Quantum dynamics and thermodynamics of a Minkowski-Minkowski wormhole

TL;DR

The paper investigates quantum dynamics and thermodynamics of a Minkowski-Minkowski cut-and-paste wormhole using a minisuperspace Lorentzian path integral for the throat radius $a( au)$, built from an effective non-local action derived via Israel junction conditions. In a WKB analysis, topology-changing transitions are suppressed by the Jacobi determinant, aligning with Wheeler–DeWitt-type results that constrain topology change. Through a Euclidean treatment with a thin-shell, the authors derive a gravitational temperature and entropy that depend on the extrinsic-curvature jump and the shell EOS, with entropy scaling as $S\propto T^{-2}$. The work connects junction data to a first-law-like thermodynamics and discusses prospects for embedding these results into a full quantum gravity path integral, highlighting open questions about the role of reparametrization invariance and the interpretation of throat entropy.

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-local 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 Jacobi 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.

Figures (4)

• Figure 1: Onshell wormhole action $S$ as well as real and imaginary parts of the Jacobi factor $\mathcal{J}$ as a function of the initial and final throat radius $a_0$ and $a_1$.
• Figure 2: Real and imaginary parts of $G$ as a function of the initial and final throat radius $a_0$ and $a_1$.
• Figure 3: Probability distribution $\abs{G}^2 =GG^*$ as a function of the initial and final throat radius $a_0$ and $a_1$.
• Figure 4: Real and imaginary parts of $G$ as a function of the initial and final positions $x_0$ and $x_1$.