Continuous imaginary time histories representing black hole nucleation in de Sitter spacetime.

摘要

We address the issues involved in finding and constructing continuous imaginary time histories (CITHs) representing black hole nucleation in a background de Sitter spacetime. Such rates are often calculated by adopting the instanton methods used to calculate ordinary particle-antiparticle production rates in background fields. Unlike the particle production case, there are certain instances of black hole nucleation described by two separate and distinct solutions to the Euclidean Einstein's equations, i.e., the instanton is disconnected. Hence, one must justify including such histories in a path integral.;We first discuss the existence of continuous imaginary time histories for black hole nucleation in theories consisting of modifications to Einstein's equations. First, we consider adding powers of the Ricci scalar to Einstein-Hilbert gravity with a cosmological constant. When the higher curvature coupling constants are negative, we find continuous instantons describing a background de Sitter to de Sitter transition characterized by a periodic, non-singular scale factor a(tau). Negative coupling constants imply an equivalent theory of Einstein gravity coupled to a negative energy density scalar field. This motivates our exploration of Einstein gravity coupled to Narlikar's negative energy density C-field. We again find a continuous background instanton, but such a solution exists only when small violations of the Hamiltonian constraint are allowed.;Because of the unattractive features of the above solutions, we explore how one can construct CITHs by surgically altering the disconnected instanton. In the spirit of the path integral, we claim that one should sum over all possible geometries which can connect the instanton. We limit attention to connections with topology S3 and S1 x S2. We find that the S3 connection is preferred in the context of "no-boundary" quantum cosmology. However, we believe that the S1 x S 2 connection may be more preferred for two reasons. First, the S1 x S2 connection allows two of its dimensions to be large, implying via holography, that information from the initial state can "survive" the near-annihilation, recreation process. Second, Planck sized perturbations on the S 2 portion of the connection give rise to more histories over which to sum in the path integral.