativistic effects in astrophysical problems.
There a more detailed formulation is given. SINGULARITY r = 2 (M+m) EVENT HORIZON APPARENT HORIZON APPARENT HORIZON r=2M COLLAPSING SHELL OF MASS m EVENT HORIZON EVENT HORIZON COLLAPSING STAR OF MASS M Fig. 2. The “teleological” behaviour of the event horizon during the gravitational collapse of a star, followed by the collapse of a shell. The event horizon moves outwards because it will be crossed by the shell. The apparent horizon moves outwards discontinuously (adapted from [74]). 4 25 The Schwarzschild–Kruskal Spacetime In the remarks above we considered the Schwarzschild solution outside a static (possibly oscillating, or expanding from r > 2M ) star, and outside a star collapsing into a black hole.
Both right and left infinities are represented, and the causal structure is well illustrated because worldlines of radial light signals (radial null geodesics) are 45-degree lines in the diagram. In particular the black hole region II and a “newly emerged” (as a consequence of the analytical continuation) white hole region IV (with the white-hole singularity at r = 0) are exhibited. g. [18,19,26,76]. Here we wish to turn in some detail to two very important concepts in black hole theory which were first understood by the analytic extension of the Schwarzschild solution, and which are not often treated in standard textbooks.