Thermal properties of time machines

Connections between universes through tunneling space-times could make the multiverse a physical entity able to be observed from our own single universe. In this paper we first study the thermal properties of the static Klein-bottle holes and then consider one of the potentially observable effects from wormholes, ringholes, and nonorientable tunnelings when they are converted into time machines connecting other universes with ours own, that is a randomly varying in space and time thermal radiation which, with an unpredictable cadence, randomly manifested to a far observer as a short, occasional pulse with very high intensity and fluence which would be made of black body phantom or ordinary radiation. We discuss the odds for these bursts of thermal radiation to be eventually observable.

Figure 1

Pictorial representation of a Klein-bottle hole showing the nonorientable topology of its throat and some of the parameters in terms of which metric (1) is defined.

Figure 2

Limiting Klein-bottle holes in which $a_i^2=b_i^2$, $i=1$, 2. We have then three possible final situations. (A) if both $a_1=b_1$ and $a_2=b_2$, then the process of thermal emission of positive and negative radiation tends to that limiting geometry where all ordinary energy contributing to the Klein-bottle hole with $a_i>b_i$ is exhausted, leaving a double geometry which is equivalent to that of a couple of wormholes in that the surface embedding them flares outward but not inward, and are both therefore made out of exotic, phantomlike energy characterized by a negative temperature; (B) if both $a_1=-b_1$ and $a_2=-b_2$ then the process of thermal emission tends to that limiting geometry where now all exotic energy contributing the Klein-bottle hole with $|a_i|>|b_i|$ is exhausted, leaving a double geometry which is now equivalent to that of a pair of black holes, instead of wormholes, in that the surface embedding the Klein-bottle hole space-time metric (1) always flares inward, being therefore made out of ordinary matter with positive internal energy, which is characterized by a positive temperature; and (C) if any of the two ${\phi }_1$-intervals making the manifold nonorientable satisfies the condition that $a$ and $b$ become the same and the other reaches a situation where $a=-b$, the final double limiting geometry would be equivalent to that of a wormhole plus a black hole in that the one part of the surface embedding them flares outward and the rest of it flares inward, the former being therefore made of exotic, phantomlike energy with negative temperature, and the latter by ordinary energy with positive temperature.