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

TL;DR

The work addresses the analytical challenge of baryonic charge dynamics in strong gravity and magnetic fields by establishing an exact mapping between Einstein–scalar–Maxwell theory and gauged Skyrme–Maxwell–Einstein theory in (3+1) dimensions. This mapping relies on a simple ansatz that preserves nonzero baryonic density, reducing the GSMT–GR equations to the Einstein–Maxwell–scalar system and making the Skyrme sector effectively decoupled except for the Callan–Witten contribution, which yields a baryon density proportional to the magnetic field dotted with the scalar gradient, $\rho_B \sim \mathbf{B}\cdot\nabla \Psi$. The key contributions include enabling the transfer of solution-generating techniques from electrovacuum to GSMT–GR, and demonstrating the construction of exact rotating solutions with quantized baryonic charge via a Kerr–Newman–like seed dressed by a scalar, with explicit expressions for the net topological charge $n$ and angular-momentum quantization $a_n^{(\pm)}$. This framework broadens the analytic toolkit for exploring baryonic degrees of freedom in regimes of strong gravity and magnetization, with potential cosmological and astrophysical implications and directions for future work on additional seed solutions and physical applications.

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.

Figures (2)

• Figure 1: spatial distribution of the topological charge density $\rho_B$ (units of cm$^{-3}$ where we have used stereographic coordinates to represent the concentration of the charges such that the center of the graphics represent the outer horizon and the borders represents spatial infinity. We have used $\Theta=180$, $M=4$, $e=1$ and $a=1$.
• Figure 2: Discrete spectrum of the specific angular momentum $a_{n}^{+}$ (units of $a_{\odot}$) as a function of the topological charge $n$. Parameters are fixed at $M=M_{\odot}$, $e=e_{\text{max}}$, and $\Theta=180$. The inset highlights the linear growth of $a_{n}^{(+)}$ for small $n$ values.