From: tjroberts137@sbcglobal.net   
      
   On 10/31/18 1:05 AM, Sabbir Rahman wrote:   
   > In general people have to be more specific when they refer to "negative   
   > mass". There are three mass types that enter into Newton's law of   
   > gravitation for example - inertial, active and passive mass.   
      
   Sure. But the context here is General Relativity, not Newton. In GR   
   there is just a single "type" of mass: that which enters into the   
   energy-momentum tensor in the field equation.   
      
   If one considers the motion of a "test particle" [#], then in the   
   absence of any forces the particle follows a timelike geodesic path in   
   the geometry determined by the (non-negligible) masses in the manifold.   
   Note the mass of the test particle does not enter into its equation of   
   motion (including its sign, if any).   
      
   	[#] An object whose size and mass are very much smaller   
   	than the scale of the geometry, so it can be neglected in   
   	determining the geometry.   
      
   > [... 8 or 4 possibilities in Newtonian gravitation]   
      
   But Newtonian gravitation is not very interesting, as it is solidly   
   refuted. Nor is it relevant in this discussion in the context of GR.   
      
   For a test particle and a mass, in GR there are only two cases: the mass   
   is negative or the mass is positive. For these cases the structure of   
   the geometry is known: for positive mass the geodesics converge on the   
   mass, and for negative mass the geodesics diverge from the mass.   
      
   	Note that many authors consider at least one of the energy   
   	conditions to be part of GR, so the case of negative mass   
   	is excluded. Here, for the sake of discussion, I ignore the   
   	energy conditions.   
      
   > If antimatter falls upwards [...]   
      
   	[I note that you switched from negative mass to antimatter   
   	 -- these are VERY different.]   
      
   Attempting to argue about GR by analogy with NM is hopeless -- that boat   
   has already sailed. For test particles the GR prediction is unambiguous:   
   regardless of the test particle's mass (including sign, if any) it   
   "falls downward" toward a positive mass and "falls upward" away from a   
   negative mass.   
      
   While there is currently no experimental evidence of antimatter's   
   behavior in gravity, the mass of every known antiparticle is   
   unequivocally positive.   
      
   	[There are theoretical arguments that imply that in   
   	 gravity antimatter must behave essentially the same   
   	 as matter. There are several efforts underway to   
   	 measure its behavior experimentally.]   
      
   Note also that antimatter is described ONLY in quantum theories; no   
   classical theory includes it. So it is stretching the boundaries to   
   consider antimatter in GR.   
      
   For two massive objects there are clearly four choices of their masses'   
   signs in GR, but I don't know how the math works out for any case except   
   "++", in which case they converge together. Given the absence of a   
   general 2-body solution to the field equation, the other 3 cases require   
   numerical calculations; I don't know how they work out [@]. I also don't   
   consider them very relevant, as we have yet to observe anything with a   
   negative mass, much less an object large enough to affect the geometry.   
      
   	[@] I also know enough about the subtleties of GR to not   
   	believe any claims without a calculation to back them up.   
      
   > [... non-mathematical speculations about black holes]   
      
   Your discussion here goes well beyond GR, seemingly into never-never   
   land. To support it you need to formulate a complete theory, not just   
   give idle speculations based on a fuzzy mish-mash of GR and a very   
   different and refuted Newtonian theory. That's a challenge, as there is   
   no expectation of ever being able to test it experimentally.   
      
   Tom Roberts   
      
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