Abstract
In 2011, Jun Ni published the solution of the Tolman-Oppenheimer-Volkoff equations describing the structure of stable neutron stars, which implies that 1) there is no upper mass limit of these objects, 2) their outer physical surface is always situated above the corresponding event horizon, and 3) the object is a hollow sphere with the inner physical surface and cavity inside. In our paper, we propose to “purify” the general relativity, as the geometrical theory, from the concept of mass. If we get rid of the concept of mass and Newtonian-type potential, then we obtain such the behavior of gravity which results in the above mentioned stable Ni’s object. It is farther pointed out that the distribution of matter, which is observed as spherically symmetric by the observer in its center, is not longer observed as spherically symmetric by an observer aside the center in a curved spacetime of general relativity. This fact implies, in contrast to the Newtonian physics, the non-zero and outward oriented gravitational attraction of upper layers of star. Ni considered positive energy density and pressure. In addition, gravity had everywhere attractive character. No “exotic” assumption was made. Hence, there is no reason why his concept of hollow sphere should not be applicable to the models of real objects.
Highlights
In their famous work published in 1939, Oppenheimer and Volkoff [1] concluded that there is no solution for a stable configuration of dead star, without an internal source of energy, if the mass of the star exceeds a certain critical limit, which was later named by them
When we speak about the gauging of the constants produced by the integrations of the Einstein field equations (EFEs), the most common example is, likely, the gauging of the constants in the OSS, which describes the vacuum metrics shaped by a point-like particle
Since the geometry of spacetime is determined by stress-energy tensor, the quantities as energy and gravitational potential are the integral part of the theory, except of the geometrical aspects
Summary
In their famous work published in 1939, Oppenheimer and Volkoff [1] concluded that there is no solution for a stable configuration of dead star, without an internal source of energy, if the mass of the star exceeds a certain critical limit, which was later named by them. Ni attempted to reproduce the creation of the Oppenheimer-Volkoff model of neutron star. He proceeded in the same way as the original authors of the model, except of the starting point of the numerical integration of the differential equations, which are relevant to the model. The inward proceeded part of the Ni’s integration always ended with zero pressure and energy density in a finite star-centric distance, i.e. he obtained a model with an inner physical surface of the object. He concluded that there is no upper-mass limit. The Ni’s result evokes some fundamental questions on the principles and postulates within the general relativity, especially those, which were originally established within the Newtonian physics and appeared in general relativity after their formal generalization
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