The horizon-entropy increase law for causal and quasi-local horizons and conformal field redefinitions

Abstract

We explicitly prove the horizon-entropy increase law for both causal and quasi-locally defined horizons in scalar-tensor and $f(R)$ gravity theories. Contrary to causal event horizons, future outer trapping horizons are not conformally invariant and we provide a modification of trapping horizons to complete the proof, using the idea of generalised entropy. This modification means they are no longer foliated by marginally outer trapped surfaces but fixes the location of the horizon under a conformal transformation. We also discuss the behaviour of horizons in "veiled" general relativity and show, using this new definition, how to locate cosmological horizons in flat Minkowski space with varying units, which is physically identified with a spatially flat FLRW spacetime.

23 pages

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Cited by in corpus (13)

• Searching for dynamical black holes in various theories of gravity
• Conformally rescaled spacetimes and Hawking radiation
• The Campanelli-Lousto and veiled spacetimes
• Horizon thermodynamics and spacetime mappings
• Black holes and wormholes subject to conformal mappings
• Geometric surfaces: An invariant characterization of spherically symmetric black hole horizons and wormhole throats
• Revisiting black holes and wormholes under Weyl transformations
• Cosmological applications of the Brown-York quasilocal mass
• Interpreting the conformal cousin of the Husain-Martinez-Nunez solution
• More on spacetime thermodynamics in the light of Weyl transformations
• Spacetime mappings of the Brown-York quasilocal energy
• The holographic bound in the scalar-tensor and $f(R)$ gravities
• What can we learn from the conformal noninvariance of the Klein-Gordon equation?