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a matter - antimatter mix is generally expected to annihilate . however , under certain conditions a trend might appear , which leads to a matter - antimatter space separation .
the problem was discussed elsewhere ( see , for example @xcite ) . in the present work
an original approach is discussed .
our formulation of the problem is as follows .
* an _ open system _ of material objects and radiation is considered in a flat space - time .
there is no phisical cause for preference in choosing inertial reference frames .
thus , the system is assumed to be baryon symmetric , uniform and isotropic on average _ in any reference frame_. it leads to specific requirement for a matter coordinate - momentum distribution , as shown further .
* material objects are characterized by a mass distribution ( in a unit volume ) @xmath0 , which is the same for matter and antimatter .
baryon charge is conserved .
in addition , the system is characterized by a uniform coordinate - momentum distribution ( in a unit volume ) .
@xmath1 where @xmath2 , @xmath3.1 in  space and momentum 3-vectors . *
all known physical interactions are allowed between system constituents
.    the above formulation of the problem reflects the idea of a generalized matter transport equation . in the present work a treatment of the problem will be as much simplified as possible to concentrate our attention on the question of matter - antimatter separation .
we do not specify the physical nature of material objects .
any concrete astrophysical picture of a matter structure might be embedded , if needed , into the frame under consideration . in general , an object is meant to be a free microscopic or macroscopic particle , free solid body or a gravitationally linked system ( particle cloud , multi - body association , galaxy etc ) .
we assume that a free object is made of either matter or antimatter .
hence , an object is characterized by its mass at rest and baryonic type , its internal evolution being ignored . for the purpose of this work it seems sufficient to consider object - object interaction in general terms of a random collision followed by a formation of a compound system , which may disintegrate into new objects with channel probabilities of fragmentation , annihilation , and merge processes .
we assume that matter - antimatter annihilation results in gamma radiation being a source of a following pair production .
it means that annihilated matter is regenerated in the `` first group '' of a mass distribution .
the `` first group '' may be referred , in principle , to elementary particles as a `` seed matter '' and plays a role of a source term in a kinetic equation .
next comments concern relativistic properties of an open system .
first of all , we need to explain the term `` relativistic material system '' .
a uniform isotropic matter distribution in a flat space is characterized by a uniform coordinate - momentum distribution function ( 1 ) .
it is lorentz - invariant , that is unchanged if measured in any inertial reference frame .
such a state of matter can be treated as a `` maximal chaos '' in terms of bayesian approach for description of relativistic gas @xcite .
actually , this is an approximation of non - interacting particles .
it is worth noting that the relativistic gas model has nothing in common with friedmann - lemaitre expanding universe model @xcite , which treats matter like dust - like matter - made particles with small relative velocities in an observer s vicinity .
the expanding universe itself plays a role of the absolute reference frame . in our approach
an opportunity of introducing the absolute reference frame is denied .
however , the above approximation of non - interacting particles leads to an infinite energy density . in a more rigorous relativistic gas model one has to take into account that physical processes locally observed under conditions of an open system should be characterized by retarded casual connections with the rest of the space , and inertial systems must be referred to a limited space - time volume depending on how precise they are needed to be defined .
hence , a `` realistic '' coordinate - momentum distribution must be characterized by some space - energy correlation and must have a smooth cut - off at however high energy range , or an effective temperature parameter . now any local energy density will be found limited and invariant in a broad set of inertial systems ( the higher temperature , the broader set ) .
we assume that the temperature is well above the threshold needed for pair production process being effective .
under above conditions annihilation and pair production processes have to be balanced , for there is no energy dissipation in the open system . in other words ,
the system is expected to be in a self - sustained baryon symmetric state .
if a mass distribution function is not degenerated into the `` first source group '' one can state that a matter - antimatter space separation takes place .
the mass distribution function should be found from a material balance ( kinetic ) equation .
let a mass distribution function for like matter objects ( in a unit volume ) be given in a mass group form for matter @xmath4 or antimatter @xmath5 : @xmath6 with a total mass conserved : @xmath7    next we use so called _ one velocity approximation _ , that is an equation being averaged over momentum distribution .
let us introduce a generation rate @xmath8 of matter - made objects in a group @xmath9 in a result of matter - matter @xmath10 type object collisions .
if widths of groups are narrow enough we may ignore interactions inside groups .
@xmath11\rightarrow m_i ) > ~,\ ] ] here the brackets @xmath12 symbolize averaging over momentum distribution , @xmath13 is a relative velocity , @xmath14 is an object - object collision cross - section , and @xmath15\rightarrow m_i)$ ] is a `` channel function '' , describing a probability of an object to appear in a group @xmath9 in a result of decay of compound system [ @xmath16,@xmath17 .
masses are conserved due to a proper k - function normalization .
similarly , an object generation rate @xmath18 resulting in matter - antimatter type collision ( * symbolize `` antimatter participant '' , as before ) may be given : @xmath19\rightarrow m_i ) > ~.\ ] ]    in this case , the k - function is normalized to ensure a correct mass balance , annihilated mass in a form of gamma - radiation being taken into account .    choosing a proper summation rule we come to expressions for a removal rate @xmath20 and @xmath21 in matter - matter and matter - antimatter types of collision , correspondingly .
@xmath22\rightarrow m_k)>\ ] ] @xmath23\rightarrow m_k)>\ ] ]    as is said above , an annihilation rate @xmath24 is followed by a matter recreation in the first group , @xmath25 , masses of radiation @xmath26 and recreated matter @xmath27 being in balance : @xmath28\rightarrow m_\gamma ) > ~.\ ] ]    finally , we have a stationary kinetic equation : @xmath29 where @xmath30 for @xmath31 , and @xmath32 for @xmath33 .    due to a symmetry of physical properties of matter and antimatter
one can get the same equation starting considering generation / removal rates for antimatter - made objects .
the equation ( 9 ) may be written in an integral form .
it is easy to see that the equation has a non - trivial solution if a merge channel providing a transfer from a mass group @xmath9 to a mass group @xmath34 is open .
since microscopic and macroscopic merging processes are known from conventional physics we may conclude that the above equation has a physical meaning .
to demonstrate a solution we realized the monte carlo method for k - functions reduced to delta - functions .
in other words , the fragmentation process has been ignored .
we checked that it does not appreciably influence the form of solution though a computing time significantly increases .
obviously , a solution depends on a collision cross - section as a function of an object mass .
four variants were studied : constant cross - section , cross - section , proportional to the mass of a target object , cross - section proportional to both the mass of target and the mass of incident object , finally cross - section proportional to the squared mass of the target object .
the last two variants were expected to have only slightly different solutions .
the variants seem to include typical types of mass - dependent cross - sections of body - body physical interactions . however , concrete energy - dependent cross - sections for specific interactions may differ significantly in magnitude in different mass intervals .
we do not know to what extent the solutions are influenced by `` one velocity approximation '' .
this important question needs a special study on open relativistic matter system properties , their dependence on energy density , in particular . besides
, taking into account an object internal evolution might be important also if the results were used for their speculative applications concerning astrophysical problems @xcite .
all these questions are out of the scope of the present work .
the main conclusion we would like to emphasize is that an open steady - state isotropic system consisted of baryon symmetric uniformly distributed matter should be characterized by a relativistic momentum distribution with an effective high temperature parameter .
subsequently , a space matter - antimatter separation takes place resulted from random interactions within the system .
the possible scale of separation may be seen from the statistical assessments of stationary mass distribution functions in fig .  1 .
the picture gives us the idea of a solution of a simple model kinetic equation describing the above system : the solution may be approximated by a function @xmath35 with @xmath36 ranging between 2 and 3.5 , depending on model parameters .
apparently , there might be a trend of decreasing @xmath36 for asymptotic solution .
the latter should be found by analytical method .
the result shows that an open baryon symmetric matter system reveals a structure containing matter or antimatter - made objects of any size .
there is no material limit for their construction because of the system being unlimited in space .
the bigger size ( age ) objects have , the less their population is .
further computer simulations with more sophisticated models might show more physically meaningful features of the baryon symmetric open system .
99 r.omnes .
* 23 * , 38 ( 1969 ) .
science , * 171 * , 339 ( 1971 ) .
f.m.stecker ,  d.l.morgan ,  j.bredekamp . phys.rev.lett .
* 27 * , 1469 ( 1971 ) .
c.e.fichtel  and  p.sreekumar .
proc . of the fourth compton conf .
, 436 , aip ( 1997 ) .
j.l.synge . the relativistic gas . north - holland publishing co. ( 1967 ) .
zeitschrift fur physik , * 10 * , 377 ( 1922 ) , also * 21 * , 326 ( 1924 ) ( in german ) .
national academy of science , * 15 * , 822 ( 1929 ) .
principles of physical cosmology .
princeton university press ( 1993 ) .
a.vankov . lanl e - print archive http://xxx.lanl.gov : astro - ph9811165 ( 1998 ) ; astro - ph/9812230 ( 1998 ) ; astro - ph/9904045 ( 1999 ) .
an open ( having no physical boundaries ) baryon symmetric system is considered in a flat space - time . 
 we assume that a space is uniformly filled with electromagnetic radiation and material objects , and the system is isotropic in any inertial reference frame . 
 it means that a coordinate - momentum distribution of radiation and material objects does not depend on a reference frame , and the system should be in a state of chaotic relativistic motion . 
 the dominant interaction processes are like - matter merge , unlike - matter annihilation and pair production . in this approximation 
 we came to the conclusion that matter and antimatter exist in a form of mix of material objects characterized by a stationary baryon symmetric mass distribution in a broad mass range . 
 in other words , a matter - antimatter space separation takes place . 
 + pacs number : 95.35.+d