Gravitational field of a pit and maximal mass defects

Abstract

© 2020 American Physical Society. A general relativistic solution, composed of a Zel'dovich-Letelier interior made of radial strings matched through a spherical thin shell at radius r0 to an exterior Schwarzschild solution with mass m, is presented. It is the Zel'dovich-Letelier-Schwarzschild star. When the radius r0 of the star is shrunk to its own gravitational radius 2m, r0=2m, the solutions that appear have very interesting properties. There are solutions with m=0 and r0=0 that further obey 2mr0=1. These solutions have a horizon, but they are not exactly black holes; they are quasiblack holes, though atypical ones. Moreover, the proper mass mp of the interior is nonzero and made of one string. Hence, a Minkowski exterior space hides an interior with matter in a pit. These are the pit solutions. These pits thus show a maximal mass defect. There are two classes of pit solutions: The first encloses a finite string and the second a semi-infinite one. These pits are really string pits, which can be seen as Wheeler bags of gold, albeit totally squashed bags. There is also another class, which is a compact stringy star at the 2mr0=1 limit with m, and thus r0, nonzero. It is a typical quasiblack hole and it also shows maximal mass defect. A generic analysis is presented that shows that pit solutions with 2mr0=1 and m=0 can exist displaying maximal mass defect. The Zel'dovich-Letelier-Schwarzschild star at the r0=2m limit is actually an instance of the generic case. Notably, these three classes of static solutions yield the same spectrum of solutions that appear in critical gravitational collapse-namely, there are solutions that yield naked null singularities, which here are the two string pit classes of solutions, and there are solutions that yield black holes, which here are represented by the class of compact stringy stars at the quasiblack hole limit, the solutions that disperse away in critical gravitational collapse here are the static Zel'dovich-Letelier-Schwarzschild stars themselves. A thermodynamic treatment of the string pit and stringy star quasiblack hole solutions is provided, and connections to other solutions are mentioned.