Self-sustained wormholes in modified dispersion relations

TL;DR

This paper investigates the possibility that quantum fluctuations, influenced by modified dispersion relations, can sustain wormhole geometries, leading to solutions with specific properties in different energy regimes.

Contribution

It introduces a semi-classical model where quantum graviton fluctuations support wormholes within modified dispersion relations, providing new solutions in cis-planckian and trans-planckian regimes.

Findings

Trans-planckian regime yields asymptotically flat wormholes with constant shape function.

Quantum corrections are exponentially suppressed in the trans-planckian regime.

Matching conditions are needed for non-asymptotically flat solutions.

Abstract

In this work, we consider the possibility that wormhole geometries are sustained by their own quantum fluctuations, in the context of modified dispersion relations. More specifically, the energy density of the graviton one-loop contribution to a classical energy in a wormhole background is considered as a self-consistent source for wormholes. In this semi-classical context, we consider specific choices for the Rainbow's functions and find solutions for wormhole geometries in the cis-planckian and trans-planckian regimes. In the former regime, the wormhole spacetimes are not asymptotically flat and need to be matched to an exterior vacuum solution. In the latter trans-planckian regime, we find that the quantum corrections are exponentially suppressed, which provide asymptotically flat wormhole geometries with a constant shape function, i.e., b(r)=r_t, where r_t is the wormhole throat. In addition to this analysis, we also fix the geometry by considering the behaviour of a specific shape function through a variational approach which imposes a local analysis to the problem at the wormhole throat. We further explore the respective parameter range of the Rainbow's functions, and find a good agreement with previous work.