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

TL;DR

This paper proves the horizon-entropy increase law for various horizons in modified gravity theories, introduces a modified trapping horizon concept to account for conformal invariance issues, and explores horizon behavior in different spacetime models.

Contribution

It provides a new definition of trapping horizons that remains invariant under conformal transformations, extending the horizon-entropy law to scalar-tensor and $f(R)$ gravity theories.

Findings

Proved the horizon-entropy increase law for scalar-tensor and $f(R)$ gravity.

Introduced a modified trapping horizon concept for conformal invariance.

Analyzed horizon behavior in veiled general relativity and flat FLRW spacetime.

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.