We provide general arguments regarding the connection between low-energy
theories (gravity and quantum field theory) and a hypothetical fundamental
theory of quantum gravity, under the assumptions of (i) validity of the
holographic bound and (ii) preservation of unitary evolution at the level of
the fundamental theory. In particular, the appeal to the holographic bound
imposed on generic physical systems by the Bekenstein-Hawking entropy implies
that both classical geometry and quantum fields propagating on it should be
regarded as phenomena emergent from the dynamics of the fundamental theory. The
reshuffling of the fundamental degrees of freedom during the unitary evolution
then leads to an entanglement between geometry and quantum fields. The
consequences of such scenario are considered in the context of black hole
evaporation and the related information-loss issue: we provide a simplistic toy
model in which an average loss of information is obtained as a consequence of
the geometry-field entanglement.Comment: 10 pages, 2 figure
By an argument similar to that of Gibbons and Stewart [10], but in a different coordinate system and less restrictive gauge, we show that any weaklyasymptotically-simple, analytic vacuum or electrovacuum solutions of the Einstein equations which are periodic in time are necessarily stationary.
We extend the work in our earlier paper (Bičák J et al 2010 Class. Quantum Grav. 27 055007 ) to show that time-periodic, asymptotically flat solutions of the Einstein equations analytic at I, whose source is one of a range of scalarfield models, are necessarily stationary. We also show that, for some of these scalar-field sources, in stationary, asymptotically flat solutions analytic at I, the scalar field necessarily inherits the symmetry. To prove these results we investigate miscellaneous properties of massless and conformal scalar fields coupled to gravity, in particular Bondi mass and its loss.
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