Slice Energy in Higher Order Gravity Theories and Conformal Transformations

TL;DR

This paper investigates how energy is transferred between scalar fields and matter in higher-order gravity theories under conformal transformations, highlighting conditions affecting energy conservation in dynamic spacetimes.

Contribution

It provides explicit relations for slice energy exchange in higher-order gravity theories and clarifies the role of conformal frames and matter geodesics in energy conservation.

Findings

Slice energy transfer depends on spacetime stationarity.

Energy conservation is linked to whether matter follows geodesics.

Differences between conformal frames affect energy exchange.

Abstract

We study the generic transport of slice energy between the scalar field generated by the conformal transformation of higher-order gravity theories and the matter component. We give precise relations for this exchange in the cases of dust and perfect fluids. We show that, unless we are in a stationary spacetime where slice energy is always conserved, in non-stationary situations contributions to the total slice energy depend on whether or not test matter follows geodesics in both frame representations of the dynamics, that is on whether or not the two conformally related frames are physically indistinguishable.