General Relativity: In Acknowledgement Of Professor Gerardus ‘t Hooft, Nobel Laureate Stephen J. Crothers Queensland, Australia [email protected] 4th August 2014 ABSTRACT I extend my thanks to Professor Gerardus ‘t Hooft, Nobel Laureate in Physics, for making more widely known my work on black hole theory, big bang cosmology, and Einstein’s General Theory of Relativity, by means of his personal website, and for providing me thereby with the opportunity to address th e subject matter - supported by extensive references to primary sources for further info rmation - in relation to his many comments, by means of this dedicated paper. The extensive mathematical appendices herein are not prerequisite to understanding the text. Table of contents I. Introduction II. Black holes and big bangs III. A black hole universe (p.6) in contrast (p.2) IV. Gravitational collapse (p.8) V. Black hole escape velocity VI. The radius of a black hole (p.10) (p.14) VII. Metric ‘extensions’ (p.20) VIII. Black hole universes IX. Big bang universes (p.33) (p.28) X. Gravitational waves and XI. Functional analysis (p.40) Appendix A: Gaussian conservation laws (p.34) curvature (p.40) Appendix B: Riemannian Appendix C: Acceleration Appendix D: Isotropic curvature (p.50) invariant (p.64) coordinates (p.67) Appendix E: The Appendix F: Geodesic Kretschmann scalar (p.92) completeness (p.97) I got my own way, to go, I. Introduction And now I want, To take your minds; Gerardus ‘t Hooft is a Dutch professor of I, believe, if you could see, physics at the University of Utrecht in the The blood between the lines, Netherlands. He is a winner of the Nobel I, believe, that you could be, Prize for physics. He is currently, and for A better kind; some years has been, the Editor in Chief of Please lead the way so the unborn can play, the journal Foundations of Physics. He has On some greener hill; kindly brought attention to my writings on Laugh as the flames eat their burning remains, black holes, big bang cosmology, and General Fools die laughing still.1 Relativity, on his personal website. I’m honoured that Professor ‘t Hooft has taken the time and trouble to inform people of my research proving the falsity of black hole 1 ‘Fools’, Deep Purple, Fireball, 1971, (Gillan, I., theory, big bang cosmology, and Einstein’s Glover, R., Lord, J., Blackmore, R., Paice, I.) www.sjcrothers.plasmaresources.com/index.html 1 General Theory of Relativity. Although he characteristics of all black hole universes with comments on the works of five particular those of all big bang universes [2, 3, 4, 5]. scientists, he has allocated perhaps the most All black hole universes: of his comments to me. (1) are spatially infinite Mr. ‘t Hooft [1] refers cryptically to the five (2) are eternal scientists as Mr. L, Mr. C, Mr. DC, Mr. E, (3) contain only one mass and Mr. AL, although it is a well known (4) are not expanding (i.e. are static or secret that Mr. L is Dr. Chung Lo of the stationary) Applied and Pure Research Institute, Mr. C is (5) are either asymptotically flat or me, Mr. DC is Dimi Chakalov (independent asymptotically curved. researcher)2, Mr. E is Professor Myron W. Evans of the Alpha Institute for Advanced All big bang universes: Study, and Mr. AL is Professor Angelo Loinger of the Dipartimento di Fisica, (1) are either spatially finite (1 case; k = 1) or Universitá di Milano, Italy; for those Readers spatially infinite (2 different cases; k = -1, who were not aware of the well known secret. k = 0) Mr. ‘t Hooft provided a link on his webpage (2) are of finite age (~13.8 billion years) to an interesting paper by Professor Loinger, (3) contain radiation and many masses but none, unfortunately, to me or the other (4) are expanding (i.e. are non-static) scientists. I therefore elaborate herein on the (5) are not asymptotically anything. many comments Mr. ‘t Hooft has made on his webpage concerning me and my scientific Note also that no black hole universe even work. possesses a big bang universe k-curvature. I shall begin by comparing the generic Comparison of the defining characteristics of defining characteristics of all alleged black all black hole universes with all big bang hole universes to all alleged big bang universes immediately reveals that they are universes as they require no mathematics to contradictory and so they are mutually fully understand. exclusive; they can’t co-exist. No proposed black hole universe can be superposed with II. Black holes and big bangs in contrast any other type of black hole universe, with any big bang universe, or with itself. There are four different types of black hole Similarly, no proposed type of big bang universes advanced by the astrophysical universe can be superposed with any other scientists; (a) non-rotating charge neutral, (b) type of big bang universe, with any black hole non-rotating charged, (c) rotating charge universe, or with itself. All proponents of neutral, (d) rotating charged. Black hole black holes are blissfully unaware of these masses or ‘sizes’, are not types, just masses or simple contradictions and so they combine sizes of the foregoing types. There are three (i.e. superpose) their black hole universes purported types of big bang universes and with black hole universes and with big bang they are characterised by their constant k- universes to conjure up black hole big bang curvatures; (a) k = -1, negative spacetime hybrid universes ad arbitrium, and without curvature and spatially infinite, (b) k = 0, flat ever specifying what black hole universes in spacetime and spatially infinite, (c) k = 1, what big bang universes they intend. positive spacetime curvature and spatially finite. Compare now the generic defining Furthermore, General Relativity is a nonlinear theory and so the Principle of Superposition is invalid therein. Let X be some alleged black hole universe and Y be some alleged big bang 2 http://www.god-does-not-play-dice.net www.sjcrothers.plasmaresources.com/index.html 2 universe. Then the linear combination (i.e. All so-called black hole solutions for various superposition) X + Y is not a universe. Indeed, respective sets of Einstein field equations are X and Y pertain to completely different sets of also said to pertain to stars and other masses, Einstein field equations and so they have including the Sun and the Earth. For instance, absolutely nothing to do with one another according to Mr. ‘t Hooft [7], whatsoever. “Einstein’s equation, (7.26), should be exactly Despite the contradictory nature of the valid. Therefore it is interesting to search for defining characteristics of black hole exact solutions. The simplest and most universes and big bang universes, and despite important one is empty space surrounding a the fact that the Principle of Superposition is static star or planet. There, one has invalid in General Relativity, Mr. ‘t Hooft [1, 6] superposes and says that multiple black T = 0.” µν holes exist, along with other matter such as stars and galaxies, and all together in some Consequently, all the generic defining (unspecified) big bang universe [7]. characteristics listed above for black hole universes apply equally to stars and planets “We not only accept the existence of black and such, and they too are supposed to subsist holes, we also understand how they can in some unspecified big bang universe. Black actually form under various circumstances. hole universes differ however to those of stars Theory allows us to calculate the behavior of and planets described by the very same material particles, fields or other substances equations on a secondary level. For instance, near or inside a black hole. What is more, all black holes have a so-called ‘event astronomers have now identified numerous horizon’ within which is located an ‘infinitely objects in the heavens that completely match dense singularity’ at which spacetime is the detailed descriptions theoreticians have ‘infinitely curved’; stars and planets have no derived. These objects cannot be interpreted event horizons or singularities. Mr. ‘t Hooft [1, as anything else but black holes. The 6, 7], as is usual for cosmologists, urges that ‘astronomical black holes’ exhibit no clash singularities, which are actually just places in whatsoever with other physical laws. Indeed, a mathematical expression where it is they have become rich sources of knowledge undefined, are physical entities. Mr. ‘t Hooft, about physical phenomena under extreme along with the astrophysical scientists, reifies conditions. General Relativity itself can also points in an equation where that equation is now be examined up to great accuracies.” [6] undefined. Mr. ‘t Hooft [7] begins his exposition of big Since Einstein’s gravitational field is bang creationism with the following words, spacetime curvature, it follows that the cosmologists, including Mr. ‘t Hooft, “General relativity plays an important role in necessarily maintain that Einstein’s gravity is cosmology. The simplest theory is that at a infinite at a black hole singularity. These certain moment “t = 0”, the universe started infinities of density, spacetime curvature, and off from a singularity, after which it began to gravity are also said to be physically real. For expand.” instance, according to Hawking [8], and he concludes from the Friedman- “The work that Roger Penrose and I did Robertson-Walker metrics that, between 1965 and 1970 showed that, according to general relativity, there must be “All solutions start with a ‘big bang’ at t = a singularity of infinite density, within the 0.” [7] black hole.” www.sjcrothers.plasmaresources.com/index.html 3 According to Carroll and Ostlie [9], infinite density, within the black hole.” Penrose has already told us that spacetime “A nonrotating black hole has a particularly curvature becomes “theoretically infinite at r simple structure. At the center is the = 0.” singularity, a point of zero volume and infinite density where all of the black hole’s It is not difficult to see when a limiting mass is located. Spacetime is infinitely curved procedure is employed or not, and it is at the singularity. . . . The black hole’s certainly not employed by the foregoing singularity is a real physical entity. It is not a Authors, in their very own words. Such is the mathematical artifact . . .” nature of the alleged black hole. According to Dodson and Poston [10], There are two types of black hole singularity reported by cosmologists and astronomers, “Once a body of matter, of any mass m, lies according to whether or not their black hole is inside its Schwarzschild radius 2m it rotating. In the case of no rotation the undergoes gravitational collapse . . . and the singularity is a point; in the case of rotation singularity becomes physical, not a limiting the singularity is the circumference of a circle. fiction.” Cosmologists and astronomers call them ‘physical singularities’; and so does Mr. ‘t According to Penrose [11], Hooft [6]. These and other mathematical singularities of black hole equations are “As r decreases, the space-time curvature reified so as to contain the masses of black mounts (in proportion to r−3), becoming holes and to locate their event horizons. Black theoretically infinite at r = 0. holes are said to range in size (by means of their masses) from micro to mini to And according to Mr. ‘t Hooft [1], intermediate to supermassive to ultra- supermassive, up to billions of solar masses. “C is ‘self taught’, so he had no math courses and so does not know what almost means here, Since singularities are actually only places in in terms of carefully chosen limiting an equation where the equation is undefined, procedures.” owing for example, to a division by zero, singularities are not real physical entities, How does Mr. ‘t Hooft know if I have taken contrary to the claims of the cosmologists and any mathematics courses or not? He doesn’t! astronomers. He certainly never asked me about it. What evidence does he adduce for his charge? None! Similarly, astrophysical scientists assert that Mr. ‘t Hooft just invented this charge for his there was a big bang singularity, also own convenience. And for what it’s worth, I possessing various associated physically real have taken formal university courses in infinities. According to Hawking [12], mathematics; not that it makes any difference to the scientific realities. “At the big bang itself, the universe is thought to have had zero size, and to have been As for “carefully chosen limiting procedures”, infinitely hot.” Dodson and Poston have already told us that a black hole singularity is “not a limiting That which has zero size has no volume and fiction”. Carroll and Ostlie have already told hence can’t contain mass or have a us that “The black hole’s singularity is a real temperature. What is temperature? According physical entity. It is not a mathematical to the physicists and the chemists it is the artifact”. Hawking and Penrose have already motion of atoms and molecules. The more told us that “there must be a singularity of energy imparted to the atoms and molecules www.sjcrothers.plasmaresources.com/index.html 4 the faster they move about and so the higher Just how close to infinite must one get to be the temperature. In the case of a solid the “near infinite”? There are no such things as atoms or molecules vibrate about their infinite or “near infinite” density and pressure equilibrium positions in a lattice structure and either, just as nothing can have infinite this vibration increases with increased gravity. temperature. According to Pauling [13], Near infinities of various sorts are routinely “As the temperature rises, the molecules entertained by cosmologists and astronomers. become more and more agitated; each one Here is another example; this time it’s bounds back and forth more and more Professor Lawrence Krauss [18] of Arizona vigorously in the little space left for it by its State University, who says, neighbours, and each one strikes its neighbours more and more strongly as it “But is that, in fact, because of discovering rebounds from them.” that empty space has energy, it seems quite plausible that our universe may be just one Increased energy causes atoms or molecules universe in what could be almost an infinite of a solid to break down the long range order number of universes and in every universe the of its lattice structure to form a liquid or gas. laws of physics are different and they come Liquids have short range order, or long range into existence when the universe comes into disorder. Gases have a great molecular or existence.” atomic disorder. In the case of an ideal gas its temperature is proportional to the mean Just how close to infinite is “almost an kinetic energy of its molecules [14, 15, 16], infinite number”? There is no such thing as “almost an infinite number” at all. 3 1 kT = m v2 Krauss [18] reaffirms Hawking’s zero size 2 2 beginning of the big bang universes with the wherein <v2> is the mean squared molecular following, speed, m the molecular mass, and k is Boltzman’s constant3. “There’s no real particles but it actually has properties but the point is that you can go much further and say there’s no space, no Now that which has zero size has no space for time, no universe and not even any atoms and molecules to exist in or for them to fundamental laws and it could all move about in. And just how fast must atoms spontaneously arise and it seems to me if you and molecules be moving about to be have no laws, no space, no time, no particles, infinitely hot? Zero size and infinitely hot - no radiation, it is a pretty good there is no such thing. Nonetheless, according approximation of nothing.” to Misner, Thorne and Wheeler [17], Thus, the Universe sprang into existence from “One crucial assumption underlies the absolutely nothing, by some big bang standard hot big-bang model: that the creationism, “at time t = 0” [7] and nothing, universe ‘began’ in a state of rapid expansion apparently, is “a good approximation of from a very nearly homogeneous, isotropic nothing” [18]. And not only is nothing a condition of infinite (or near infinite) density good approximation of nothing, Krauss [18] and pressure.” says, “But I would argue that nothing is a physical 3 It has been shown that Boltzman’s constant is not quantity. It’s the absence of something.” constant, since Kirchhoff’s Law of Thermal Emission is not universal [100-103]. www.sjcrothers.plasmaresources.com/index.html 5 Krauss [19] reiterated the big bang universes According to the Dictionary of Geophysics, creation ex nihilo dogma, thus, Astrophysics and Astronomy [20], “There was nothing there. There was absolutely no space, no time, no matter, no “Black holes were first discovered as purely radiation. Space and time themselves popped mathematical solutions of Einstein’s field into existence which is one of the reasons why equations. This solution, the Schwarzschild it is hard …” black hole, is a nonlinear solution of the Einstein equations of General Relativity. It Yet despite the zero size, the infinities and contains no matter, and exists forever in an near infinities possessed by nothing, and big asymptotically flat space-time.” bang creation ex nihilo, Hawking [12] still admits that, According to Penrose [11], “energy cannot be created out of nothing” “The Kerr-Newman solutions … are explicit asymptotically flat stationary solutions of the Thus stands yet another contradiction. Einstein-Maxwell equation (λ = 0) involving just three free parameters m, a and e. … the III. A black hole is a universe mass, as measured asymptotically, is the parameter m (in gravitational units). The Consider now a black hole universe; the type solution also possesses angular momentum, of does not matter. Each and every black hole is magnitude am. Finally, the total charge is indeed an independent universe by the very given by e. When a = e = 0 we get the definition of a black hole, no less than the big Schwarzschild solution.” bang universes are independent universes, although the proponents of black holes and According to Wald [21], big bangs, including Mr. ‘t Hooft, do not realise this. “The charged Kerr metrics are all stationary and axisymmetric … They are asymptotically The black hole universe is not contained flat…” within its so-called ‘event horizon’ because its spacetime supposedly extends indefinitely I illustrate the black hole universe in figure 1. far from its so-called ‘singularity’. Recall from the list of generic defining characteristics that all types of black hole universes are spatially infinite and eternal, and that they are either asymptotically flat or asymptotically curved. There is no bound on ‘radius’ x 2 asymptotic, for otherwise it would not be asymptotic, and so every type of black hole constitutes an independent universe, bearing in mind also that each different type of black hole universe pertains to a different set of Einstein field equations as well, and therefore have nothing to do with one another Figure 1 whatsoever. Without the asymptotic condition one can write as many non-asymptotic non- As the ‘radial’ distance from the black hole equivalent solutions to the corresponding singularity increases indefinitely the Einstein field equations for the supposed spacetime curvature asymptotically different types of black holes as one pleases, approaches either flat or curved spacetime; none of which contains a black hole. thus, if R is the radial distance, R → ∞. Note p p www.sjcrothers.plasmaresources.com/index.html 6 again that at the singularity gravity is infinite singularity of the other. This is true no matter owing to infinite spacetime curvature there. how far from one another the black holes This is what Mr. ‘t Hooft [6] calls a “physical might be imagined, because there is no bound singularity” or “curvature singularity”. on asymptotic, for otherwise it would not be Furthermore, as the ‘radial distance’ increases asymptotic. Thus the presence of another it approaches and then grows larger than the black hole violates the very definition of a radius of the event horizon of the black hole, black hole itself and so there can’t be multiple the so-called ‘Schwarzschild radius’, also black holes. Thus the black hole is necessarily sometimes called the ‘gravitational radius’. a one-mass universe, on the assumption that The ‘Schwarzschild radius’ is what Mr. ‘t the related equations even contain a mass in Hooft and the astrophysical scientists call a the first place. Such a model bears no relation ‘coordinate singularity’, which they say can to reality. Nonetheless it is routinely claimed be removed by some change of coordinate by cosmologists and astronomers that not system. only are there billions of black holes (types unspecified), they are all present in some big Consider now a black hole ‘binary system’. bang universe (also unspecified), none of Such a binary system is also supposed to be in which can be superposed. NASA scientists, some (unspecified) big bang universe. I have for example, have reported that they have already shown above that no black hole found 2.5 million black holes (types universe can be combined with any other unspecified) with their WISE survey [22]. But universe or with itself, and so the notions of a then none of their black holes are black hole binary system and black hole asymptotically anything since each and every collisions and mergers are inconsistent with one of them encounters 2, 499, 999 infinite the theory of black holes itself. To reaffirm spacetime curvatures around it, and so none this conclusion refer to figure 2 in which two of their black holes even satisfies the supposed black holes are depicted. definition of a black hole. And all these black hole universes, despite being eternal, are inside some big bang expanding universe of finite age, ~13.8 billion years. Notwithstanding, Daniel Stern [22], a Principal Scientist for the NASA/JPL WISE Survey, reports, “We’ve got the black holes cornered.” Astronomer Royal, Martin Rees [23], says, “Black holes, the most remarkable Figure 2 consequences of Einstein’s theory, are not just theoretical constructs. There are huge Recall again that the spacetimes of all black numbers of them in our Galaxy and in every hole universes are either asymptotically flat or other galaxy, each being the remnant of a star asymptotically curved, by definition. Note and weighing several times as much as the that in figure 2 it is immediately apparent that Sun. There are much larger ones, too, in the each black hole significantly disturbs the centers of galaxies.” asymptotic nature of the spacetime of the other black hole and so neither of their All the different black hole ‘solutions’ are spacetimes is asymptotically anything. Indeed, also applicable to stars and planets and such. each black hole encounters an infinite Thus, these equations don’t permit the spacetime curvature (infinite gravity) at the presence of more than one star or planet in the www.sjcrothers.plasmaresources.com/index.html 7 universe. In the case of a body such as a star, Recall that all the purported black hole the only significant difference in figures 1 and solutions to Einstein’s field equations each 2 is that the spacetime does not go to infinite constitute an independent universe that curvature at the star, because there is no contains only one mass, that of the black hole singularity and no event horizon in the case of itself, on account of the asymptotic nature of a star (or planet). their respective spacetimes. Mr. ‘t Hooft [1, 6, 7] refers only to asymptotically flat black hole IV. Gravitational collapse universes, by virtue of his invoking of only Schwarzschild, Reissner-Nordström, Kerr, Mr ‘t Hooft [1] adds his own invention to the and Kerr-Newman black holes. Recall further, notion of the mass of a black hole and its that all black hole equations, according to the infinite gravity, in his discussion of the proponents thereof, pertain to the ‘outside’ of formation of a black hole. a star without any change in their form; the only difference being that a star has no event “Matter travels onwards to the singularity at horizon and no singularity, and so all the r = 0, and becomes invisible to the outside generic defining characteristics of all black observer. All this is elementary exercise, and hole universes also pertain to stars. not in doubt by any serious researcher. Consequently, to result in any one of these However, one does see that the Schwarzschild solutions for the formation of a black hole it solution (or its Kerr or Kerr-Newman must begin with a universe that contains only generalization) emerges only partly: it is the one mass, such as a lone star. If Mr. ‘t Hooft, solution in the forward time direction, but the to form a black hole, begins, as he apparently part corresponding to a horizon in the past is does, with a universe full of stars, since he actually modified by the contracting ball of talks of clusters of stars [1], he does not begin matter. All this is well-known. An observer with a relativistic universe, but a Newtonian cannot look that far towards the past, so he universe. Indeed, according to Mr. ‘t Hooft will interpret the resulting metric as an [1], accurate realization of the Schwarzschild metric. And its mass? The mass is dictated by “And now there is a thing that L and C fail to energy conservation. What used to be the grasp: a black hole can be seen to be formed mass of a contracting star is turned into mass when matter implodes. Start with a regular, of a ‘ball of pure gravity’. I actually don’t spherically symmetric (or approximately care much about the particular language one spherically symmetric) configuration of should use here; for all practical purposes the matter, such as a heavy star or a star best description is that a black hole has cluster.” formed.” [1] Since a black hole is actually, according to the Note that Mr ‘t Hooft urges that a cosmologists’ actual definition of a black hole, mathematical point (and indeed the a one mass universe, with the collapse of Mr circumference of a circle too) can contain ‘t Hooft’s star into a black hole, the rest of the matter. But that is quite impossible - one Universe must somehow completely might just as well claim that the centre of disappear, but without falling into his newly mass of a body (a mathematical artifice) is a formed black hole. Energy is therefore not real object, and has an infinite density. Also conserved at all. And a Newtonian universe, note that this mass, from a star, that forms his which contains as many stars as one pleases black hole, produces a “ball of pure gravity”. to consider, can’t magically transform itself However, the mathematical point he reifies, at into a one-mass black hole universe by means his “singularity at r = 0”, for infinite gravity, of the irresistible ‘gravitational collapse’ of a is not a ball, and neither is the universe that single star. Since the black hole equations contained his star in the first place. (metrics) also apply to a star or planet, the star www.sjcrothers.plasmaresources.com/index.html 8 that ‘collapses’ to form a black hole must be behaviour of bodies and the motion of clocks the only mass in the Universe in the first place. rather depend on gravitational fields, which Furthermore, the gravity at the singularity of a in their turn are produced by matter.” black hole is infinite because spacetime is supposedly infinitely curved there – so a finite According to Pauli [26], amount of mass ‘collapses’ to produce infinite gravity! This finite mass is converted into “Since gravitation is determined by the matter infinite “pure gravity” by Mr. ‘t Hooft [1]. present, the same must then be postulated for Moreover, according to him, matter no longer geometry, too. The geometry of space is not even induces spacetime curvature by its given a priori, but is only determined by presence: gravity can exist without matter to matter.” cause it. Indeed, according to Mr. ‘t Hooft [1], According to Weyl [27], “But where does the black hole mass come from? Where is the source of this mass? R “Again, just as the electric field, for its part, µν = 0 seems to imply that there is no matter at depends upon the charges and is instrumental all, and yet the thing has mass! Here, both L in producing mechanical interaction between and C suffer from the misconception that a the charges, so we must assume here that the gravitational field cannot have a mass of its metrical field (or, in mathematical language, own. But Einstein’s equations are non-linear, the tensor with components g ) is related to ik and this is why gravitational fields can be the the material filling the world.” source of additional amount of gravity, so that a gravitational field can support itself. In According to McMahon [28], particle theories, similar things can happen if fields obey non-linear equations, we call these “In general relativity, the stress-energy or solutions "solitons". A black hole looks like a energy-momentum tensor Tab acts as the soliton, but actually it is a bit more source of the gravitational field. It is related complicated than that.” to the Einstein tensor and hence to the curvature of spacetime via the Einstein Mr. ‘t Hooft alters Einstein’s theory ad equation.” arbitrium so that he can have gravitational fields not caused by the presence of material According to Carroll and Ostlie [9], sources and that have a mass of their own. Contrast his notions with Einstein’s actual “Mass acts on spacetime, telling it how to theory. According to Einstein [24], curve. Spacetime in turn acts on mass, telling it how to move.” “We make a distinction hereafter between ‘gravitational field’ and ‘matter’ in this way, According to Einstein [29], that we denote everything but the gravitational field as ‘matter’. Our use of the “space as opposed to ‘what fills space’, which word therefore includes not only matter in the is dependent on the coordinates, has no ordinary sense, but the electromagnetic field separate existence” as well.” According to Einstein [30], Einstein [25] also asserts, “I wish to show that space-time is not “In the general theory of relativity the necessarily something to which one can doctrine of space and time, or kinematics, no ascribe a separate existence, independently of longer figures as a fundamental independent the actual objects of physical reality.” of the rest of physics. The geometrical www.sjcrothers.plasmaresources.com/index.html 9 Thus, Einstein’s gravitational field does not However, weight is a force, Newton’s force of have a mass of its own at all, although it is gravity, not a curvature of spacetime. Despite fancied to possess energy and momentum [1, the methods of Mr. ‘t Hooft, although also 24, 31, 32]. routine for astronomers and cosmologists, Newtonian forces of gravity can’t be invoked Although, on the one hand, Mr. ‘t Hooft [1] for gravity in General Relativity. As de Sitter alleges, incorrectly, that Einstein’s [33] remarked, gravitational field does not require a material source, because it “can have a mass of its “In Einstein’s new theory, gravitation is of a own”, he also, on the other hand, says that much more fundamental nature: it becomes Einstein’s gravitational field must have a almost a property of space. … Gravitation is material source, thus, properly speaking, not a ‘force’ in the new theory.” “Clearly, the mass density, or equivalently, r energy density ρ(x;t) must play the role as a V. Black hole escape velocity source. However, it is the 00 component of a They don’t realise it, but according to all tensor T (x), the mass-energy-momentum µν proponents of black holes, of which Mr. ‘t distribution of matter. So, this tensor must act Hooft is a typical example, their black holes as the source of the gravitational field.” [6] all have both an escape velocity and no escape velocity simultaneously at the very Mr. ‘t Hooft [1] says he does not care about same place; which is of course quite the language used in describing a black hole. impossible, and therefore again completely Indeed; and so he foists his own language invalidates the theory of black holes. upon black hole mass and its related infinite However, since none of the proponents of gravity merely by means of linguistic black holes understands what escape velocity licentiousness. means, this additional contradiction has also escaped them. Now gravity is not a force in General Relativity because it is curvature of spacetime On the one hand it is asserted by cosmologists according to Einstein, but gravity is a force in and astronomers that their black holes have an Newton’s theory. Nonetheless, Mr. ‘t Hooft escape velocity. According to the Dictionary invokes Newton’s gravitational forces to of Geophysics, Astrophysics and Astronomy enable black hole forming ‘gravitational [20], collapse’. Mr. ‘t Hooft [1] says of his collapsing star or star cluster, “black hole A region of spacetime from which the escape velocity exceeds the velocity of “Assume that it obeys an equation of state. If, light.” according to this equation of state, the pressure stays sufficiently low, one can According to Hawking [8], calculate that this ball of matter will contract under its own weight.” “I had already discussed with Roger Penrose the idea of defining a black hole as a set of Mr. ‘t Hooft [6] also says, events from which it is not possible to escape to a large distance. It means that the “One must ask what happens when larger boundary of the black hole, the event horizon, quantities of mass are concentrated in a small is formed by rays of light that just fail to get enough volume. If no stable soution (sic) away from the black hole. Instead, they stay exists, this must mean that the system forever hovering on the edge of the black collapses under its own weight.” hole.” www.sjcrothers.plasmaresources.com/index.html 10