Mass gap for black hole formation in higher derivative and ghost-free gravity

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The problem of the gravitational collapse of small mass in the higher derivative and ghost free theories of gravity is discussed. It will be demonstrated how higher derivative and non-local modifications of gravity equations regularizes static and dynamical solutions. Boosting a static solution of the linearized equations for the gravitational potential of a point mass we obtain a solution for the field of the ultra-relativistic source (gyraton). Using the latter we construct solutions for the collapsing spherical (thin and thick) null shell. By analysing the obtained solutions we demonstrate that for small enough value of the mass M an apparent horizon is not formed for the gravitational collapse of small mass in the higher-derivative and ghost free theories of gravity. We demonstrate that this “mass gap” property is connected with the presence of the UV cut-off in such theories.