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We discuss some properties of recently proposed models of a ghost-freegravity. For this purpose we study solutions of linearized gravitationalequations in the framework of such a theory. We mainly focus on the version ofthe ghost-free theory with the exponential modification$\exp(\Box/\mu^2)\Box^{-1}$ of the free propagator. The following threeproblems are discussed: (i) Gravitational field of a point mass; (ii) Penroselimit of a point source boosted to the speed of light; and (iii) Sphericalgravitational collapse of null fluid. For the first problem we demonstrate thatit can be solved by using the method of heat kernels and obtain a solution in aspacetime with arbitrary number of dimensions. For the second problem we alsofind the corresponding gyraton-type solutions of the ghost-free gravitationalequations for any number of dimensions. For the third problem we obtainsolutions for the gravitational field for the collapse of both "thin" and"thick" spherical null shells. We demonstrate how the ghost-free modificationof the gravitational equations regularize the solutions of the linearizedEinstein equations and smooth out their singularities.

Spherical collapse of small masses in the ghost-free gravity