A recent discovery by two priests at the Vatican Observatory “could reshape our understanding of Black Holes, the Big Bang model, and the quest for a consistent theory of Quantum Gravity.”
Newsroom (14/07/2025, Gaudium Press) In a groundbreaking study, two researchers from the Vatican Observatory, Fr. Gabriele Gionti, S.J., and Fr. Matteo Galaverni, have revealed a profound connection between two mathematical frameworks used to describe gravity in the presence of a scalar field: the Jordan frame and the Einstein frame. Their findings, published in the European Journal of Physics (https://epjc.epj.org/articles/epjc/abs/2025/07/10052_2025_Article_14447/10052_2025_Article_14447.html), demonstrate that these frameworks, when analyzed with the right mathematical tools, not only describe the same physics but can also unlock entirely new solutions to Einstein’s Equations, which govern the universe’s large-scale structure.
The researchers employed the ADM–Hamiltonian formalism, a rigorous method that accounts for all aspects of gravitational theory, to prove that the Jordan and Einstein frames are mathematically equivalent under specific conditions. Without this formalism, the equivalence remains obscured, limiting the understanding of the underlying physics. A key innovation in their work lies in the meticulous treatment of boundary terms—mathematical components at the edges of space-time surfaces that are critical for deriving accurate dynamical equations.
“Careful consideration of boundary terms is essential,” Gionti and Galaverni explained. “Only by properly handling these terms can the correct equations of motion be derived. Previous studies in the literature often produced incomplete equations due to inadequate treatment of these components.”
By incorporating these boundary terms correctly, the researchers derived the full and accurate equations of motion in both frames for the first time, overcoming limitations in earlier studies. Their work further explored the effects of switching between the two frames using a canonical transformation. When this transformation is regular, the frames remain equivalent, with every solution in the Jordan frame corresponding to one in the Einstein frame. However, when the transformation becomes singular, the results are striking: entirely new gravitational solutions, such as black holes or naked singularities, emerge—solutions that would remain hidden if confined to a single frame.
This discovery carries significant implications for cosmology and theoretical physics. The choice of mathematical framework, the researchers argue, is not merely a matter of convenience but can fundamentally alter the physical solutions discovered. These findings could reshape our understanding of black holes, the Big Bang model, and the ongoing search for a consistent theory of quantum gravity.
The Vatican Observatory, accessible at www.vaticanobservatory.org and www.vaticanobservatory.va, continues to contribute to cutting-edge astronomical research, blending rigorous science with a commitment to exploring the universe’s deepest mysteries. Gionti and Galaverni’s work underscores the power of mathematical precision in unveiling new perspectives on the cosmos.
- Raju Hasmukh with files from the Vatican
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