Generation of gravitating solutions with Baryonic charge from Einstein-Scalar-Maxwell seeds

TL;DR

This paper establishes an exact correspondence between Einstein-scalar-Maxwell and gauged Skyrme-Maxwell-Einstein theories, enabling solution generation and exploration of gravitating solutions with baryonic charge in a unified framework.

Contribution

It introduces a novel exact mapping between two complex theories, facilitating the transfer of solution techniques and expanding the scope of solutions with baryonic charge in gravitational models.

Findings

Constructed a consistent ansatz revealing equivalence in a sector with baryonic charge.

Applied the correspondence to a rotating Kerr-Newman-like spacetime with scalar fields.

Derived bounds and quantization conditions linking baryonic charge and rotation parameter.

Abstract

We establish, for the first time, an exact correspondence between Einstein-scalar-Maxwell theory and gauged Skyrme-Maxwell-Einstein models in (3+1) dimensions. By constructing the simplest consistent ansatz within the gauged Skyrme-Maxwell framework, we reveal a remarkable equivalence in a sector that admits nonvanishing, highly magnetized baryonic charge. This correspondence has a particularly appealing consequence: it transfers the full power of solution-generating techniques developed for electrovacuum systems-many of which naturally accommodate scalar fields to the considerably more intricate setting of gauged Skyrme-Maxwell theory minimally coupled to General Relativity. As a result, it opens the door to a systematic and much broader exploration of exact solutions in Skyrme-Maxwell-Einstein theory and of their potential applications in cosmology and astrophysics. Notably, the resulting configurations carry nonzero baryonic charge whenever the derivative of the hadronic profile along the magnetic field lines does not vanish. As an illustrative example, we apply this new dictionary to a rotating Kerr-Newman-like spacetime dressed with a scalar field. In the corresponding Skyrme-Maxwell-Einstein solution, the quantization of the baryonic charge enforces a quantization of the Kerr rotation parameter. We derive an upper bound on the baryonic charge in terms of the integration constants of the solution and show that, in the regime of small baryonic charge, the rotation parameter depends linearly on the baryonic charge.