Giant wormholes in ghost-free bigravity theory

TL;DR

This paper explores the existence and properties of giant Lorentzian wormholes in ghost-free bigravity theory, revealing solutions that could be as large as the universe and discussing their stability and potential holographic interpretations.

Contribution

It demonstrates that bigravity theory admits large wormhole solutions violating energy conditions, with detailed analysis of their geometry, stability prospects, and implications for holography.

Findings

Wormholes can be as large as the universe, with throat sizes related to the inverse graviton mass.

Two types of wormholes (W1 and W2) are identified with distinct geometric properties.

W1 wormholes have horizons and tachyonic graviton behavior, while W2 are globally regular with traversable throats.

Abstract

We study Lorentzian wormholes in the ghost-free bigravity theory described by two metrics, g and f. Wormholes can exist if only the null energy condition is violated, which happens naturally in the bigravity theory since the graviton energy-momentum tensors do not apriori fulfill any energy conditions. As a result, the field equations admit solutions describing wormholes whose throat size is typically of the order of the inverse graviton mass. Hence, they are as large as the universe, so that in principle we might all live in a giant wormhole. The wormholes can be of two different types that we call W1 and W2. The W1 wormholes interpolate between the AdS spaces and have Killing horizons shielding the throat. The Fierz-Pauli graviton mass for these solutions becomes imaginary in the AdS zone, hence the gravitons behave as tachyons, but since the Breitenlohner-Freedman bound is fulfilled, there should be no tachyon instability. For the W2 wormholes the g-geometry is globally regular and in the far field zone it becomes the AdS up to subleading terms, its throat can be traversed by timelike geodesics, while the f-geometry has a completely different structure and is not geodesically complete. There is no evidence of tachyons for these solutions, although a detailed stability analysis remains an open issue. It is possible that the solutions may admit a holographic interpretation.