Ramon Lapiedra

Joint reality and Bell inequalities for consecutive measurements

Some new Bell inequalities for consecutive measurements are deduced under joint realism assumption, using some perfect correlation property. No locality condition is needed. When the measured system is a macroscopic system, joint realism assumption substitutes the non-invasive measurability hypothesis advantageously, provided that the system satisfies the perfect correlation property. The new inequalities are violated quantically. This violation can be expected to be more severe than in the case of precedent temporal Bell inequalities. Some microscopic and mesoscopic situations, in which the new inequalities could be tested, are roughly considered.

Intrinsic vanishing of energy and momenta in a universe

We present a new approach to the question of properly defining energy and momenta for non asymptotically Minkowskian spaces in General Relativity, in the case where these energy and momenta are conserved. In order to do this, we first prove that there always exist some special Gauss coordinates for which the conserved linear and angular 3-momenta intrinsically vanish. This allows us to consider the case of creatable universes (the universes whose proper 4-momenta vanish) in a consistent way, which is the main interest of the paper. When applied to the Friedmann-Lemaître-Robertson-Walker case, perturbed or not, our formalism leads to previous results, according to most literature on the subject. Some future work that should be done is mentioned.

Intrinsic energy of Lemaı̂tre-Tolman-Bondi models and cosmological implications

Recently, some Lema{\^{\i}}tre-Tolman-Bondi metrics have been considered as models alternative to the dark energy within the Friedmann-Lema{\^{\i}}tre-Robertson-Walker universes. The vanishing of the intrinsic energy of these metrics is examined since such a vanishing, in the present case and in general, could be interpreted as a necessary condition to consider the possibility of the quantum creation of a metric. More specifically, this vanishing is examined in the particular case where the Lema{\^{\i}}tre-Tolman-Bondi metrics behave asymptotically like a Friedmann-Lema{\^{\i}}tre-Robertson-Walker universe. Finally, we deal with a particular model ruled out after being confronted with cosmic observations. In a minimal agreement with this negative result, leaving aside an unstable case, the value of the intrinsic energy of this particular model does not vanish and becomes in fact minus infinite.

On the uniqueness of the space-time energy in General Relativity: the illuminating case of the Schwarzschild metric

The case of asymptotic Minkowskian space-times is considered. A special class of asymptotic rectilinear coordinates at the spatial infinity, related to a specific system of free falling observers, is chosen. This choice is applied in particular to the Schwarzschild metric, obtaining a vanishing energy for this space-time. This result is compared with the result of some known theorems on the uniqueness of the energy of any asymptotic Minkowskian space, showing that there is no contradiction between both results, the differences becoming from the use of coordinates with different operational meanings. The suitability of Gauss coordinates when defining an intrinsic energy is considered and it is finally concluded that a Schwarzschild metric is a particular case of space-times with vanishing intrinsic 4-momenta.

Geodesic family of spherical instantons and cosmic quantum creation

The Einstein field equations for any spherically symmetric metric and a geodesic perfect fluid source are cast in a canonical simple form, both for Lorentzian metrics and for instantons. Both kinds of metrics are explicitly written for the Lemaître–Tolman–Bondi family and for a general

Stability of the intrinsic energy vanishing in the Schwarzschild metric under a slow rotation

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Spherical symmetric parabolic dust collapse: 𝒞1 matching metric with zero intrinsic energy

Λ-Friedmann–Lemaître–Robertson–Walker universe. In the latter case (including of course the instanton version) we study whether the probability of quantum creation of our Universe vanishes or not. It is found, in accordance with previous results, that only the closed model can have a nonzero probability for quantum creation. To obtain this result, we resort to general assumptions, which are satisfied in the particular creation case considered by Vilenkin. On the other hand, Fomin and Tryon suggested that the energy of a quantically creatable universe should vanish. This is in accordance with the above result in which only the closed