Global monopoles and scalar fields as the electrogravity dual of Schwarzschild spacetime

TL;DR

This paper demonstrates that global monopoles and certain scalar fields are electrogravity duals of Schwarzschild spacetime, sharing the same equation of state, with the scalar field dual to flat space, revealing new duality relationships in gravitational physics.

Contribution

It establishes for the first time that minimally coupled scalar fields are electrogravity duals of Schwarzschild spacetime, extending known dualities for global monopoles.

Findings

Global monopoles and scalar fields share the same equation of state.

Scalar field solutions are dual to flat space.

The duality extends the understanding of gravitational-electromagnetic correspondences.

Abstract

We prove that both global monopole and minimally coupled static zero mass scalar field are electrogravity dual of the Schwarzschild solution or flat space and they share the same equation of state, $T^0_0 - T^i_i = 0$. This property was however known for the global monopole spacetime while it is for the first time being established for the scalar field. In particular, it turns out that the Xanthopoulos - Zannias scalar field solution is dual to flat space.