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according to the birkgoff theorem @xcite _ the metric of a vacuum spherically symmetric space time is static , singular in the origin , unique and in spherically symmetric coordinates has the well - known schwarzschild form _ ( when @xmath0 signature form is chosen ) @xmath1 where @xmath2 is the schwarzschild radius . we define the regularity of a metric at a point as i ) an indefinite differentiability of all metric components at this point ; ii ) the condition @xmath3 holds true at this point relative to any coordinate system associated with our system by a unique and continuous transformation . petrov @xcite has shown a counterexample of the metric contradicting the birkgoff theorem @xmath4 where @xmath5 . metric ( [ e02 ] ) is not static . here it is necessary to note that ( [ e01 ] ) and ( [ e02 ] ) are defined in the same coordinate system . further , one can find another argument against the uniqueness of ( [ e01 ] ) .the vacuum einstein equations @xmath6 , @xmath7 are nonlinear second order differential equations . therefore , according to the general theory of differential equations@xcite one should have at least two constants of integration in the solution , but schwarzschild metric ( [ e01 ] ) has only one .    in this letter we would like to show that it is possible to construct more general metrics in the spherically symmetric and axially symmetric cases . because of the letter format we have to restrict the consideration only to the main results without proving the theorems , which we plan to do in the next paper . the question about the applicability of our results in brane models with noncompact extra dimensions and in astrophysics will also be discussed in subsequent publications . * theorem 1 . * _ the _ _ spherically symmetric , static and asymptotically free metric , which is a solution of vacuum einstein equations @xmath6 , @xmath7 has the following form : _ @xmath8{r^{3 }   +   b^{3}}}\biggr ) dt^{2 }    -    \frac {    r^{4 }   dr^{2}}{\biggl(\sqrt[3]{r^{3 }   +    b^{3 } } \biggr)^{4 } \biggl(1   -   \frac{a}{\sqrt[3   ] { r^{3 }   + b^{3 } } } \biggr ) } \nonumber \\ & -   &   \biggl(\sqrt[3]{r^{3 }   + b^{3}}\biggr)^{2}\biggl(d\theta^{2 } + \sin^{2 } \theta d\varphi^{2 } \biggr ) , \label{e03}\end{aligned}\ ] ] _ where @xmath9 is the schwarzschild radius and @xmath10 is an additional parameter of the metric . this metric is unique to within conformal transformations . _    * conclusion 1 . * _ at @xmath11 we obtain schwarzschild metric ( [ e01 ] ) . _    * conclusion 2 . * _ at @xmath12 we obtain particle- like version ( analogously to ref . @xcite ) of schwarzschild metric @xcite . it was first obtained by k.schwarzschild under the condition @xmath13 , which has violated the general covariance of the theory . _    thus , metric ( [ e03 ] ) has the following properties :    1 . when @xmath11 ( the classical schwarzschild case ) it has the curvature singularity at @xmath14 and the coordinate singularity at @xmath15 ; 2 .   when @xmath16 it has only the coordinate singularity at @xmath17 { a^{3}-b^{3}}$ ] ; 3 .   when @xmath18 metric ( [ e03 ] ) is regular everywhere . the fulfillment of the last contention can be verified by the transformation to the kruskal - type coordinates @xmath19 where @xmath20{r^{3}+b^{3}}$ ] . accordingly , metric ( [ e03 ] ) takes the form @xmath21    it is necessary to call the reader s attention to the fact that formally ( [ e03 ] ) corresponds to all the metric requirements of the differentiable manifold only in the case @xmath18 . the case @xmath22 requires singular coordinate transformations , and that is not completely correct from the formal mathematical point of view while working with smooth manifolds .    * remark . * _ by chainging radial coordinate _ @xmath23 _  to _ @xmath24 _ metric ( [ e03 ] ) may be represented in the schwarzschild form _ @xmath25    it seems that parameter @xmath26 can be cancelled completely , but it would not be correct . in fact parameter @xmath26 is included into the @xmath24 domain of definition , namely @xmath27 for this reason variable @xmath24 is not equal to the radial coordinate in all the domain of definition . therefore , any attempt to neglect the parameter @xmath26 leads to a loss of generality of the results obtained . moreover , if the schwarzschild radius @xmath28 is defined in such a manner that it corresponds to newton s law at @xmath29 , then , the value of @xmath26 only changes the geodesics deviations near the origin . * lemma . * _ if one has spherically symmetric space time with metric ( [ e03 ] ) , the radial null geodesic equation is _ @xmath30 _ at @xmath31 the asymptotic behavior is : _ @xmath32    theorem 1 perhaps improved if one could cancel the condition of staticity . however , the requirement of asymptotical flatness of the metric is essentially necessary due to the petrov example . further , the unexpected behaviour of the newton gravity force near the origin when a particle like version of the metric ( with the appropriate choice of the value of parameter @xmath26 ) occurs . the gravity force vanishes at the origin when @xmath12 and tends to infinity as @xmath33 at @xmath34 . such unusual behaviour may be responsible for a gravitational collapse without finishing in a black hole configuration @xcite . * theorem 2 . * _ the three parametric generalization of reissner - nordstrom metric is given by _ @xmath35 _ where @xmath20{r^{3}+b^{3}}$ ] and @xmath36 is a u(1 ) type charge . this metric is regular at the origin when @xmath37 and everywhere when @xmath38 and @xmath39 . _    * theorem 3 . * _ the three parametric generalization of the kerr metric is given by _ @xmath40 _ where @xmath41 is a specific inertia moment , this metric is regular everywhere when @xmath37 and coordinate singularities are not taken into account . in this letter the metric that generalizes the well - known schwarzchild ( reissner - nordstrom , kerr ) metric is considered . this metric includes ( as a partial case ) the schwarzchild metric ( when an additional parameter @xmath26 vanishes ) , a class of metrics containing only the event horizon without the origin singularity and , finally , a class of singularity free particle - like metrics . the proof of the theorems follows . the applicability of this type of metric rather than the schwarzchild metric to describe the existing astrophysical data ( on accretion , for instance ) and to increase the generality of our knowledge of string black holes are under the investigation . the author would like to thank s.alexeyev and all the participants of the zelmanov memorial seminar ( http://xray.sai.msu.ru/sciwork/zelmanov ) for the useful discussions on the subject of this paper .
regular generalizations of spherically and axially symmetric metrics and their properties are considered . 
 newton gravity law generalizations are reduced for null geodesics .