Pseudo-Complex General Relativity: Schwarzschild, Reissner-Nordstr\"om and Kerr Solutions

TL;DR

This paper explores pseudo-complex General Relativity, proposing a new projection method, and shows it naturally introduces dark energy, leading to non-singular, horizonless objects called gray stars, challenging traditional black hole concepts.

Contribution

It introduces a novel projection method in pc-GR and demonstrates how it naturally incorporates dark energy, resulting in non-singular, horizonless stellar objects.

Findings

Dark energy terms emerge naturally in pc-GR.

Black holes are replaced by horizonless gray stars.

Possible experimental tests via orbital speed measurements.

Abstract

The pseudo-complex General Relativity (pc-GR) is further considered. A new projection method is proposed. It is shown, that the pc-GR introduces automatically terms into the system which can be interpreted as dark energy. The modified pseudo-complex Schwarzschild solution is investigated. The dark energy part is treated as a liquid and possible solutions are discussed. As a consequence, the collapse of a large stellar mass into a singularity at $r=0$ is avoided and no event-horizon is formed. Thus, black holes don't exist. The resulting object can be viewed as a gray star. It contains no singularity which emphasizes, again, that it is not a black hole. The corrections implied by a charged large mass object (Reissner- Nordstr\"om) and a rotating gray star (Kerr) are presented. For the latter, a special solution is presented. Finally, we will consider the orbital speed of a mass in a circular orbit and suggest a possible experimental verification.