The partition is Z = ∫D[g]exp(-i[S_∂M + S_M])
where the sum is over not just metric configurations of the manifold M, but its boundary as well. This tends to suggest the boundary conditions are themselves dynamics. A pocket world in an internal inflating spacetime would have this feature. I though conjecture this may be a transient state of affairs. The boundary action may transition into an action over a field theory. This has some holographic content, and it would replace these boundary dynamics with a quantum field. Further, the pocket world becomes a complete manifold without boundary. LC On Monday, October 7, 2019 at 1:20:05 AM UTC-5, Philip Thrift wrote: > > > https://arxiv.org/abs/1808.10448 > > > Action Principle for Isotropic General Relativity > Thomas C. Bachlechner > <https://arxiv.org/search/hep-th?searchtype=author&query=Bachlechner%2C+T+C> > (Submitted on 30 Aug 2018) > > We study the generally covariant theory governing an isotropic spacetime > region with uniform energy density. Gibbons, Hawking and York showed that > fixing the induced boundary metric yields a well-posed variational problem. > However, as we demonstrate, fixing the boundary metric violates general > covariance and allows the mass of a back hole to vary. This observation has > dramatic consequences for path integrals: A sum over spacetimes with fixed > boundary metrics is a sum over classically distinct black holes. Instead, > we merely demand that coordinates exist such that the metric at the > boundary is the Schwarzschild-(A)dS metric of fixed mass M and two-sphere > radius R. We derive the action that yields a well-posed variational problem > for these physical boundary conditions. The action vanishes for all > stationary and isotropic spacetimes. A vanishing action implies that both a > Schwarzschild black hole and pure de Sitter space each have one unique > semiclassical state. Our results provide a novel and radically conservative > approach to several long-standing issues in quantum gravity, such as the > wavefunction of the universe, the black hole information paradox, vacuum > decay rates and the measure problem of eternal inflation. > > > > @philipthrift > -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/48018487-ae83-4610-916b-d5ba195edece%40googlegroups.com.
