Scientists have introduced the Effective Metric Description (EMD) to map how black holes could differ from predictions of general relativity. The EMD is a model‑independent method that uses physical, coordinate‑invariant quantities—such as the proper distance from the horizon or the free‑falling time—to describe deformations in the black‑hole metric.

In practice, the EMD writes deviations as a series expansion around the horizon. By solving the resulting consistency equations, the framework guarantees a finite Hawking temperature and curvature invariants. It also links different ways of parametrising black‑hole spacetimes, enabling direct translation between the EMD, Johannsen–Psaltis, and Rezzolla–Zhidenko schemes.

The authors tested the EMD on many spacetimes that appear in alternative‑gravity theories, using Padé resummation to extend the description away from the horizon. The method successfully reproduced features such as the black‑hole shadow and quasinormal‑mode frequencies in the test‑field approximation.

A limitation is that the current EMD formulation covers only static, spherically symmetric black holes, along with some charged or lower‑dimensional cases. Extending the framework to rotating geometries will require further work.