Vacuum fluctuation inside a star and their consequences for neutron stars, a simple model

Abstract

Applying semi-classical Quantum Mechanics, the vacuum fluctuations within a star are determined, assuming a constant mass density and applying a monopole approximation. It is found that the density for the vacuum fluctuations does not only depend linearly on the mass density, as assumed in a former publication, where neutron stars up to 6 solar masses were obtained. This is used to propose a simple model on the dependence of the dark energy to the mass density, as a function of the radial distance r. It is shown that stars with up to 200 solar masses can, in principle, be obtained. Though, we use a simple model, it shows that in the presence of vacuum fluctuations stars with large masses can be stabilized and probably stars up to any mass can exist, which usually are identified as black holes.

Kerr Black Holes within a Modified Theory of Gravity

“…independent from a. In case b = b n max , there is a zero of the orbital frequency, coinciding with a horizon (19), and it is also independent on a. r 0 is at the estimated position of the star's surface. For 0 ≤ b n < b n max , the lower curves slowly merge into the upper one for b → 0.…”

“…The application of pc-GR is not only limited to the region outside of a mass distribution, but also was applied to the interior of the star [18,19,[39][40][41][42][43]. The main problem is to propose a coupling of the dark energy to the mass distribution, which, due to not knowing it from first principles, is always charged with phenomenological assumptions.…”

“…The reason is that, near the surface, the repulsion is strong enough that the star sheds its upper parts of the surface. In [19], this was resolved partially, applying a calculation within the one-loop approximation of quantized gravity [37] and using the monopole approximation. As a result, the distribution of the dark energy turns out to fall off stronger near the surface.…”

“…In addition, neutron stars were studied in [18][19][20], in addition to [9]. Including the effects of the pc-GR, stars up to six solar masses were obtained in [18,20] and up to 200 solar masses in [19].…”

Predictions of the pseudo‐complex general relativity

“…And this is the point! In pcGR there is no contradiction because one can have a neutron star and a large mass (Caspar et al ; Hess et al, ; Rodríguez et al ; ). However, with increasing mass it gets more and more difficult to see a pulsation because of the increase in the redshift, which mimics, for superheavy masses, a dark star similar to a real BH.…”