Inverse Square Law of Gravitation in (2+1)-Dimensional Space-Time as a Consequence of Casimir Energy

TL;DR

This paper demonstrates that in (2+1)-dimensional Einstein gravity, vacuum polarization leads to an inverse square law of gravity, resolving a paradox by considering a finite-sized particle and its interior vacuum effects.

Contribution

It shows that vacuum polarization results in an inverse square gravitational law in (2+1) dimensions, clarifying the role of finite particle size and interior vacuum effects.

Findings

Inverse square law emerges from vacuum polarization effects.

Negative vacuum energy does not negate gravitational attraction.

Finite particle size resolves the paradox of negative vacuum mass.

Abstract

The gravitational effect of vacuum polarization in space exterior to a particle in (2+1)-dimensional Einstein theory is investigated. In the weak field limit this gravitational field corresponds to an inverse square law of gravitational attraction, even though the gravitational mass of the quantum vacuum is negative. The paradox is resolved by considering a particle of finite extension and taking into account the vacuum polarization in its interior.