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arXiv · 2601.18205

Gluing different gravitational models: $f(R)$ case

Amin Aalipour·Nima Khosravi
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Abstract

This paper presents a comprehensive analysis of junction conditions for gluing different $f(R)$ gravitational theories across a non-null hypersurface. Using the variational approach, we systematically derive the junction conditions for both general $f(R)$ theories and the special case of Einstein gravity, for comparison. We demonstrate that when joining two distinct $f(R)$ theories, the junction conditions require continuity of $\partial f(R)/\partial R$, the extrinsic curvature $K_{\mu \nu}$, while allowing for discontinuities in the Ricci Scalar $R$. Furthermore, we establish the equivalence between Jordan and Einstein frame formulations through careful treatment of conformal transformations; Our results reveal that different $f(R)$ theories can be consistently matched provided specific relations between their functional forms and geometric quantities are satisfied at the interface.

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Amin Aalipour, Nima Khosravi. 2026-01-26. Gluing different gravitational models: $f(R)$ case. https://arxiv.org/abs/2601.18205

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