For causal diamonds in maximally symmetric spacetimes, a new bulk contribution to Abbott-Deser-Tekin charges arises from conformal symmetries, and the first law of horizon thermodynamics holds approximately on 'nice slices' off the moment-of-time symmetry surface.
Conformal Invariance of Black Hole Temperature
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Horizon Thermodynamics on Nice Slices of the Causal Diamond
For causal diamonds in maximally symmetric spacetimes, a new bulk contribution to Abbott-Deser-Tekin charges arises from conformal symmetries, and the first law of horizon thermodynamics holds approximately on 'nice slices' off the moment-of-time symmetry surface.