Although it is definitely not simple, there are many reasons to consider that baryon number can be violated, for example: - while baryogenesis there was created more matter than antimatter, - hypothetical Hawking radiation can finally turn any matter (mainly baryons) into massless radiation (photons), - some GUT models require proton decay: https://en.wikipedia.org/wiki/Proton_decay , - while charge conservation is guarded by Gauss law, there is nothing like that for baryon number. Sure, the search for proton decay in huge room temperature water tanks was unsuccessful. However, if proton can be destroyed, it would require relatively huge energy – the assumption that it can spontaneously thermally localize on a single proton in room temperature water might be just wrong (?) In contrast, baryogenesis and Hawking radiation examples suggest that really extreme conditions would be necessary to destroy a proton (like temperature). So another candidate might be LHC, but if happening in tiny amounts, the calorimetry has no chance to catch it, and to consider it in Monte Carlo we would need the exact parameters … is proton decay considered for LHC? More important candidate as environment with the most extreme conditions is the center of neutron star. There are real issues with understanding the huge amounts of energy released in gamma-ray bursts – from Wikipedia: “The means by which gamma-ray bursts convert energy into radiation remains poorly understood". Or ultraluminous X-ray sources, especially the M82 X-2: pulsar radiating ~10 million times more energy than our sun. Hypothetically, reaching extreme conditions to start statistically essential “baryon burning” (total matter->energy conversion) in the center of neutron star, might help explaining these extreme energy sources. So I wanted to ask if proton/neutron decay is considered in neutron star models? Should it?