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Treves, Fr. ( 1982) Introduction to Pseudoditferential and Fourier Integral Opemtors, Vol.1,2 [15] Bateman, H., Erdelyi, A (1953) Higher Transcendental Fu11ctio11.1· Vol.2, Mc Graw Hill, N.Y [16] Vilenkin, N Ya. (1965) Special Functions and the Theory of Group Representations, Nauka, Moscow (in Russian). [17] Michlin, S.G (1977) Linear Equations in Partial Derivatives, Moscow (iu Russian). Gravity, Astrophysics, ancJ Strings'04 P. P. Fiziev (eds.) and M, D Todorov St Kliment Ohridski University Press, Sofia,On the solutions of Einstein equations with massive point source Plamen Fiziev Faculty or Physics, SL Kliment Ohridski University of Sofia, 5 James T3ourchicr Blvd., Sofia 11 M. Bulgaria Abstract Wc, sh()w that Einstein equations arc rn111p<1tiblc with the presence or l!lassivc poi11t partidcs and li11d c1HH:spu11di11g two para111ctc1 larnily ()rsol11tio11s. They arc cklined by the barc, rncchanical mass M11 > (J and tile Keplerian 111ass JY[< fl.111 of the point source 01·g1 avity. The global analytical prnpel'lics ul' these sol11tio11s in the co1nplex plane define

1 unique prelerabk radial variable of till~ problem. 1 clear physical 111olivation for eonsidL:ration or massive point p~1rticlc sources ol,l'.1«1vi-· tational field in GR, both electrically neutral and charged onL:s, can he round as early as in llJ62-·61 Feynman lectures on gravity [I[. ln spite or this racl Lile pmhlcm i.s still OJlCll AL present Lile vasl majority or relativists do not accept the consideralion or point p~1r­

our cutting of the domain of luminosity variable places the event horizon in the nonphysical domain of the variables. This effect is well known from the solutions of Einstein equations with massive malter sources of finite dimension. The mathematical and the physical properties of the new solutions arc essentially different in comparison with the well known other spherically symmetric static solutions to the Einstein equations. All they have different type of singularities at the center of the symmetry, which is surrounded by empty space. The previously known solutions were often erroneously considered as a solutions for describing of single point mass in GR. It is clear that our solutions in generalized functions define in mathematical sense the fundamental solutions of Einstein equations, which are complete analogous to the fundamental solutions of Poisson equation in Newton theory of gravity. Thus the problem, formulated by Feynman in

is solved. Further study of the new solutions and their physical applications will be given in separate articles. · On the solutions of Einstein equations with massive point source 83 Acknowledgements. The author is grateful to the High Energy Physics Division, ICTP, Trieste, for the hospitality and for the nice working conditions during his visit in the autumn ofwhere an essential development of the present article was done. He is grateful, too to the JJNR, Dubna, for the financial support of the present article and for the hospitality and good working conditions during his three months visits inand in 2004

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It turns out that Lhese.f/.mdamentaf solutions are described by mathematical distributions and own the necessary jumps in the first derivatives of the metric, needed Lo satisfy the Einstein equations al Lhe place of the point source. The new solutions form a two-parameters ramily of metrics on singular manifolds !VJ[(l,:l) fo1 w }, much like the corresponding fundamental solutions with poinl source in all other branches of physics. The fundamental solutions of Einstein equations are defined by the bare mass J\1/0 and by the Keplerian mass.M of the source, or equivalently, by lhe Keplerian mass AI and the ratio of the masses: (} = JM/J..10 E (0, J). This ratio describes the gravitational mass defect of the point particle. The mathematical and Lhe physical properties of the new solutions are essentially different in comparison with the well known other spherically symmetric static solutions to the Einstein equations with different type of singularities at the center of the symmetry, which is surrounded by an empty space. The previously known solutions were often considered as a solutions for describing of single point particle in GR. In the most of the 84.... Novel properties of bound states of Klein-Gordon equation in... 85 known cases this turns to be incorrect