Membrane paradigm

Membrane paradigm

In black hole theory, the black hole membrane paradigm is a useful "toy model" method or "engineering approach" for visualising and calculating the effects predicted by quantum mechanics for the exterior physics of black holes, without using quantum-mechanical principles or calculations. It models a black hole as a thin classically-radiating surface (or membrane) at or vanishingly close to the black hole's event horizon. This approach to the theory of black holes was created by Kip S. Thorne, R. H. Price and D. A. Macdonald.

The results of the membrane paradigm are generally considered to be "safe".

Contents

  • Electrical resistance 1
  • Hawking radiation 2
  • See also 3
  • References 4

Electrical resistance

Thorne (1994) relates that this approach to studying black holes was prompted by the realisation by Hanni, Ruffini, Wald and Cohen in the early 1970s that since an electrically charged pellet dropped into a black hole should still appear to a distant outsider to be remaining just outside the event horizon, if its image persists, its electrical fieldlines ought to persist too, and ought to point to the location of the "frozen" image (1994, pp. 406). If the black hole rotates, and the image of the pellet is pulled around, the associated electrical fieldlines ought to be pulled around with it to create basic "electrical dynamo" effects (see: dynamo theory).

Further calculations yielded properties for a black hole such as apparent electrical resistance (pp. 408). Since these fieldline properties seemed to be exhibited down to the event horizon, and general relativity insisted that no dynamic exterior interactions could extend through the horizon, it was considered convenient to invent a surface at the horizon that these electrical properties could be said to belong to.

Hawking radiation

After being introduced to model the theoretical electrical characteristics of the horizon, the "membrane" approach was then pressed into service to model the Hawking radiation effect predicted by quantum mechanics.

In the coordinate system of a distant stationary observer, Hawking radiation tends to be described as a quantum-mechanical particle-pair production effect (involving "virtual" particles), but for stationary observers hovering nearer to the hole, the effect is supposed to look like a purely conventional radiation effect involving "real" particles. In the "membrane paradigm", the black hole is described as it should be seen by an array of these stationary, suspended noninertial observers, and since their shared coordinate system ends at the event horizon (because an observer cannot legally hover at or below the event horizon under general relativity), this conventional-looking radiation is described as being emitted by an arbitrarily-thin shell of "hot" material at or just above the event horizon, where this coordinate system fails.

As in the "electrical" case, the membrane paradigm is useful because these effects should appear all the way down to the event horizon, but are not allowed by GR to be coming through the horizon – blaming them on a hypothetical thin radiating membrane at the horizon allows them to be modelled classically without explicitly contradicting general relativity's prediction that event horizon surface is inescapable.

In 1986, Kip S. Thorne, Richard H. Price and D. A. Macdonald published an anthology of papers by various authors that examined this idea: "Black Holes: The membrane paradigm".

See also

References

  • require('Module:No globals')

local function getCatForId( id )

   local title = mw.title.getCurrentTitle()
   local namespace = title.namespace
   if namespace == 0 then

return ''

   elseif namespace == 2 and not title.isSubpage then

return ''

   else

return ''

   end

end

local function viafLink( id )

   if not string.match( id, '^%d+$' ) then
       return false
   end
   return '.. id .. ' ' .. id .. '' .. getCatForId( 'VIAF' )

end

local function kulturnavLink( id )

   return '.. id .. ' id' 

end

local function sikartLink( id )

   return '.. id .. '&lng=en ' .. id .. '' 

end

local function tlsLink( id ) local id2 = mw.ustring.gsub(id, '%s', function(s) return mw.uri.encode(s, 'WIKI') end)

   return '.. id2 .. ' ' .. id .. '' 

end


local function ciniiLink( id )

   return '.. id .. '?l=en ' .. id .. '' 

end

local function bneLink( id )

   return '.. id .. ' ' .. id .. '' 

end


local function uscongressLink( id )

   return '.. id .. ' ' .. id .. '' 

end

local function narapersonLink( id )

   return '.. id .. ' ' .. id .. '' 

end

local function naraorganizationLink( id )

   return '.. id .. ' ' .. id .. '' 

end

local function botanistLink( id ) local id2 = mw.ustring.gsub(id, '%s', function(s) return mw.uri.encode(s, 'PATH') end)

   return '.. id2 .. ' ' .. id .. '' 

end

local function mgpLink( id )

   -- TODO Implement some sanity checking regex
   return '.. id .. ' ' .. id .. '' 

end

local function rslLink( id )

   -- TODO Implement some sanity checking regex
   return '.. id .. '&CON_LNG=ENG ' .. id .. ''

end

local function leonoreLink( id ) -- Identifiants allant de LH/1/1 à LH/2794/54 (légionnaires) -- Identifiants allant de C/0/1 à C/0/84 (84 légionnaires célèbres) -- Identifiants allant de 19800035/1/1 à 19800035/385/51670 (légionnaires décédés entre 1954 et 1977, et quelques dossiers de légionnaires décédés avant 1954)

   if not string.match( id, '^LH/%d%d?%d?%d?/%d%d?%d?$' ) and
      not string.match( id, '^C/0/%d%d?$' ) and
           not string.match( id, '^19800035/%d%d?%d?%d?/%d%d?%d?%d?%d?$' ) then
       return false
   end
   return '.. id .. ' ' .. id .. '' 

end

local function sbnLink( id )

   if not string.match( id, '^IT\\ICCU\\%d%d%d%d%d%d%d%d%d%d$' ) and not string.match( id, '^IT\\ICCU\\%u%u[%d%u]%u\\%d%d%d%d%d%d$' ) then
       return false
   end
   return '.. id .. ' ' .. id .. '' .. getCatForId( 'SBN' )

end

local function nkcLink( id ) return '.. id .. '&CON_LNG=ENG ' .. id .. '' end

local function nclLink( id )

   if not string.match( id, '^%d+$' ) then
       return false
   end
   return '.. id .. '&CON_LNG=ENG ' .. id .. '' 

end

local function ndlLink( id ) return '.. id .. ' ' .. id .. '' end

local function sudocLink( id )

   if not string.match( id, '^%d%d%d%d%d%d%d%d[%dxX]$' ) then
       return false
   end
   return '.. id .. ' ' .. id .. '' 

end

local function hlsLink( id )

   if not string.match( id, '^%d+$' ) then
       return false
   end
   return '.. id .. '.php ' .. id .. ''

end

local function lirLink( id )

   if not string.match( id, '^%d+$' ) then
       return false
   end
   return '.. id .. '.450.0.html ' .. id .. ''

end

local function splitLccn( id )

   if id:match( '^%l%l?%l?%d%d%d%d%d%d%d%d%d?%d?$' ) then
       id = id:gsub( '^(%l+)(%d+)(%d%d%d%d%d%d)$', '%1/%2/%3' )
   end
   if id:match( '^%l%l?%l?/%d%d%d?%d?/%d+$' ) then
        return mw.text.split( id, '/' )
   end
   return false

end

local function append(str, c, length)

   while str:len() < length do
       str = c .. str
   end
   return str

end

local function lccnLink( id )

   local parts = splitLccn( id )
   if not parts then
       return false
   end
   local lccnType = parts[1] ~= 'sh' and 'names' or 'subjects'
   id = parts[1] .. parts[2] .. append( parts[3], '0', 6 )
   return '.. lccnType .. '/' .. id .. ' ' .. id .. '' .. getCatForId( 'LCCN' )

end

local function mbLink( id )

   -- TODO Implement some sanity checking regex
   return '.. id .. ' ' .. id .. '' .. getCatForId( 'MusicBrainz' )

end

--Returns the ISNI check digit isni must be a string where the 15 first elements are digits local function getIsniCheckDigit( isni )

   local total = 0
   for i = 1, 15 do
       local digit = isni:byte( i ) - 48 --Get integer value
       total = (total + digit) * 2
   end
   local remainder = total % 11
   local result = (12 - remainder) % 11
   if result == 10 then
       return "X"
   end
   return tostring( result )

end

--Validate ISNI (and ORCID) and retuns it as a 16 characters string or returns false if it's invalid --See http://support.orcid.org/knowledgebase/articles/116780-structure-of-the-orcid-identifier local function validateIsni( id )

   id = id:gsub( '[ %-]', ):upper()
   if not id:match( '^%d%d%d%d%d%d%d%d%d%d%d%d%d%d%d[%dX]$' ) then
       return false
   end
   if getIsniCheckDigit( id ) ~= string.char( id:byte( 16 ) ) then
       return false
   end
   return id

end

local function isniLink( id )

   id = validateIsni( id )
   if not id then
       return false
   end
   return '.. id .. ' ' .. id:sub( 1, 4 ) .. ' ' .. id:sub( 5, 8 ) .. ' '  .. id:sub( 9, 12 ) .. ' '  .. id:sub( 13, 16 ) .. '' .. getCatForId( 'ISNI' )

end

local function orcidLink( id )

   id = validateIsni( id )
   if not id then
       return false
   end
   id = id:sub( 1, 4 ) .. '-' .. id:sub( 5, 8 ) .. '-'  .. id:sub( 9, 12 ) .. '-'  .. id:sub( 13, 16 )
   return '.. id .. ' ' .. id .. '' .. getCatForId( 'ORCID' )

end

local function gndLink( id )

   return '.. id .. ' ' .. id .. '' .. getCatForId( 'GND' )

end

local function selibrLink( id ) if not string.match( id, '^%d+$' ) then

       return false
   end
   return '.. id .. ' ' .. id .. '' .. getCatForId( 'SELIBR' )

end

local function bnfLink( id )

   --Add cb prefix if it has been removed
   if not string.match( id, '^cb.+$' ) then
       id = 'cb' .. id
   end
   return '.. id .. ' ' .. id .. ' .. id .. ' (data)' .. getCatForId( 'BNF' )

end

local function bpnLink( id )

   if not string.match( id, '^%d+$' ) then
       return false
   end
   return '.. id .. ' ' .. id .. '' .. getCatForId( 'BPN' )

end

local function ridLink( id )

   return '.. id .. ' ' .. id .. '' .. getCatForId( 'RID' )

end

local function bibsysLink( id )

   return '.. id .. '&feltselect=bs.autid ' .. id .. '' .. getCatForId( 'BIBSYS' )

end

local function ulanLink( id )

   return '.. id .. ' ' .. id .. '' .. getCatForId( 'ULAN' )

end

local function nlaLink( id ) return '.. id .. ' ' .. id .. '' .. getCatForId( 'NLA' ) end

local function rkdartistsLink( id ) return '.. id .. ' ' .. id .. '' .. getCatForId( 'RKDartists' ) end

local function getIdsFromWikidata( item, property )

   local ids = {}
   if not item.claims[property] then
       return ids
   end
   for _, statement in pairs( item.claims[property] ) do
         if statement.mainsnak.datavalue then
          table.insert( ids, statement.mainsnak.datavalue.value )
         end
   end
   return ids

end

local function matchesWikidataRequirements( item, reqs )

   for _, group in pairs( reqs ) do
       local property = 'p' .. group[1]
       local qid = group[2]
       if item.claims[property] ~= nil then
           for _, statement in pairs ( item.claims[property] ) do
                if statement.mainsnak.datavalue ~= nil then
                        if statement.mainsnak.datavalue.value['numeric-id'] == qid then
                        return true
                end
            end
           end
       end
   end
   return false

end

local function createRow( id, label, rawValue, link, withUid )

   if link then
       if withUid then
           return '* ' .. label .. ' ' .. link .. '\n'
       else
           return '* ' .. label .. ' ' .. link .. '\n'
       end
   else

return '* \n'

   end

end

--In this order: name of the parameter, label, propertyId in Wikidata, formatting function local conf = {

   { 'VIAF', 'VIAF', 214, viafLink },
   { 'LCCN', 'LCCN', 244, lccnLink },
   { 'ISNI', 'ISNI', 213, isniLink },
   { 'ORCID', 'ORCID', 496, orcidLink },
   { 'GND', 'GND', 227, gndLink },
   { 'SELIBR', 'SELIBR', 906, selibrLink },
   { 'SUDOC', 'SUDOC', 269, sudocLink },    
   { 'BNF', 'BNF', 268, bnfLink },
   { 'BPN', 'BPN', 651, bpnLink },
   { 'RID', 'ResearcherID', 1053, ridLink },
   { 'BIBSYS', 'BIBSYS', 1015, bibsysLink },
   { 'ULAN', 'ULAN', 245, ulanLink },
   { 'HDS', 'HDS', 902, hlsLink },
   { 'LIR', 'LIR', 886, lirLink },
   { 'MBA', 'MusicBrainz', 434, mbLink },
   { 'MGP', 'MGP', 549, mgpLink },    
   { 'NLA', 'NLA', 409, nlaLink },
   { 'NDL', 'NDL', 349, ndlLink },
   { 'NCL', 'NCL', 1048, nclLink },
   { 'NKC', 'NKC', 691, nkcLink },
   { 'Léonore', 'Léonore', 640, leonoreLink }, 
   { 'SBN', 'ICCU', 396, sbnLink },     
   { 'RLS', 'RLS', 947, rslLink },
   { 'Botanist', '[[Author ci