<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>If matter collapses to infinite density at a singularity, what distinguishes one collapsed mass from another? Wouldn't that mean that space was infinitely curved at that point? Isn't it more likely that matter collapses to some very highly dense but still finite state (quark star, string star etc) at the centre of a black hole, resulting in the different sizes of the event horizons?I don't understand where the assumption that matter must collapse to a singularity comes from when we still don't know how to reconcile General Relativity with Quantum Mechanics. <br /> Posted by pendelton</DIV></p><p> </p><p class="MsoNormal">In relation to my previous post on this topic I might as well make the following additional remarks. </p> <p class="MsoNormal"> </p> <p class="MsoNormal">According to Einstein, in his gravitational field, gravitational mass and inertial mass are equivalent, and also, in a sufficiently small region of his gravitational field his laws of Special Relativity must hold. Einstein's field equations for the static vacuum gravitational field, i.e. Ric = 0,violate his 'Principle of Equivalence' because the equivalence of gravitational and inertial mass, and the laws of Special Relativity, cannot manifest in a spacetime which is by definition empty; that by definition contains no matter! QED. Consequently, if his energy-momentum tensor is zero there is no Einstein gravitational field. Hence his field equations must take the following form:<br /> <br /> Gij/k + Tij = 0,<span> </span>(subscripts) i,j = 0,1,2,3,<span> </span>k = constant,<br /> <br /> wherein the Gij/k are the components of a gravitational energy tensor. Thus the total energy of the gravitational field is always zero; the Gij/k and Tij must vanish identically; there is no possibility for the localisation of gravitational energy (i.e. there is no possibility for Einstein’s gravitational waves). Moreover, this means that Einstein’s General Theory of Relativity violates the experimentally well established conservation of energy and momentum, so if the usual conservation of energy and momentum is valid (bearing in mind that there is no experimental evidence to refute it) then Einstein's General Theory of Relativity is invalid. Also, Einstein invented his pseudo-tensor by which he and subsequent big bangers and LIGOers claim that his gravitational energy can be localized. However, Einstein’s pseudo-tensor is a meaningless concoction of mathematical symbols for the following reason – it implies the existence of a 1st-order intrinsic differential invariant which depends only upon the components of the metric tensor and their 1st-derivatives (to see this just contract his pseudo-tensor and apply Euler’s theorem). But the pure mathematicians G. Ricci-Curbastro and T. Levi-Civita proved in 1900 that such invariants do not exist! In addition, Einstein and the subsequent big bangers and LIGOers resort to linearisation of Einstein’s field equations to localize his gravitational energy. This too is nonsense, because linearisation implies the existence of a tensor which, except for the particular case of being precisely zero, does not otherwise exist, as proven by H. Weyl in 1944. So the big bangers and the LIGOers and their international counterparts such as the AIGO in Australia and VIRGO in Europe, are all destined to detect nothing. </p> <p class="MsoNormal"> </p> <p class="MsoNormal">For those who want the mathematical proofs, go here: </p> <p class="MsoNormal"> </p> <p class="MsoNormal">
http://www.ptep-online.com/index_files/2008/PP-12-11.PDF</p> <p class="MsoNormal"> </p> <p class="MsoNormal">And here:
http://www.ptep-online.com/index_files/2007/PP-09-14.PDF</p> <p> </p>