GR as a Special Case of the Infinite-Dimensional Multiverse Model (IDM): Limit Transition and Consistency

This article addresses the apparent contradiction between General Relativity (GR) and the Infinite-Dimensional Multiverse Model (IDM). The IDM postulates an infinite number of spatial dimensions and an infinite set of neighbouring 3‑branes (universes). GR, on the other hand, is formulated in a 4‑dimensional spacetime. The author shows that the contradiction is only apparent: GR can be understood as a special case of the IDM under certain simplifying conditions. The argument follows the logic of known limit transitions in physics: · Special relativity reduces to Newtonian mechanics when v \ll c . · GR reduces to Newtonian gravity in weak fields and slow motion. · Similarly, the IDM reduces to GR when three conditions are met: 1. Low energies – the energy scale is much lower than the Planck energy ( E \ll E_{\text{Planck}} ), so that excitations of extra dimensions are frozen. 2. Weak influence of neighbouring universes – the interaction intensity decays with the index of the neighbouring universe (e.g., I_m \sim 1/m^\alpha ), making their cumulative effect negligible at low energies. 3. Choice of a macroscopic description level G – coarse‑graining that ignores quantum and multi‑dimensional fluctuations. The article references contemporary research on black holes in the infinite‑dimensional limit (Emparan, Suzuki, Tanabe, 2013) and classic brane models (Randall–Sundrum, 1999). It concludes that no new theory of gravity is required; GR remains fully valid in its domain of applicability. The IDM does not replace GR but places it in a broader geometric context as a low‑energy effective theory. Thus, the infinite dimensionality of the IDM does not conflict with the empirical success of GR.