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it is by now relatively well known that gravitational collapse can produce rich structure even within highly simplified systems such as spherical symmetry . in particular , near the threshold of black hole formation , the strong field dynamics of general relativity exhibits critical phenomena .    the pioneering work demonstrating this critical behavior in the collapse of a single massless scalar field @xcite has been supplemented by investigations of gravitational waves @xcite , a perfect fluid @xcite and a variety of other matter models , all of which exhibit the same general characteristics . indeed , to our knowledge no system which has been studied in this context has been shown _ not _ to exhibit this critical phenomena .    at this point in the subject s development , dynamical evolutions ( solutions of the full partial differential equations of motion ) , in tandem with analytic and perturbative calculations have given us a reasonable understanding of many of the phenomenological details of critical behavior in collapse . ( see  @xcite for an excellent review of the subject . )    in light of this , one of the more interesting discoveries in some of the more recently studied models  @xcite is the presence of two distinct types of behavior at the threshold of black hole formation . specifically , in these models , certain regions of parameter space ( initial - data space ) are found to yield near - critical collapsing configurations which display self - similarity and , in the super - critical regime , a scaling law which is continuous in the black hole mass . by analogy with the theory of phase transitions , this is called a type ii transition . however , it is found that other regions of parameter space lead to critical collapse which has a static ( or periodic ) solution as an intermediate attractor this results in a black hole transition with a nonzero mass gap . again , in analogy with the discontinuous behavior in order parameter which frequently accompanies first order phase transitions , this is called type  i behavior . for the case of the einstein - yang - mills ( eym ) model studied in  @xcite , the static solution appearing in type i collapse is the well - known @xmath0 bartnik - mckinnon solution@xcite , while for the massive scalar model considered in  @xcite , the type i threshold solutions are apparently unstable members of the family of `` oscillating soliton stars '' which have previously been constructed by seidel and suen  @xcite , albeit in a different context . finally , in the case of einstein - skyrme ( es ) collapse considered in  @xcite , a static type  i solution was observed , which , as in the eym case , had previously been constructed and studied within a purely static _ ansatz _  @xcite . as noted above , each of these three models also exhibits type  ii behavior  in the case of massive scalar collapse  @xcite , the type  ii critical solution is the same one originally observed in massless scalar collapse  @xcite , and , interestingly , in the es model , the type  ii solution is evidently identical  @xcite to that observed in the eym model  @xcite . heuristically , one expects type  ii behavior in _ any _ collapse model where the initial configuration can be made sufficiently `` kinetic - energy - dominated '' ( ultra - relativistic ) , whereas type  i behavior is expected only in those models which have an intrinsic length scale ( or equivalently , mass scale ) , and which have some type of self - interaction which can `` balance '' the attractive gravitational interaction .    as noted in the concluding remarks of  @xcite , hints of further interesting phenomenology in the eym model have been seen in the super - critical regime where all evolutions are characterized by black hole formation . in this paper we study this regime in more detail and present evidence for a new type of critical transition in which the intermediate attractors are the `` minimally unstable '' ( one unstable mode in perturbation theory ) colored black holes discovered by bizon @xcite , and independently by volkov and galtsov @xcite . this result is , of course , analogous to the discovery that the @xmath0 bartnik - mckinnon solution is the intermediate attractor for type  i collapse . crucially , in order to accurately model the dynamics of super - critical solutions for long times after the formation of an event horizon , we use black - hole excision techniques . such methods were first successfully employed in a dynamical context by seidel and suen  @xcite , and have subsequently been studied and implemented by many other authors ( see  @xcite and references therein for a more extensive discussion ) . however , to our knowledge , this is the first time that excision has been used to study critical collapse , and we feel our results highlight the power and potential of the strategy to elucidate issues relating to the formation and long - time evolution of black holes . our adoption of excising techniques necessitates the use of a different coordinate system than that used in  @xcite  that work used polar slicing and areal spatial coordinates , a system which generalizes the usual schwarzschild coordinates to time - dependent spacetimes . as is well - known , the @xmath1constant slices in the polar / areal system can not penetrate apparent horizons  thus , for all practical purposes , the slices remain outside of event horizons and therefore can not be used in conjunction with excision . we therefore retain areal spatial coordinates , but adopt maximal slicing  in this case the slices _ do _ cross apparent and event horizons , and excision techniques _ can _ be used . the outline of the remainder of the paper is as follows . the next section describes the eym model and the equations of motion we subsequently solve numerically . we pay particular attention to gauge and coordinate choices , as well as to regularity , boundary and initial conditions for the fields . in section  [ sec : excision ] we describe our numerical scheme , focusing on our specific coordinate choices and on some details of our black - hole excising technique . in sections  [ sec : results ] and [ sec : discussion ] we describe our results and conclusions . we are interested in investigating the gravitational collapse of a self - gravitating yang - mills gauge field . to begin , let us consider the action for an eym theory s = d^4x where @xmath2 is the yang - mills field strength tensor . on varying the action with respect to the metric , @xmath3 , and the gauge connection , @xmath4 , we get the general equations of motion . we simplify these further by making some additional assumptions . in particular , we choose the gauge group to be @xmath5 and focus on spherically symmetric gravitational collapse . this places restrictions on both the spacetime metric and the form of the gauge connection . even so , the equations we derive have a rather general form as can be seen in equations ( [ eom_first][eom_last ] ) . subsets of these equations have been considered in a variety of different contexts . in particular @xcite evolved a version of the einstein - yang - mills equations in polar ( @xmath6 ) , areal ( @xmath7 ) coordinates with the additional assumption on the yang - mills field that the connection @xmath8 was purely magnetic . since our interest here is to consider the same model studied in  @xcite , but to penetrate into the super - critical regime of the phase space , we will likewise make the  magnetic _ ansatz_. " as described in the appendix , together with appropriate gauge choices , this _ ansatz _ effectively sets all but one of the components of the gauge connection to zero . in addition to making these gauge choices we must also choose a coordinate system . as mentioned in the introduction , in order to evolve the system for long times to the future of black hole formation , we choose maximal time slices and areal ( or radial ) spatial coordinates . as detailed in the appendix , the equations can now be written in the following form . the evolution equations are [ eq : evpi ] & = & + ar^2 w ( 1-w^2 ) + & = &  + [ eq : evw ] & = & a + w and the constraint equations are w & = & + [ eq : alpha ]  & = &  ( aa - 2r ) + 2r^2 ( a^2 - 1 + 2r aa ) + 4 g ( s - 3 ) + [ eq : a ] a & = & a 1-a^2 2r + 32 ra^3 k_^^2 + 4 g r a + [ eq : ktt ] k_^ & = & -3r k_^ + 4 g ( g^2 a r^2 ) where the matter stress - energy terms are given by s - 3 & = & a^2 ( 1-w^2)^2 2 g^2 r^4 + 1 g^2 r^2 ( ^2 + ^2 ) + & = & a^2 ( 1-w^2)^2 4 g^2 r^4 + 1 2 g^2 r^2 ( ^2 + ^2 ) . we also note that we have an algebraic relation for the sole component , @xmath9 , of the shift vector , @xmath10 : = r k_^ . in addition to the equations of motion , we need boundary conditions on the fields . these are determined by demanding regularity at the origin of spherical symmetry , and by enforcing an outgoing condition on the radiation fields at large radius . this latter condition assumes that there is no radiation coming in from outside our finite mesh . this is not completely true , as in general there will be backscattering of the propagating fields off regions of high curvature . however , if our domain of integration is large enough , the contributions from this scattering are dynamically negligible . the demand for a regular origin results in boundary conditions on the fields at @xmath11 . from equations  ( [ eq : alpha ] ) and ( [ eq : a ] ) it can be seen that @xmath12 , as well as @xmath13 . in addition , @xmath14 . for the matter fields , @xmath15 and @xmath16 , so that the auxiliary variables @xmath17 and @xmath18 are both zero at the origin . we note that these conditions constrain the yang - mills field , @xmath19 , to be in a vaccum state at @xmath11 .    for initial data , we choose a time - symmetric kink for the gauge potential which was previously used in @xcite . this pulse is given by [ eq : kink ] w(0,r ) & = & ( x - r s ) + ( 0,r ) & = & 0 . with the parameters @xmath20 and @xmath21 chosen such that @xmath22 and @xmath23 . the two parameters @xmath24 and @xmath25 define the center and width of the pulse respectively . they also serve as the two parameters which we will vary in order to explore the phase space . we note that the implementation of this data in @xcite was incorrect but ultimately had no effect on the overall conclusions of that work . we have fixed the implementation of the kink data here and note a minor improvement in the conservation of energy . it should be emphasized that we do not incorporate any form of adaptive mesh refinement into our numerical approach . instead , we use a fixed uniform grid with a mesh spacing which is sufficiently fine to uncover the new critical behavior . the drawback to this approach , of course , is that we are unable to fully resolve the discretely self similar solutions which arise near the type  ii black hole threshold . however , our primary interest here is in the supercritical regime , and we are satisfied that previous work has established the nature of the type  ii transition . what _ is _ important in this work is the use of black hole excision techniques which allow us to evolve well beyond the formation of the black hole . we discretize the evolution equations ( [ eq : evpi][eq : evw ] ) using two time levels with centered time differences , and angled spatial differences as described in @xcite . the constraint equations are then integrated outward from the origin . equation ( [ eq : alpha ] ) , the slicing equation , is rewritten in first order form  & = & ( aa - 2r ) + 2r^2 ( a^2 - 1 + 2r aa ) + 4 g ( s - 3 ) +  & = & .    the apparent horizon equation in maximal - areal coordinates is simply a r k^_= 1 . thus , we can compute a characteristic function @xmath26 such that @xmath27 where @xmath28 is a threshold value , ostensibly unity , but set to a slightly larger value in practice  typically , @xmath29to ensure that the inner boundary lies strictly within the apparent horizon . at any time , the characteristic function tells us which grid points are deemed to be inside ( @xmath30 ) or outside ( @xmath31 ) the horizon . as the system evolves , we recompute @xmath26 at each time step and simply `` discard '' any grid points for which @xmath32 . the radial locations of these grid points will then generally satisfy @xmath33 , where @xmath34 is the instantaneous inner boundary of the computational domain , and roughly coincides with the location of the apparent horizon . we need _ no _ boundary conditions for the functions evolved with equations ( [ eq : evpi][eq : evw ] ) since the characteristic directions at @xmath35 are such that only events with @xmath36 are in the past domain of dependence . we can therefore use the discrete form of the evolution equations up to _ and including _ the inner boundary point . however , the constraint equations ( [ eq : alpha][eq : ktt ] ) must have an inner boundary condition . until a horizon is formed , we can simply use conditions derived from regularity . once a horizon forms , however , we need an alternative . if the horizon initially forms at time @xmath37 and radial coordinate @xmath38 , then for a function @xmath39 , we use @xmath40 as the initial boundary value for @xmath41 . we then evolve @xmath41 along this boundary using the evolution equation for @xmath41 . the evolution equations that we use are as follows :    & = & + r a k^ _ - 4 r a j_r , + & = & 3 k^ _ ( 12 k^_- r ) + 4 ( s^r_r - j_r ) + ( a^2 - 1 ) - . since the lapse @xmath42 does not have an evolution equation , we simply leave @xmath42 and @xmath43 `` frozen '' at whatever specific values they have when excision at that particular radius , @xmath34 , begins . finally , we note that the programs which we used to generate the results that we will describe below were written in rnpl ( rapid numerical prototyping language ) @xcite . this language has been specifically designed to facilitate the differencing and subsequent numerical solution of partial differential equations . on evolution of the equations , we verify previously examined aspects of this system as discussed in @xcite . in particular , we find that in different regions of the parameter space , there are both types of critical behavior at the threshold of black hole formation . we observe type  i behavior , wherein black holes turn on at finite mass and the intermediate attractor is the @xmath0 bartnik - mckinnon solution . we also confirm aspects of type  ii collapse in the appropriate region of parameter space . this includes such things as echoing and the scaling relation for the black hole mass . however , because our code does not employ mesh - refinement , we are unable to fully reproduce the results of @xcite . however , as discussed previously , our main emphasis here is to address the outstanding question of what happens in the super - critical region and to the future of black hole formation .    on evolving into the supercritical ( black hole ) regime , we find that the dynamics of the resulting spacetimes exhibit two distinct types of behavior which we describe below . it turns out that these can be characterized by the asymptotic vacuum state of the yang - mills potential @xmath19 . these two behaviors are related to the type  i and type  ii critical collapses identified previously . the original type  i collapse is described , in part , by a black hole which forms with finite mass . slightly super - critical type  i evolutions , now continued well to the future of black hole formation confirm this behavior , as one would expect . in addition , after the black hole is formed , part of the remaining yang - mills field outside the horizon radiates to infinity and some of it falls down the black hole causing the black hole to grow . how much larger the initial black hole becomes through the infall of additional matter depends , in part , on where in the parameter space the evolution begins . eventually , however , and in accordance with what might be expected from the no - hair theorems , the exterior spacetime settles down to a schwarzschild black hole with the yang - mills field in its vacuum state . in general , for slightly super - critical collapse ( either type  i or type  ii ) , as the remaining mass - energy radiates away the gauge potential approaches one of its two vacuum values : @xmath44 . for the case of slightly super - critical type  i collapse , in the asymptotic regime , the gauge potential always picks the @xmath45 vacuum state ( recall that our initial data family  ( [ eq : kink ] ) has @xmath46 and @xmath47 ) . this turns out to be true even for collapsing configurations which are no longer just slightly super - critical but are , in fact , well into the black hole regime . we can thus characterize a sort of  generalized " super - critical type  i collapse by the asymptotic value of the gauge potential @xmath19 . when type  ii collapse is considered , the overall picture is broadly the same . again , after the original black hole forms ( at _ finite _ mass since we are slightly super - critical ) some of the matter remaining in the region exterior to the black hole falls into the black hole causing it to grow and the rest is radiated off to infinity . the resulting exterior spacetime agains settle down to schwarzschild with the yang - mills field in its vacuum state . however , the gauge potential in the slightly super - critical type  ii collapse approaches its other vacuum value : @xmath48 . similarly , further into the type  ii super - critical regime ( where we should emphasize the discretely self - similar nature of the critical solution is no longer clear and where the black holes which form all have finite mass ) we find generalized " super - critical type  ii collapse which can be characterized by an asymptotic value of the gauge potential of @xmath49 . it is worth commenting here that our terminology has become a bit loose . we have been speaking of type  i and type  ii collapse well into the super - critical regime when in fact these terms originally referred to types of critical behavior in a very small neighborhood of the exact critical solutions . for instance , as one moves away from the type  ii threshold , the discrete self - similarity of the exactly critical solution is no longer clearly exhibited by configurations which collapse to a black hole . in addition , a significant fraction of the mass present will end up in the black hole . this is to be contrasted with the tiny black holes that can be formed in near - critical type  ii collapse . it should also be made clear that type  i and type  ii do not refer to different _ types _ of black holes . the end - state exterior geometry in all of these evolutions is a schwarzschild black hole . however , we are , in a sense , generalizing the concepts of type  i and type  ii collapse to distinguish two kinds of collapse _ dynamics _ in the super - critical regime . it quickly becomes clear that these regions are well defined in parameter space and it becomes natural to try and find the boundary separating them . indeed , the problem reduces to tuning a single parameter across the threshold between these two types of collapse dynamics . what we find is that at the threshold between these two types of dynamics a static solution emerges as the intermediate attractor for this new near - critical collapse . the type  ii side of this threshold exhibits the following near - critical evolution . as the field collapses , a finite mass black hole is formed . the remaining field exterior to the black hole then approaches a static , non - trivial configuration . after some time the field then departs from the static configuration and disperses to infinity leaving the original black hole virtually unchanged . the gauge potential in this case approaches the vacuum value of @xmath50 and thus this side of the threshold is part of the generalized type  ii collapse dynamics . the type  i side of this threshold has , of course , a very similar development initially . again , a black hole of finite mass is formed exactly as before and is followed by the approach of the exterior yang - mills field to the static solution . however , as the field leaves the static solution , most of the matter collapses into the black hole with only a small portion radiating off to infinity . the gauge potential , in this case , approaches the vacuum state of @xmath45 . figures  [ fig : showevolve ] and  [ fig : showevolve_log ] show the development of these two cases overlayed with the static , intermediate attractor which is the exactly critical solution . since we are in the super - critical regime , these new , exactly critical solutions are themselves black holes with yang - mills hair . indeed , these attractors are the colored black holes discovered by bizon and independently by volkov and galtsov @xcite shortly after the discovery of the bartnik - mckinnon solutions . in general , these colored , static black hole solutions are described by their horizon radius ( or , relatedly , their mass ) @xmath51 and the number @xmath52 of zero crossings of the yang - mills potential @xmath19 . the solutions which serve here as intermediate attractors in the dynamical collapse are the lowest lying colored black holes with @xmath0 . subsequent to their discovery , it was shown that these black holes are unstable . in particular , the colored black holes with label @xmath52 have @xmath53 unstable modes @xcite . of these @xmath53 unstable modes , @xmath52 arise from spherically symmetric perturbations in the gravitational sector away from staticity and another @xmath52 unstable modes arise from perturbations in the sphaleron sector , _ i.e. _ away from the magnetic _ ansatz _ for the yang - mills fields . since we are solving the nonlinear evolution equations while remaining within the magnetic _ ansatz _ we would expect our data to excite all the unstable modes within the gravitational sector while exciting none of the unstable modes in the sphaleron sector . as a result , we would expect the @xmath0 family of solutions to have a single unstable mode , thus making it relevant to critical collapse . the picture of this new critical solution in the black hole regime having a single unstable mode thus accords perfectly with previous understanding of both type  i and type  ii collapse . this new critical behavior within the black hole regime is , in many ways , qualitatively similar to that of the type  i collapse . solutions in one of these new interpolating families asymptote to one of the static , colored black hole solutions , @xmath54 . initial data for collapsing configurations close to one of the critical solutions will approach @xmath54 , and remain in its vicinity for some amount of time @xmath55 , as measured , for example , by an observer at infinity . the evolution will then peel off the static solution with the remaining field either dispersing to infinity or collapsing and adding a finite amount of mass to the already present black hole . one can quantify the amount of time spent near the static solution in the same way as with the type  i collapse . the time , as measured by an asymptotic observer , is @xmath56 , where the coefficient @xmath57 is the characteristic time scale for the collapse of the unstable solution @xmath54 or , in other words , the inverse lyapounov exponent of the single unstable mode .    with our evolutions , we confirm this relation and can calculate the value of @xmath57 in the manner described in @xcite . for figures  [ fig : showevolve ] and [ fig : showevolve_log ] , where the static solution has a black hole radius of @xmath58 , we confirm the linear relation and find @xmath59 as shown in figure  [ fig : time_exponent ] . once we have established the existence of these new , colored critical solutions , it then becomes straightforward to map out parameter space for our choice of initial data . figure  [ fig : phase_space ] does this for the main region of interest . figure  [ fig : phase_space ] should be compared to figure 1 in @xcite . there , it was suggested that there was a coexistence between black holes exhibiting both types of critical behavior . however , that suggestion was based on evolutions which did not actually continue to the future of the resulting black hole . thus , up to this point , only the region marked  dispersion " had been well explored . evolutions had been performed in the black hole regime , but detailed understanding of what happened in collapse was largely limited to times prior to the formation of the black hole . now , with our use of apparent horizon boundary conditions , we can explore more completely this super - critical region . thus , what is actually present is two well - demarcated regions in the black hole regime separated by a critical line , as described above . = 7.5 cm    = 7.5 cm we have presented evidence for the existence of a new type of critical phenomena within the black hole regime of the spherically symmetric einstein - yang - mills model . previous work on critical behavior in this model has established that both type  i and type  ii critical solutions emerge in sufficiently general families of initial data . however , that earlier work was unable to accurately evolve to the future of black hole formation . using a different coordinate system and horizon excision techniques , we are able to evolve well into the black hole regime . we find that these two different types of critical collapse can be generalized to types of collapsing spacetimes with a distinguishing characteristic being the asymptotic vacuum value of the yang - mills potential . these two  phases " of black hole formation are separated by a critical line in phase space such that dynamically forming black hole solutions exactly at criticality are the static , @xmath0 colored black holes @xcite . this , of course , fits nicely within our conceptual framework that critical solutions are intermediate attractors of co - dimension one . it is worth emphasizing a few observations at this point . first , it is important to note that the mass of the final schwarzschild black hole in the evolution will be discontinuous across this new critical line in figure  [ fig : phase_space ] . ( in fact , indications of jumps in the black hole mass - spectrum in the super - critical regime were present in earlier calculations  @xcite . ) naively , this might be somewhat surprising since it means that nearby configurations in the space of initial data can have , in principle , very different sized black holes as their end - states . further , we note that when the colored black holes were originally investigated , it was found that the @xmath52th static colored black hole is parameterized by its horizon radius , @xmath51 . in addition , as @xmath60 , the black hole solution approaches the corresponding @xmath52th bartnik - mckinnon solution . in the dynamical context discussed here for the @xmath0 solutions , one notices an interesting manifestation of this result . the colored black hole attractors separating the type  i and type  ii regions in figure  [ fig : phase_space ] , are likewise parameterized by their horizon radius in such a way that as the triple point " is approached , @xmath60 , and the bartnik - mckinnon solution emerges as the relevant attractor separating type  i collapse from dispersion . finally , it is natural to ask if other collapsing systems might exhibit similar behavior . indeed , one can simply look in the literature on static , hairy black holes and point to a number of systems that one would conjecture should have a  phase diagram " similar to figure  [ fig : phase_space ] . such theories should include einstein - yang - mills coupled to a dilaton ( eymd ) and the einstein - skyrme system . however , there are other examples of systems which exhibit both type  i and type  ii critical behavior . these include a massive scalar field and ( it is conjectured ) a massive , charged scalar field @xcite . these latter systems are particularly intriguing in light of the results presented here because though they do exhibit type  i and type  ii critical behavior , no - hair theorems suggest that these systems do not have static black hole solutions . it should thus be of interest to investigate the nature of the super - critical regime for these , and possibly other , systems . this research has been supported in part by nsf grants phy93 - 18152 , phy94 - 07194 and phy97 - 22068 . mwc would like to thank p.  bizon and t.  chmaj for useful communications  @xcite , including descriptions of unpublished results which indicated that the parameter - space regime studied here might lead to colored black holes . we collect here some of the details involved in deriving the equations of motion used in the paper , and to present a somewhat more general framework for future work on the einstein - yang - mills system ( eym ) . the action for our model is s = d^4x where @xmath2 is the yang - mills field strength tensor . as usual , greek indices range over the four spacetime dimensions and latin indices indicate group indices . spacetime indices are raised and lowered by the metric @xmath3 while we will not lower group indices . thus , repeated upper group ( latin ) indices will be summed over . the equations of motion are found by varying the action with respect to the fields . varying with respect to the metric yields the einstein equations g _ & = & t _ + & = & 1 g^2(2 f^a _ f^a_^ - 12 g _ f^a _ f^a ) . varying with respect to the connection @xmath4 gives d _ f^a = _ f^a + ^abc a_^b f^c = 0 .    with the general equations in hand we are in a position to make some simplifying assumptions . to begin , we assume that we have an @xmath5 gauge field . in addition we will assume spherical symmetry . the most general parameterization of the spacetime metric is then ds^2 = ( -^2 + a^2 ^2 ) dt^2 + 2 a^2dt dr + a^2 dr^2 + b^2 r^2 d^2 where the metric coefficients @xmath61 and @xmath21 will depend on the temporal and radial coordinates @xmath62 and @xmath63 and @xmath64 is the usual metric on the unit two - sphere . likewise , the most general parameterization of the gauge connection is now @xmath65 where the coefficients @xmath66 and @xmath67 will all depend on @xmath62 and @xmath63 . the @xmath68 are the spherical projection of the pauli spin matrices and form an anti - hermitian basis for the group @xmath5 satisfying @xmath69 = \epsilon^{abc}\tau^{c}$ ] with @xmath70 . we note that this connection is invariant under a gauge transformation of the form @xmath71 . the field strength derived from this connection is f & = & ^r ( - u ) dtdr + & & + ( ^ d+ ^ d ) + & & + ( ^ d- ^ d ) + & & - ( 1 - w^2 -^2 ) ^r dd    with these assumptions , the equations of motion for the yang - mills fields can now be written in first order ( in time ) form as [ eom_first ] & = &  + up - v ( p + a q ) + ab^2 r^2 w ( 1-w^2-^2 ) + & = &  - u + v ( + a ) + ab^2 r^2 ( 1-w^2-^2 ) y & = & - wp + & = & a(- wq ) + ( - wp ) where we have used the definitions [ eq : defpi ] & = & a   + [ eq : defphi ] & = & w - v + p & = & a   + [ eq : defq ] q & = &  + vw + [ eq : defy ] y & = & b^2 r^2 2a ( - u ) . we also have evolution equations for @xmath18 and @xmath72 : & = &  + uq - v - 2 a b^2 r^2 y + & = &  - u + v + w 2 a b^2 r^2 y , which follow from differentiation of  ( [ eq : defphi ] ) and ( [ eq : defq ] ) with respect to time , and elimination of explicit time derivatives using the definitions  ( [ eq : defpi]-[eq : defy ] ) .    finally , the relevant einstein equations are the evolution equations for the metric components and the components of the extrinsic curvature , together with the hamiltonian and momentum constraints , as follows : & = & - a k^r_r + ( a )  + [ eq : bdot ] & = & - b k^ _ + r ( rb) ^r_r & = & k^r_r + k^r_r k - 1 a( a) - 2arb + 4 g + ^ _ & = & k^ _ + k^ _ k + ( rb)^2 - 1 a(rb)^2 ( r b a(rb)) + 4 g -2 arb+ 4 k^r_r k^ _ + 2 k^_^2 = 16g[eom_last ] - ( rb) rb ( k^ _ - k^r_r)- k^_ = 4 g j_r . here , @xmath73 is the energy density , @xmath74 is the momentum density and @xmath75 , @xmath76 and @xmath77 are the stress energy components projected onto our spacelike hypersurface . explicitly , we have = 14g^2 \ { 4 y^2 b^4 r^4 + ( 1-w^2-^2)^2 b^4 r^4 + 2 b^2 r^2 a^2 } s^r_r = 14g^2 \ { - 4 y^2 b^4 r^4 - ( 1-w^2-^2)^2 b^4 r^4 + 2 b^2 r^2 a^2 } s^_= 14g^2 \ { 4 y^2 b^4 r^4 + ( 1-w^2-^2)^2 b^4 r^4 } s^_= s^_j_r = - 1 g^2 a b^2 r^2 ( + pq ) . as can be seen , we have chosen to write things in a fairly general form . indeed , this is the most general eym theory we could consider in spherical symmetry . we can thus consider more general matter configurations , together with a greater variety of coordinate systems than have been considered to date . subsets of these equations have been investigated before in different contexts . for example , static versions of these equations have been studied in order to understand particle - like solutions and colored black holes . in addition , @xcite evolved a version of these equations in polar ( @xmath6 ) , areal ( @xmath7 ) coordinates with the additional assumption on the yang - mills field that the connection @xmath8 was purely magnetic .    for our work here , we will also make this more specifically , we will assume that the electric charge density , @xmath78 , is identically zero . in addition to this _ ansatz _ , we also make the following gauge choice : @xmath79 . making this gauge choice leaves the connection invariant under a gauge transformation of the form @xmath80 . from the definition for @xmath78 in equation  ( [ eq : defy ] ) we see that the function @xmath81 , by these assumptions , depends only on @xmath62 however , the residual gauge freedom implies that @xmath81 is arbitrary up to a function of @xmath62 . we can thus completely fix the remaining gauge freedom by choosing @xmath82 as well . a consequence of these choices is that the remaining coefficients of the gauge connection will no longer be independent and one of them ( we choose @xmath67 ) can be set to zero without loss of generality . thus , in the context of this particular problem , the magnetic _ ansatz _ has effectively set all the fields but @xmath19 to zero .    as discussed in the body of the paper , we want to be able to evolve the system for long times to the future of any black hole formation . to this end , we choose a coordinate system with maximal slicing : @xmath83 . we will retain the choice of areal , or radial , coordinates ( @xmath7 ) so that the coordinate @xmath63 is immediately related to the area of origin - centered two - spheres . given all these assumptions , the equations which we must solve simplify considerably . the evolution equations are & = & + ar^2 w ( 1-w^2 ) + & = &  + & = & a + w and the constraint equations are w & = & +  & = &  ( aa - 2r ) + 2r^2 ( a^2 - 1 + 2r aa ) + 4 g ( s - 3 ) + a & = & a 1-a^2 2r + 32 ra^3 k_^^2 + 4 g r a + k_^ & = & -3r k_^ + 4 g ( g^2 a r^2 ) where the matter stress - energy terms are given by s - 3 & = & a^2 ( 1-w^2)^2 2 g^2 r^4 + 1 g^2 r^2 ( ^2 + ^2 ) + & = & a^2 ( 1-w^2)^2 4 g^2 r^4 + 1 2 g^2 r^2 ( ^2 + ^2 ) . finally , we have an algebraic condition for the non - vanishing component of the shift vector = r k_^ , which follows from  ( [ eq : bdot ] ) with @xmath84 .
we extend the investigation of the gravitational collapse of a spherically symmetric yang - mills field in einstein gravity and show that , within the black hole regime , a new kind of critical behavior arises which separates black holes formed via type  i collapse from black holes formed through type  ii collapse . 
 further , we provide evidence that these new attracting critical solutions are in fact the previously discovered colored black holes with a single unstable mode . 
 i#1    # 1    epsf