Alonso Serrano, AnaGaray Elizondo, Luis JavierLiška, Marek2025-12-122025-12-122025Ana Alonso-Serrano (†Institut fr Physik, Humboldt-Universitt zu Berlin, Zum Groen Windkanal 6, 12489 Berlin, Germany‡Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut), Am Mühlenberg 1, 14476 Potsdam, Germany), Luis J. Garay (§Departamento de Física Teórica and IPARCOS, Universidad Complutense de Madrid, 28040 Madrid, Spain), and Marek Liška (School of Theoretical Physics, Dublin Institute for Advanced Studies, 10 Burlington Road, Dublin 4, Ireland) International Journal of Modern Physics D 2025 34:160218-271810.1142/s021827182544002Xhttps://hdl.handle.net/20.500.14352/128893© World Scientific Publishing Company This essay received an Honorable Mention in the 2025 Essay Competition of the Gravity Research FoundationThe equivalence principle for test gravitational physics strongly constrains dynamics of spacetime, providing a powerful criterion for selecting candidate theories of gravity. However, checking its validity for a particular theory is often a very difficult task. We devise here a simple theoretical criterion for identifying equivalence principle violations in black hole thermodynamics. By employing this criterion, we prove that Lanczos-Lovelock gravity violates the strong equivalence principle, leaving general relativity as the only local, diffeomorphism-invariant theory compatible with it. However, we also show that certain nonlocal expressions for black hole entropy appear to obey the strong equivalence principle.engjournal article1793-6594https://doi.org/10.1142/s021827182544002xhttps://www.worldscientific.com/doi/full/10.1142/S021827182544002Xhttps://arxiv.org/abs/2505.10934open access53530.145524.88Equivalence principlesBlack hole thermodynamicsLovelock gravityFísica (Física)2212 Física Teórica2212.05 Gravitación2212.14 Teoría de la Relatividad