Imprints of quantum vacuum fluctuations on the gravitational field of a spherical mass

A bstract The Schwarzschild geometry, describing the gravitational field of a spherical mass in classical vacuum, is one of the most famous vacuum solutions of the Einstein field equations. Classical vacuum is an idealization that does not include quantum vacuum fluctuations of quantum fields, and determining the form of the gravitational field of a spherical mass in quantum vacuum is an important step towards understanding the interplay between gravity and quantum field theory. We formulate and prove general results on the space of static, spherically symmetric and asymptotically flat spacetimes sourced by quantum vacuum fluctuations, obtained under the broad assumptions that the quantum vacuum energy density is negative and unbounded on Killing horizons. In particular, we show the generic replacement of Killing horizons by wormhole throats. We discuss how previous calculations in the literature that have used different prescriptions for the regularized vacuum expectation value of the quantum stress-energy tensor are particular cases of our general results.