From: stargene@sbcglobal.net   
      
   I have an embarrassing query... Firstly:   
   An elementary particle falling effectively "from infinity" toward a   
   neutron star (NS), say, will hit its its surface with a relativistic speed   
   equal to the star's escape velocity.  From its relativistic mass increase   
   (maybe by a factor of ~1.5 or so), the particle will then add that extra   
   amount of relativistic energy/mass-equivalent onto the NS.  Similarly   
   with trillions of other particles raining down onto the NS.  They confer   
   not only their rest or invariant mass/energy, but something extra due   
   to spec. relativity.  Okay so far, I think.  Great.   
      
   ...But, then:   
   I have a conundrum when the massive body is a black hole, say   
   Cyg-X1.  If I understand correctly, elementary particles falling toward   
   its event horizon, will reach ultra-relativistic speeds.  Perhaps even   
   reaching light speed at the EH?  Which would seem to add extremely   
   ultra-relativistic mass to each such particle.  Since,  roughly, ~10^58   
   mass particles would have experienced this in the history of Cyg-X1,   
   from its time zero, beginning as a micro black hole, to the present,   
   this would seem also to confer a mass M for this black hole vastly   
   greater than its actual mass by orders of magnitude.  As though   
   the BH should be bending the scales to the tune of many thousands   
   of solar masses.  Yet Cyg-X1 has a "mere" 14.8 solar masses,   
   latest measurement.   
      
   I know that there is something wrong with my thinking, but it eludes   
   me.   
   Thanks,   
   Gene   
      
   [[Mod. note --   
      
   1. Phrases like "ultra-relativistic speeds" have to be used with   
      some care when near a BH.  That is, we need to be careful to define   
      the (a) reference frame for such a speed measurement.  Close to the   
      BH, it's not sufficient to just say "speed relative to the BH" --   
      there's more than one way (in fact, there are infinitely many ways)   
      to define a coordinate system near the BH, and any speed measurement   
      needs to implicitly or explicitly specify which coordinate system   
      it's referred to.   
      
   2. For a reasonable choice of coordinates for radial motion near the   
      horizon (say, areal radius and Eddington-Finkelstein time), I don't   
      think an infalling particle (with nonzero rest mass) will actually   
      reach "ultra-relativistic speeds" (special-relativistic gamma >> 1)   
      before crossing the event horizon.   
      
   3. In analyzing this system, we need to do the "energy accounting"   
      consistently.  What we can actually measure (e.g., by observing   
      stars or gas orbiting the BH) is mass-energy-at-infinity; any energy   
      "down near the BH" is effectively redshifted in its contribution   
      to mass-energy-at-infinity.  So, if an infalling particle has a   
      non-trivial special-relativistic gamma factor when close to the BH,   
      that kinetic energy needs to be redshifted (divided) by that same gamma   
      factor before being included in the total mass-energy-at-infinity.   
      
   4. Conservation of mass-energy still applies to the system consisting   
      of the BH and the infalling matter.  Thus 1 kg of infalling matter   
      can't add more than 1kg to the BH mass; if it adds less then the   
      difference must be radiated away (e.g., as photons).   
      
   5. If the infalling matter has *zero* angular momentum relative to   
      the BH, and we treat it as "dust" (a set of non-interacting particles),   
      then we have an "advection-dominated accretion flow", where all   
      (or almost all) of the infalling matter's mass-energy is captured   
      by the BH.   
      
   6. If the infalling matter has *nonzero* angular momentum relative   
      to the BH, then it won't fall straight in to the BH, but will rather   
      orbit the BH, forming accretion disk.  Any individual matter particle   
      will then spiral in over a relatively long time-scale, and its   
      interaction ("friction") with other infalling matter will heat the   
      accretion disk to high temperature, so the accretion disk will radiate   
      photons.  This is the underlying process behind (e.g.) Cygnus X-1's   
      observed X-ray luminosity.  This process can in theory radiate   
      a substantial fraction of the mass-energy in the infalling matter.   
      
   -- jt]]   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)