Covariant phase space approach to Einstein-æther gravity
Year: 2026
Type: article
Abstract: Black hole thermodynamics in Lorentz-violating gravity is subtle because different excitations propagate at different speeds and hence identify different causal horizons. We revisit Einstein–æther gravity using the covariant phase space formalism with boundaries and derive a consistent first law for stationary black holes. For a mode of propagation speed s , we introduce a disformal frame in which the corresponding s -horizon is a Killing horizon, so that a standard Wald-type derivation can be carried out. We then map the result back to the original (horizon) frame, showing that the first law retains the same formal structure. The associated horizon charge contains, besides the usual geometric (Komar/Wald) contribution, an irreducible æther term that admits an interpretation as an additional entropy sourced by the æther flux across the horizon; accordingly, the total entropy splits into a gravitational part and an æther part. We further develop an extended-thermodynamics framework in which the couplings (and Λ ) are allowed to vary, obtaining generalized Smarr relations. Finally, we analyze the probe-mode limit c s → + ∞ , clarifying its connection to universal-horizon thermodynamics and resolving the apparent tension in the literature between approaches that (i) fix the entropy to be proportional to the area and infer a corresponding temperature, and (ii) impose the Hawking temperature associated with modes peeling from the universal horizon and infer a nonarea entropy. Once the independent æther entropy contribution is properly taken into account, the two prescriptions are reconciled.
DOI: 10.1103/gwmt-ywwy
Authors: Walter Arata, Stefano Liberati, Giulio Neri
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W7147570119
FWCI:
Cites:
Cited by:
Related to: