TL;DR
This paper extends classical theorems to higher order gravity theories, demonstrating the uniqueness of Schwarzschild solutions under specific conditions and analyzing static solutions with matter.
Contribution
It generalizes the Lichnerowicz and Israel theorems to higher order gravity, establishing uniqueness of Schwarzschild and vacuum solutions in these theories.
Findings
Schwarzschild is the unique spherically symmetric, static, asymptotically flat black-hole solution under certain curvature conditions.
In presence of matter satisfying positivity, only vacuum solutions of GR are also solutions of higher order gravity.
The results constrain static solutions in higher order gravity theories, extending classical theorems.
Abstract
The Lichnerowicz and Israel theorems are extended to higher order theories of gravity. In particular it is shown that Schwarzschild is the unique spherically symmetric, static, asymptotically flat, black-hole solution, provided the spatial curvature is less than the quantum gravity scale outside the horizon. It is then shown that in the presence of matter (satisfying certain positivity requirements), the only static and asymptotically flat solutions of General Relativity that are also solutions of higher order gravity are the vacuum solutions
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