Speaker
Description
"We investigate a covariant extension of General Relativity in which the local effective dimension of spacetime is promoted to a dynamical, curvature-induced degree of freedom on an underlying four-dimensional manifold. Deviations from four dimensions are encoded through a scalar field ε(x), defining D_eff(x)=4−ε(x), which enters the gravitational action through a dimension-dependent weight multiplying the Einstein–Hilbert term together with an associated scalar potential.
The resulting field equations can be expressed in terms of a curvature-sensitive effective potential V(ε,R), allowing the effective spacetime dimensionality to respond dynamically to the local Ricci curvature. In the limit ε→0 and v(ε)→1, the weak-field regime of General Relativity is continuously recovered. The theory therefore has a scalar–tensor-like structure, with the additional field governing effective dimensionality rather than representing an independent matter component.
We examine two benchmark applications: static, spherically symmetric configurations and a spatially flat FLRW cosmological background. In both cases, curvature-induced dimensional effects lead to controlled departures from standard General Relativity, producing modifications of compact-object mass–radius relations and small corrections to the cosmological expansion history.
This framework provides an effective relativistic setting for studying curvature-dependent spacetime dimensionality and its possible role in strong-gravity and cosmological regimes while retaining a controlled General-Relativistic limit [1].
[1] L. Yıldız, D. Kaykı, and E. Güdekli, “Curvature-Induced Dynamical Effective Spacetime Dimension in an Extension of General Relativity,” The European Physical Journal C 86, 267 (2026). https://doi.org/10.1140/epjc/s10052-026-15514-5"