The field equations, which are the mathematical basis of the theory of general relativity, provide us with a much larger variety of solutions to model the neutron stars and other compact objects than are used in the current astrophysics. We point out some important consequences of the new kind of solutions of the field equations, which can be obtained if the astrophysical usage of general relativity is not constrained, and outline an impact of these solutions on the models of internal structure of compact objects. If general relativity is not constrained, it enables to construct the stable object, with the outer surface above the event horizon, of whatever large mass. A new concept of relativistic compact object is a consequence of newly discovered property of gravity, yielded by the field equations in a spherically symmetric configuration of matter: in comparison with the Newtonian case, a particle is more effectively attracted by a nearer than a more distant matter.

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Using the Lynch method, we continue the discussion on the statistical significance of agreement between planetary distributions and a power law. The Lynch method determines the probability that a power law (e.g. the Titius-Bode law) will agree by chance, at the observed level, with a given sequence of planetary distances. We find interesting results by assuming not only that the mean asteroid-belt distance should be considered as a regular planetary distance, but also that the current distance of the Earth should be regarded as peculiar and omitted from the Titius-Bode law. We examine these assumptions under two cases: (a) where no physical limitations are imposed and (b) where relatively close planetary orbits are excluded. We find that the corresponding sequence of distances matches the power law by chance with a probability of only 0.3 per cent for case (a) and 3 per cent for (b). These values are in direct contrast to those corresponding to the traditional Titius-Bode law as well as those corresponding to some common alternative assumptions. These range from 29 to 100 per cent for (a) and 95 to 100 per cent for (b).