I've been wondering about the effects of the gravitational interaction of a body on itself according to the laws of general relativity. The general relativity courses that I have taken in the past haven't touched on this issue, and I wonder if anyone on this forum would be able to help. In classical electrodynamics, an electrically charged object interacts with itself so that its effective mass is greater than its bare mass. For point particles, this leads to problems as the contribution to the effective mass due to electromagnetic interactions is infinite. Are there similar issues with general relativity? Does gravitational self-interaction lead to a change in the effective mass of an object? If there is such an effect, what sign is it, and is this "gravitational mass" always finite? By a naive comparison with electrodynamics I'd expect the gravitational field to reduce the mass, because the different parts of the body attract each other rather than repel.