Creation of a child universe by the shell radiating negative energy flux

Abstract

One possibility for the creation of a child universe by producing a false vacuum bubble in the laboratory is discussed. We obtain a simple equation of motion of the spherically symmetric thin shell of radiating out-going null energy flux. Analysing the equation, we show that the shell radiates negative energy flux and the false vacuum bubble becomes a child universe in the case of a certain kind of surface stress tensor.

WKB metastable quantum states of a de Sitter Rei ner Nordstr m dust shell

“…In this section we determine the leading contribution to the logarithmic (and thus integrable) singularity on the integration path that appears in the evaluation of the integral in (24). The logarithmic character stems from the definition of the inverse hyperbolic tangent in terms of the logarithm and from the fact that its argument is a rational function with the following properties♯: We then compute F ′ (|Θ|; Θ) and F ′′ (|Θ|; Θ), i.e.…”

“…x = is thus a singularity on the integration path, but, being of the logarithmic type, it is integrable (the leading contribution to the singularity is determined in appendix D). The integral in (24) is not exactly computable analytically but, being reassured by the considerations above about its existence, the integration can be performed numerically. We have performed this kind of analysis with Mathematica , evaluating the integral numerically for 10 000 equally spaced test values of in the interval [10 −4 , (3/4) 3/2 ] and for other 10 000 test values in the interval [10 −16 , 10 −4 ] taken as a sequence converging to 0 + as 1/n 4 for n → +∞.…”

“…To fulfil the above requirements we first analyse the leading dependence of the action S, expressed as the integral (24). From appendix E we see that P (x) ∼ x 2 + O(x) 2 and the upper turning point x min ( ) ∼ + O( ), so that S( ) ∼ 3 + O( ) 3 .…”

“…Moreover, at larger scales, specific configurations of shells have also been considered to construct cosmological models [18] (even with hierarchical (fractal) structure [19]), to analyse phase transitions in the early universe [20] or to describe cosmological voids [21]; semiclassical models have tackled the problem of avoiding the initial singularity of the big-bang scenario by quantum tunnelling [22][23][24].…”

“…In these and other studies, different cases of junctions between spacetimes have been considered: for example, between anti de Sitter and anti de Sitter [62], Friedmann-Robertson-Walker and Friedmann-Robertson-Walker [34], Minkowski and Minkowski [37,38], Schwarzschild and Schwarzschild [36,11,9,6], Reißner-Nordström and Reißner-Nordström [15,33], de Sitter and Reißner-Nordström [63], de Sitter and Schwarzschild [64,23,81], de Sitter and Schwarzschild-de Sitter [65], de Sitter and Vaidya [24], Friedmannlike and Reißner-Nordström [66], Minkowski and Friedmann [21], Minkowski and Reißner-Nordström [15,41,67], Minkowski and Schwarzschild [28,31,25,14,43,29], Minkowski and Vaidya [12], Schwarzschild and Reißner-Nordström [67], Schwarzschild and Schwarzschildanti de Sitter [47], Schwarzschild and Vaidya [46], Tolman and Friedman [19], Lemaître-Tolman-Bondi and Lemaître-Tolman-Bondi [18].…”