Hyperverse, 5-dimensional Gravity and Multiverses: 5-dimensional Einstein Equations

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22 Feb 2024

This paper is available on arxiv under CC 4.0 license.

Authors:

(1) Igor Yu. Potemine, Institut de Math´ematiques, Universit´e Paul Sabatier.

2 5-dimensional Einstein equations

Consider the 5-dimensional Einstein equation in the following form:

Gogberashvili searched for a Schwarzschild-like solution of the form:

where r is the 4-dimensional radial coordinate and dΩ 2 is the 3-dimensional volume element [2, eq. (2)-(4)].

The solution is given in terms of metrics of inner and outer regions:

separated by a time-like 4-dimensional spherical shell (brane, bubble) with FLRW metrics:

where τ is the intrinsic time of this spherical universe [2, eq. (13)-(14)].