Black holes of the Vaidya type with flat and (A)dS asymptotics as point particles

Abstract

A presentation of the Vaidya type Schwarzschild-like black holes with flat, AdS and dS asymptotics in 4-dimensional general relativity in the form of a pointlike mass is given. True singularities are described by making the use of the Dirac $\delta$-function in a non-contradictory way. The results essentially generalize previous derivations where the usual Schwarzschild black hole solution is represented in the form of a point particle. The field-theoretical formulation of general relativity, which is equivalent to its standard geometrical formulation, is applied as an alternative mathematical formalism. Then perturbations on a given background are considered as dynamical fields propagating in a given (fixed) spacetime. The energy (mass) distribution of such field configurations is just represented as a point mass. The new description of black holes' structure can be useful in explaining and understanding their features and can be applied in calculations with black hole models. A possibility of application of the field-theoretical formalism in studying the regular black hole solutions is discussed.