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the present article discusses a solution for the cosmological dark matter problem . the problem is over 75 years old@xcite and
has been the subject of innumerable papers , conferences and books .
there is about six times more dark matter than baryonic matter in the universe . a well - known book@xcite on the connection between particle phenomenology and theoretical cosmology discusses possible candidates 
axions , wimps , machos  for the constituents of the dark matter . in the present article
i shall provide a complete solution to the dark matter problem which is in the macho category and surprisingly simple : the dark mattter is all black holes !
let me first consider low mass dark matter candidates suggested by particle phenomenology .
there are two especially popular candidates .
the lighter is the invisible axion predicted by @xcite .
its mass denotes any integer between @xmath2 and @xmath3 .
] must be in an allowed window @xmath4 .
although there are compelling arguments@xcite that the invisible axion requires stronger fine tuning than the strong cp problem it purports to solve , it has staying power and remains the subject of experimental searches .
the other very popular low - mass dark matter candidate , at a proposed mass typcally a trillion times that of the invisible axion , is the wimp ( weakly - interacting massive particle ) exemplified by the neutralino of supersymmetry .
the fact that wimps can naturally annihilate to an acceptable present abundance of dark matter is sometimes cited as support for wimps as dark matter .
but if my proposal for identification of the constituents of dark matter as black holes with masses above @xmath5 is correct , particle - phenomenology - inspired dark matter candidates are , unfortunately for their creators , irrelevant .
higher mass dark matter constituents are generically called machos ( massive astrophysical compact halo objects ) .
my proposed constituents fall into this class with masses in the range @xmath6 where @xmath7 is the solar mass ; equivalently @xmath8 or @xmath9 gev .
even the most die - hard opponent to the large hadron collider ( lhc ) could not take seriously that the lhc could create a black hole with fifty orders of magnitude times the available lhc energy of @xmath10 so the present article thus might convince that the lhc is safe .
the machos are truly compact , all being smaller in physical size than the earth .
it is the small size and large mass which have enabled these dark matter constituents to escape detection for 75 years .
we discuss two methods for their detection , their formation then what , for me , is the best motivation - the entropy of the universe .    .
note that for the range of masses between @xmath11 and @xmath12 all halo mass can be imbhs .
taken from @xcite.,height=491 ]
in the late twentieth century heroic searches were made for microlensing events and many spectacular examples @xcite of machos were identified with masses up to @xmath11 .
the length of time of a microlensing event depends on the velocity and mass of the lensing macho .
since the velocities do nor vary widely it is the macho mass which is most crucial in determining longevity .
the longevity is directly proportional to the square root of the lens mass .
machos were discovered with microlensing longevities up to about 400 days .
insufficient machos to account for more than a few percent of the dark matter were discovered . to detect machos up to mass @xmath12 , the current upper limit for halo black holes , necessitates study of microlensing events with duration up to 4.5 years .
nature has provided delicate astrophysical clocks whose accuracy is sensitive to the possible proximity of machos .
these clocks are binaries with separations up to 1 pc and therefore can be bigger than the solar system in which the distance from the sun to the outermost planet is only @xmath13 pc .    because these wide binaries are so weakly bound they are the most sensitive to disruption by nearby machos .
after formation they retain their original orbital parameters as a reliable clock except when affected by gravitational encounters with machos .
the detailed study of wide binaries is a young and promising technique for macho detection . in the first pioneering presentation@xcite the range of masses allowed for machos which provide all dark matter was @xmath14 .
it seemed unlikely , though logically possible , that all dark matter machos could have masses within such a narrow range .
a revisit and reanalysis@xcite of wide binaries has , however , recently discovered that one of the key examples used in @xcite was spurious .
this leads to quite different and much more promising restrictions on machos , with the allowed mass range extending up to @xmath12 .
the new constraint is displayed in fig . 1 . and
it is now far more likely that all dark matter is in the form of black hole machos .
because intergalactic dust shows evidence of metallicity which involves nuclei heavier than lithium , the heaviest element formed during big - bang nucleosynthsis , it has been hypothesized @xcite that there must have existed pop iii stars in an era before galaxy formation .
these subsequently exploded producing the dust nuclei heavier than lithium , and leaving massive black holes which are macho candidates .
numerical simulations of dark matter halos@xcite have given insight into the likely general features of the halo profile .
the spatial resolution of such simulations is , however , far too coarse to study the formation of machos smaller than the earth whose radius is @xmath15 .
nevertheless , dark matter is known to clump at large scales and may well do so at such far smaller scales .
i have assumed that dark energy possesses no entropy .
let me argue that this is a very weak assumption .
recently the planck satellite was launched and is on its way to lagrangian point 2 where it will attempt to measure with unprecedented accuracy the dark energy equation of state @xmath16 where @xmath17 are respectively pressure , density .
the key quantity is @xmath18 . if @xmath19 vanishes identically the assumption of zero entropy for dark energy is justified because it is fully described by one parameter , the cosmological constant .
if non - zero @xmath19 were observationally established , it would imply a dynamical dark energy with concomitant entropy .
however , without black holes , the dark energy dimensionless entropy would be much less than one googol and so the identification of the dark matter as black holes and the rest of the present discussion would be unchanged .
the identification of the dark matter constituent has been an intellectual pursuit for over 75 years .
particle theorists have naturally suggested light mass solutions which include the invisible axion and wimps . according to theoretical cosmology , however , the most likely solution is that all dark matter is black holes .
according to the recently updated analysis of wide binaries the permitted mass range is between 30 and 500 solar masses .
taking a universe comprised of @xmath20 halos each of mass @xmath21 , and using a central macho mass @xmath22 , there are @xmath23 machos per halo and @xmath24 in the universe .
the dimensionless entropy per macho , using the pbh formula @xcite is @xmath25 and the total is 1000 googols . for galactic - core supermassive black holes ( smbhs ) , there are @xmath20 of them so that for a central mass @xmath26 and individual entropy @xmath27 their total entropy is also 1000 googols .    because @xmath28 , the total mass of machos is much larger than that of smbhs . for the central values
it is @xmath29 times larger .
the total macho mass is @xmath30 so i hereby predict several thousand trillion trillion trillion trillion kilograms of black holes !
while the energy of the universe has been established to be about 0.04 baryons , 0.24 dark matter and 0.72 dark energy , the cosmological entropy is almost entirely , about @xmath0 , from black holes and only @xmath1 from everything else . 
 this identification of all dark matter as black holes is natural in statistical mechanics . 
 cosmological history of dark matter is discussed .    * black holes as dark matter *    .5 in    * paul h. frampton *    department of physics and astronomy , university of north carolina at chapel hill    cb3255 , chapel hill , nc 27599 - 3255 , usa    .4 in