Energy conditions in static, spherically symmetric spacetimes and effective geometries

Abstract

Classical energy conditions are investigated in generic static and spherically symmetric spacetimes. In setups with nonconstant $g_{tt} g_{rr}$, the appearance of horizons can signal the violation of the null energy condition and the breakdown of some standard near-horizon properties. For configurations satisfying $g_{tt}g_{rr}=-1$, we devise a systematic algorithm to generate solutions of the Einstein field equations that automatically obey the null energy condition. Within this family, we select a particularly significant metric that incorporates a logarithmic correction to the Schwarzschild model and fulfills all standard energy criteria. We examine its main features, including the horizon structure, geodesic behavior, and junction conditions. Our analysis shows that this geometry can be interpreted as an effective exterior description for both horizon-bearing and horizonless compact objects, and suggests that it can potentially act, in certain regimes, as a black hole mimicker.