An upper limit to the lifetime of stellar remnants from gravitational pair production

Abstract

Black holes are assumed to decay via Hawking radiation. Recently we found evidence that spacetime curvature alone without the need for an event horizon leads to black hole evaporation. Here we investigate the evaporation rate and decay time of a non-rotating star of constant density due to spacetime curvature-induced pair production and apply this to compact stellar remnants such as neutron stars and white dwarfs. We calculate the creation of virtual pairs of massless scalar particles in spherically symmetric asymptotically flat curved spacetimes. This calculation is based on covariant perturbation theory with the quantum field representing, e.g.,\ gravitons or photons. We find that in this picture the evaporation timescale, $τ$, of massive objects scales with the average mass density, $ρ$, as $τ\proptoρ^{-3/2}$. The maximum age of neutron stars, $τ\sim 10^{68}\,\text{yr}$, is comparable to that of low-mass stellar black holes. White dwarfs, supermassive black holes, and dark matter supercluster halos evaporate on longer, but also finite timescales. Neutron stars and white dwarfs decay similarly to black holes, ending in an explosive event when they become unstable. This sets a general upper limit for the lifetime of matter in the universe, which in general is much longer than the Hubble--Lemaître time, although primordial objects with densities above $ρ_\text{max} \approx 3\times 10^{53}\,\text{g/}\text{cm}^3$ should have dissolved by now. As a consequence, fossil stellar remnants from a previous universe could be present in our current universe only if the recurrence time of star forming universes is smaller than about $\sim 10^{68}\,\text{years}$.