Aspects of (4 + 4)-Kaluza–Klein type theory

Abstract

We develop a type of Kaluza-Klein formalism in (4 + 4)-dimensions. In the framework of this formalism we obtain a new kind of Schwarzschild metric solutions that via Kruskal-Szequeres can be interpreted as mirror black and white holes. We found that this new type of mirror black and white holes solutions in (3 + 1)-dimensions support the idea that the original space-time can be extended to (4 + 4)-signature. Using octonions, we also discus linearized gravity in (4 + 4)-dimensions.On the other hand, it is well known that the Kruskal-Szekeres coordinates give an alternative description of the event horizon of black-holes [21,22]. Traditionally, one starts with the Schwarzschild metric described by the coordinates t, r and the angular coordinates θ and φ associated with a unit sphere and after several algebraic steps one computes the Kruskal-Szekeres coordinates T and X which become functions of t and r. The key result of this process is that while the Schwarzschild metric is singular at the horizon r = 2GM = r s the Kruskal-Szekeres metric is not. However, the final transformations between the coordinates t, r and T and X seems to be, in a sense, intriguing because instead of describing only two regions (2-region) as in the case of Schwarzschild black-holes (interior and exterior) one

Black-Hole duality in four time and four space dimensions

“…First, the Dirac equation in (4 + 4)-dimensions is consistent with Majorana-Weyl spinors which give exactly the same number of components as the complex spinor of 1/2spin particles such as the electron or quarks [6,7]. Second, the most general Kruskal-Szekeres transformation of a blackhole coordinates in (1+3)-dimensions leads to 8-regions (instead of the usual 4-regions), which can be better described in (4 + 4)-dimensions [8]. Third, loop quantum gravity in (4 + 4)-dimensions [9-10] admits a self-duality curvature structure analogue to the traditional (1 + 3)-dimensions.…”

“…First, it may be interesting to consider a generalized Kruskal-Szekeres transform of the line element (32). This must lead to a connection with the observation [8] that in the (4 + 4)-world such a transform implies 8-regions instead of the usual 4-regions. Second, since it has been shown that in (4 + 4)-dimensions there exist a kind of duality of the cosmological constant one wonders what is the relation of such a duality with dual black-hole solution developed in this work (see Ref.…”

From a 4-Rank Totally Antisymmetric Field Strength to Two Dual Electromagnetic Fields in Four Time and Four Space Dimensions

“…[12,27]). Second, the most general Kruskal-Szekeres transformation of a black-hole coordinates in 1 þ 3 ðÞ -dimensions leads to eightregions (instead of the usual four-regions), which can be better described in 4 þ 4 ðÞdimensions [28]. Third, it also has been shown [29] that duality…”

Cosmological Duality in Four Time and Four Space Dimensions

“…Note that the reason to write the quantum operators ε and ˆµ  in terms of P l rather than  can be traced back to the geodesic Equation (4) which is independent of the test particle mass and therefore the quantities ε and σ  that play the analo-gue role of energy and momentum, are dimensionless. Thus, the formula (7) leads to the Schrödinger equation…”

“…Second, in Ref. [7] it has been shown that a general Kruskal-Szekeres transform, in black-hole physics, implies 8 hidden regions instead of just 4-regions as it is usually believed. It turns out that this 8-regions admit better interpretation in a world of (4 + 4)-dimensions.…”