AWhat changed
Ehlers and Geroch proved a geodesic-limit theorem that permits a small body to carry its own gravitational field. Around a prescribed timelike curve, their hypotheses require arbitrarily localized nonzero bodies satisfying the dominant energy condition, with metrics and connections arbitrarily close to a smooth background. Under those conditions the limiting curve must be a geodesic of that background. The proof also applies to a conserved symmetric matter tensor satisfying the same support and energy conditions.
Scientific scope
Ehlers and Geroch proved a geodesic-limit theorem that permits a small body to carry its own gravitational field. Around a prescribed timelike curve, their hypotheses require arbitrarily localized nonzero bodies satisfying the dominant energy condition, with metrics and connections arbitrarily close to a smooth background. Under those conditions the limiting curve must be a geodesic of that background. The proof also applies to a conserved symmetric matter tensor satisfying the same support and energy conditions. This is a conditional limiting theorem. It neither makes arbitrary finite bodies exact geodesics nor supplies a uniform long-time self-force error bound. Its metric-closeness hypotheses exclude unrestricted strong self-gravity; the authors explicitly exclude black holes and singular regions. The stronger tidal bound and charged-body extension discussed in the paper are not established general-relativistic results here. The 2003 preprint and 2004 publication identity are distinguished.
Evidence
The linked original works support the scoped statement and contribution attribution. WRS has not independently replayed experiments or reconstructed a full mathematical proof. This is a conditional limiting theorem. It neither makes arbitrary finite bodies exact geodesics nor supplies a uniform long-time self-force error bound. Its metric-closeness hypotheses exclude unrestricted strong self-gravity; the authors explicitly exclude black holes and singular regions. The stronger tidal bound and charged-body extension discussed in the paper are not established general-relativistic results here. The 2003 preprint and 2004 publication identity are distinguished.
Contributors
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