Pseudo-Complex General Relativity: Schwarzschild, Reissner–nordström and Kerr Solutions

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 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.

Predictions of the pseudo‐complex general relativity

“…where the 1/r 5 dependence is strong enough, so as not to be detected yet in solar system experiments (Will 2006). With these assumptions, we obtain for the pc-Kerr solution the metric (Caspar et al 2012) g 00 = − r 2 − 2mr + a 2 cos 2 + B 2r r 2 + a 2 cos 2 , g 11 = r 2 + a 2 cos 2 r 2 − 2mr + a 2 + B 2r , g 22 = r 2 + a 2 cos 2 , g 33 = (r 2 + a 2 )sin 2 + a 2 sin 4 ( 2mr − B 2r ) r 2 + a 2 cos 2 , g 03 = −asin 2 2mr + a B 2r sin 2 r 2 + a 2 cos 2 ,…”

Walter Greiner: In Memoriam

“…In collaboration with P. O. Hess from the National University of Mexico, he addressed again this problem in a series of articles [2][3][4][5] and demonstrated another tantalizing possibility, namely that mass might change the vacuum properties of the space nearby provoking the building up of dark energy, increasing toward smaller distances to the star. This is equivalent to a Casimir effect and the theory has a so-called pseudo-symplectic structure b , a notion treated in one of the contributions of the present proceedings.…”

Simulations of accretion disks in pseudo‐complex General Relativity

“…It also allows to use an arbitrary metric which has to be provided by the user. In Schönenbach (2015), the modification of GY-OTO to the pseudo-complex metric (Hess & Greiner 2009;Caspar 2012) was published and which we use here to simulate the accretion disks viewed from different angles.…”

“…The first version of pc-GR was published in Hess & Greiner (2009) and in its final form in Caspar (2012) and Hess et al (2015). Though the pc-GR is more general, for the applications in this contribution it suffices to set y μ = 0 (Schäfer at al.…”

“…In Caspar (2012) a dark energy density with the functional form = B r 5 was proposed, which results in the g 00 component of the metric of 1 − 2m r + B 2r 3 , where B = bm 3 describes the coupling to the central object. When g 00 = 0, an event horizon appears, so in order to avoid it b has to be larger than 64 27 .…”