Quantum dynamics and thermodynamics of a Minkowski-Minkowski wormhole

Abstract

We consider the path-integral quantization of a minisuperspace cut-and-paste Lorentzian wormhole connecting two Minkowski spacetimes. The dynamics of the throat radius as a function of proper time is governed by a non-polynomial effective action derived by an application of the Israel junction condition formalism. Within a saddle-point approximation of the propagator describing the evolution from an initial to a final throat radius, we show that topology-changing transitions are suppressed by the Hessian determinant. In addition, we analyze the gravitational thermodynamics of the wormhole spacetime by a Wick rotation of the Israel-Lanczos equations in the presence of a thin-shell source. The resulting Euclideanized field equations are assumed to originate from a Euclidean effective gravity-matter action, which enters the path-integral representation of the gravitational canonical partition function. Therefrom we associate a temperature given by the inverse period of solutions, as well as a gravitational entropy as functions of the surface energy density and equation of state parameter of the shell. Both quantities are sourced entirely by the discontinuity of the extrinsic curvature across the junction. We show how this result can be applied to deduce a thermodynamic first law as the differential version of the conservation equation relating the effective mass of the shell to its surface pressure.

v2: 20 pages, published version

References in corpus (17)

• Traversable wormholes: Some simple examples
• Traversable wormholes from surgically modified Schwarzschild spacetimes
• Action functionals for relativistic perfect fluids
• Black-bounce to traversable wormhole
• The null energy condition in dynamic wormholes
• Complex actions in two-dimensional topology change
• Vaidya spacetimes, black-bounces, and traversable wormholes
• Towards a Non-singular Paradigm of Black Hole Physics
• Thin-shell traversable wormhole crafted from a regular black hole with asymptotically Minkowski core
• Quantum Dynamics of Lorentzian Spacetime Foam
• Violations of the null convergence condition in kinematical transitions between singular and regular black holes, horizonless compact objects, and bounces
• De Sitter horizon entropy from a simplicial Lorentzian path integral
• Visions in Quantum Gravity
• The enigmatic gravitational partition function
• A non-local way around the no-global-symmetries conjecture in quantum gravity?
• Asymptotic safety, quantum gravity, and the swampland: a conceptual assessment
• On the lapse contour in the gravitational path integral