Contradictions in the Definition, Creation, and Existence of Black Holes

Transcription

1 International Journal of Engineering & Tehnology IJET-IJENS Vol: No: 0 Contraditions in the Definition, Creation, and Existene of Blak Holes Shahriar Khan Independent University, Bangladesh Abstrat Although general relativity is mostly verified in astronomy, it leads to the blak hole as a solution to Einstein s field equations; a solution that also ontradits muh of the known laws of physis. The study of blak holes an be traed as attempts to reonile them with some laws of physis, whih lead to more ontraditions with other laws. The inherent ontraditions have led to imaginative and poeti theories, suh as nature hiding a singularity behind an event horizon. Even in this day of astronomy and telesopes, there is no onlusive proof of the existene of blak holes. The supermassive body at the enter of our galaxy is surprisingly alm, hardly the dramati aretion disk expeted of a supermassive blak hole. Thought experiments not very different from those that established general relativity, are used in this paper to identify the ontraditions that arise from the blak hole solution to Einstein s field equations. The event horizon is seen to have unresolved singularities, and is only valid for a body with zero verloity and energy in far away spae. The horizon diminishes to a traveler approahing a blak hole, and the horizon enlarges for a body with a finite veloity in faraway spae. The priniple that an outside observer would never see a body enter the event horizon, implies that to the outside world, no blak hole has ever been reated or will ever be reated. An observer would sense the inrease in mass of the blak hole from falling matter, while never seeing the matter atually fall inside; thus sensing the mass and gravity twie. A blak hole ollapsing towards singularity may radiate ever inreasing energy beause of inreasing rotation. These suggest that the solution of a blak hole of Einstein s field equations may need modifiation, or is trivial, without physial relevane. The elusive nature of blak holes, and the absene of onrete evidene of existene even in this age of telesopes and astronomy, suggest that general relativity is no longer appliable in extreme gravity, suh as in the ase of a star ollapsing into a blak hole. A simplisti alternative is proposed, so as to avoid the singularities inherent in the event horizon and Blak hole. Index Term General relativity, blak hole, event horizon, singularity, supermassive, astronomy, Shwarzshild radius. I. INTRODUCTION An important frontier of present human knowledge and imagination is the blak hole, with the oexistene and one way travel between two universes. The existene of blak holes is widely aepted today, in spite of the numerous ontraditions known to arise from the solution to the field equations of general relativity. This paper shows some other ontraditions in the definition, reation, and existene of blak holes. It is proposed that the sum of the ontraditions Shahriar Khan is in the Shool of Engineering and Computer Siene of Independent University, Bangladesh. khandhaka@gmail.om outweigh the belief in this limiting solution of general relativity. II. GENERAL RELATIVITY The General Theory of Relativity (G.R.), first published by Einstein in 95 [], found early verifiation in lassial ases suh as the anomalous perihelion advane of the planet merury, and defletion of light by the Sun. Today, there are many other modern tests and observations establishing G.R. However, these pratial or observational verifiations hardly extend to the more extreme ase of high gravity, typial of the gravitational ollapse of a massive star. In spite of the deades-long searh, there have been almost no verifiation of general relativity in muh higher gravities, suh as lose to the ase of blak holes. The best telesopes and the best theories of astronomy today, have been unable to verify the appliability of general relativity in the extreme gravities around the supposed super-massive blak hole at the enter of our milky way. The absene of evidene suggests the need to modify general relativity so as to avoid the reation of blak holes. Thought Experiments Speial and general relativity were largely the produt of thought experiments by Einstein, suh as inorporation of speed of light, and stationary, moving, and aelerating observers. This paper ontinues with the thought experiments on the blak hole solution of general relativity. The impliations are very profound, suh that although there is no reason to question General Relativity, there is a very strong reason to question the extreme solution, suggesting blak holes. The blak hole solution of G.R. leads to so many ontraditions, that the very truth of the blak hole, as a solution, may be questioned. The role of suh thought experiments in questioning the blak hole solution of G.R. should not be underestimated. The impliations are that general relativity must be modified so as to avoid the reation of the blak hole. Trivial Solutions to Field Equations (?) For many mathematial and differential equations applied to real-life physis, there are often mathematial solutions, sometimes alled trivial solutions, whih are not appliable to real-life. The physial ontraditions inherent in blak holes suggest the possibility that the blak hole solution to Einstein s field equations ould be a trivial solution, with no real life appliation. Moreover a body transitioning from the event April 0 IJENS

2 International Journal of Engineering & Tehnology IJET-IJENS Vol: No: 0 horizon to the singularity is apparently a omplete impossibility. It ould be a wonder that the impossibility of a trivial solution to the field equations has fuelled our halfentury long futile searh for blak holes. III. HISTORY AND DEFINITION Ever sine Einstein proposed his general relativity equations, many, inluding Shwarzhild have predited the existene of a body from whih even light ould not esape []. With muh of astronomy dediated to finding blak holes, today's prime ontenders are the supermassive bodies at the enter of galaxies suh as our own [4,5,6,7,8], where stars and gases are moving rapidly, orbiting some massive, unknown objet. Obsured by dust, this body is inferred from Newton s laws to range from millions to billions of times the mass of the sun. Rather than being the site of dramati energy release from matter being ripped apart at the aretion disk, this suspeted blak hole has been surprising quiet and elusive. At this time, there is no positive onfirmation that supermassive body so lose to the Earth is a blak hole. In 000, an intermediate sized suspeted blak hole [9], of solar masses, was laimed to be found near, but not at, the enter of the galaxy M8. In spite of these so-alled evidene of the existene, there is general onsensus that blak holes have been surprisingly elusive. Fig.. Conventional definition of a blak hole Oppenheimer showed the existene of mathematial singularities at the Shwarzshild radius, meaning some of the terms in the equations beame infinite. Beause of timestopping at the event horizon, they were alled frozen stars [3,4]. An outside observer would see the surfae of the star frozen in time at the instant where its ollapse takes it inside the Shwarzshild radius. In 958, Finkelstein laimed that the event horizon is not a singularity, but a unidiretional membrane where ausal influenes an ross in only one diretion [5]. In 965, Penrose showed that singularities our inside any blak hole [6]. The topis of interest today inlude the inorporation of quantum physis into the singularity at the enter, giving rise to a law of quantum gravity [7, 8, 9], and the expetation of the singularity shrinking to smaller than any known subatomi partile [0,, ]. Other than the onventional blak holes, supermassive blak holes are thought to exist at the enter of galaxies, inluding the Milky Way. Primordial blak holes, if they exist, would have ome into existene during the Big Bang. IV. OBSERVATIONAL EVIDENCE OF BLACK HOLES Evidene on the existene of blak holes are mostly aknowledged to be inonlusive. There is no lear method to verify that observed massive ompat bodies are blak holes, and not some other objet, suh as a neutron star. The unseen ompanion in binary systems (suh as Cygnus X- in the onstellation Cygnus), are suspeted to be blak holes [0, 3]. Intermittent X-rays and flashes (Chandra observatory in 00), are suspeted to be areting matter entering the event horizon [0]. V. CONTRADICTIONS IN DEFINITION AND EXISTENCE Blak holes violate most of the known laws of physis. The history of their researh an be traed as attempts to reonile them with some laws of physis, that ause them further violate other laws of physis. Conservation of Mass-Energy The one way travel of matter and energy into a blak hole is unlike any other known physial proess. The law of onservation of mass-energy is violated, as mass and energy disappear from the outside universe into the inner universe of the blak hole. Angular momentum It was shown (in the 970s) that a blak hole's spin annot be inreased by swallowing rotating objets []. The law of onservation of angular momentum is violated, beause one a blak hole is reated, its angular momentum will not hange; not even by external bodies. Gravitational and Eletrostati Fields As mass and harge an be sensed from the outside world, it is giving out an gravitational and eletrostati field. This is the same as emitting gravitation and an eletromagneti wave of infinite wavelength. This zero-frequeny eletromagneti waves are not being greatly weakened when penetrating the event horizon. This ontradits the definition that an eletromagneti wave will never esape, and beome infinitely weakened and red-shifted as it travels outside the event horizon. It is highly ounter-intuitive that the gravitation and an eletrostati field esapes the event horizon, yet energy annot esape. There is little reason why an eletrostati field but not an eletromagneti field annot be sensed from outside the event horizon. As a moving harge reates a magneti field, If the blak hole degenerates to anything less than absolute singularity, there ould be flow of harge inside the blak hole, April 0 IJENS

3 International Journal of Engineering & Tehnology IJET-IJENS Vol: No: 0 3 whih would allow a magneti field to esape through the event horizon. If a magneti field an be sensed, that would imply that an eletromagneti wave too an esape the event horizon. Flow of information Another ontradition is the seletive flow of information. There is flow of most information from the outside to the inside, yet partial flow of information from the inside to the outside. A blak hole is said to be fully defined to the outside universe by only it's mass, harge and angular momentum, whih an be sensed from outside the event horizon [0,0]. Paradoxially, this seleted information an be deteted outside the event horizon, but not others, suh as the nature of the matter, its omposition, and onstrution. Other laws Amidst all these violations, other laws suh as the seond law of thermodynamis are hardly appliable. However, obsure appliations of the seond law of thermodynamis have been devised, whih lead to even further ontraditions of other laws of physis [,3,4]. Obsure and poeti theories have been proposed to modify known physis, suh as the priniple of osmi ensorship [6], stating that nature always hides any singularity, inside an event horizon. The popularity of this famous priniple of osmi ensorship may have arisen more from human imagination, and poetry, rather than solid physial reasoning. VI. PRIMORDIAL UNIVERSE BECOMING A BLACK HOLE The question arises as to why the Big Bang did not degenerate into a Blak Hole. It is aepted that some 0-43 seonds after the Big Bang (Plank epoh), the fores of nature, and the laws of physis, inluding general relativity, ame into existene. The density of the early universe must have exeeded that needed for a blak hole. Amidst the existene of general relativity, the speed of the expanding universe ould not have exeeded the veloity of light. Hene the universe should not have been able to esape from itself, rather ollapsing into a blak hole. The urrently held model of the Big Bang are the Friedman- Robertson-Walker (FRW) solutions of the field equations of general relativity. Various arguments are given, suh as the early universe was expanding, rather than ontrating as in a blak hole. It is also said that the early universe was a white hole, and that the Shwarshild radius does not apply to rapidly expanding matter. These laims of the FRW model are unlear, beause the Shwarzshild radius is ompletely appliable to a body trying to esape from a blak hole. The Shwarzhild radius should be further appliable to the ase of an internal explosion, when the whole of a blak hole is trying to esape from the event horizon. The impliation of the FRW model is that if there is release of suffiient energy inside a blak hole, it may explode expanding beyond the event horizon. In ase of an infinite non-homogenous universe, there should have been the reation of multiple supermassive blak holes in the early universe. The FRW model of the big bang is another extreme appliation of the field equations of general relativity. The ontraditions of the FRW model and the blak hole model have been apparent for deades, and attempts to reonile them have left many questions unanswered. The FRW solution does not produe the insurmountable ontraditions of the blak hole solution, whih ould be another indiation of the need to modify the blak hole model. VII. SINGULARITIES AT THE EVENT HORIZON It is well aepted that when a set of physial laws give a solution of infinite or singularity, it is the physial laws whih are likely to be inorret. After Finkelstein replaed the singularity of the event horizon in 958 with a unidiretional membrane, there was a resurgene of interest in blak holes. However, the unresolved singularities at the event horizon remain and are readily apparent. By onventional definition, a projetile shot out from the event horizon must have the veloity of light and infinite energy, so as to esape to distant spae, having ultimately zero veloity. As this proess an be justified as reversible, a body drifting from distant spae should attain the veloity of light and infinite energy upon just entering the event horizon. The reversibility is justified, beause a projetile shot at V veloity from outside the event horizon, attaining a maximum height H, implies that a body dropped from the same height H will attain the same veloity V at the point outside the event horizon. Clearly, the infinite energies, and the matter traveling at speed of light are singularities. The blak hole would absorb or generate infinite energy every time a partile of dust fell into it. A orollary would be that a star ollapsing into itself would generate infinite energy. Light leaving the event horizon is supposed to be infinitely red-shifted so as to have zero frequeny, zero energy in far away spae. There is an unlimited amount of eletromagneti waves with zero energy and zero frequeny outside the event horizon. These zero energy waves would find themselves beoming of finite strength upon entering the event horizon. The blak hole would ontinually gain energy from the zero energy outside the event horizon. However, the outside universe would not lose any energy at all. These absurdities arise beause of the singularities that remain in urrently held views. VIII. TRAVELER AND OBSERVER Aording to the literature, to an external observer, a traveler falling into an event horizon (besides being torn apart by tidal fores) would appear to be falling forever or for infinite time (Figure ). This implies another singularity April 0 IJENS

4 International Journal of Engineering & Tehnology IJET-IJENS Vol: No: 0 4 It is stated that an observer at 3000 km from a blak hole of 0 solar masses, and 30 km event horizon, would see an objet falling into a blak hole forever. This implies the questionable idea that to outside observers, matter has been areting outside the event horizon for billions of years, and will ontinue to aumulate for an infinite number of years, without atually falling inside (another singularity). Fig.. Conventional belief that traveler finds himself entering event horizon, but observer sees him falling forever. The above reasoning leads to the onlusion that the same laws whih prevent matter from falling into blak holes, would prevent outside observers from ever seeing the reation of a blak hole. The matter near the surfae of the neutron star would never atually enter the event horizon, whih is just oming into existene. A resident of the neutron star will never see it's transformation to a blak hole. As a massive neutron star ontrats, the outer layers are approahing what is to beome the event horizon. However, the event horizon is never atually reated. Rather, the outer layers ontinue to move towards the event horizon, as they ompress the inner layers. Before an event horizon an be reated, time is getting distorted for the outer layers, as they move inwards. This is the same as the "frozen star" onept of the 930s, implying that observers would always see the star the way it was right before the reation of the event horizon. This implies no external observer, suh as on Earth, has seen the reation of a blak hole in the billions of years sine the existene of the universe, nor will they see it in the next infinite years (singularity). As far as outside observers, inluding those on the Earth are onerned, no blak holes have been reated, nor will they ever be reated. The only exeption would be primordial blak holes, reated during the big bang, when the present laws of physis were not appliable. Even with primordial blak holes, we would just see matter aumulating around them, without any of it atually falling inside. Thought experiments elsewhere in this paper also show that primordial blak holes should not be in existene, as they violate their own definitions. The Traveler s Viewpoint Having onsidered the outside observer's viewpoint, we now onsider the traveler's viewpoint. It is widely held today, that a traveler would find himself entering the event horizon (with a "plop,") without knowing that he has entered the event horizon. At the moment of penetration, he should have the speed of light. His relativisti kineti energy should be infinite, or another singularity. Massive body being felt outside twie. A massive body, suh as a star entering the event horizon will ause the mass of the blak hole to inrease. The inrease in mass of the blak hole from matter falling into it, will be felt by an external observer. However, he should also see the body falling forever into the event horizon. The external observer should sense the mass of the massive body twie; one from the inreased mass of the blak hole, and seondly from the falling body itself (a ontradition). Paradox of Two Travellers Another paradox is that of two travelers, with B following A (Figure 3). Aording to urrently held views, traveler B will see A approah but never enter the event horizon.. Sine B will never see A enter the event horizon, B himself annot find himself rossing the event horizon, as he annot go ahead of A. This ontradits the original idea that A finds himself entering the event horizon. Fig. 3. Traveler B will never see A enter event horizon, and therefore annot find himself entering event horizon IX. INSIDE THE EVENT HORIZON The singularity at the enter of a blak hole is a steady state solution to the Einstein field equations. This raises insurmountable questions about the transition leading to the steady-state solution. Almost nothing exists in the literature about the transition between a body entering the event horizon to the time when it joins the entral singularity. The literature however, does speak of a traveler finding himself entering the event horizon. It is said that the person may not know that they have fallen through. There is an impliation that time will ontinue as normal for the person. This is an indiation that a person entering an event horizon would still have some existene, and some semblane of the passage of time itself. This is highly inexpliable, beause of the greater than infinite/singularity nature inside the event horizon. After entering the event horizon, a body, by some streth of the imagination, should have greater-than-infinite energy, and the greater-than-light speeds. It is said that a star ollapsing into a blak hole would ollapse into a singularity in less than a April 0 IJENS

5 International Journal of Engineering & Tehnology IJET-IJENS Vol: No: 0 5 seond [4]. This suggestion of a rapid ollapse is like trying to avoid an impossible transition by saying that it happens very quikly (!). A very rapid ollapse may also be the human way to make sense of the unimaginable greater-than-infinite situation. Almost nothing is known of the dynamis inside the event horizon, that would explain the transitions inside suh an impossible situation. The proposed dubious dynamial onepts inside the event horizon, have found more aeptability, rather than the nonexistene of the event horizon itself. Analogies of the Event Horizon The event horizon and the entral singularity may have some other analogies in physis. The event horizon is like extending Boyle s Law for gases to bring down volume to zero and pressure to infinite. The inside of the event horizon is like making volume negative, and pressure beyond infinite. The singularity at the enter is the absurdity of highly infinite pressure and negative infinite volume. Another analogy for traveling towards the event horizon is a spae traveler aelerating in a roket through spae (Table ). Reahing the so-alled event horizon would be analogous to the impossibility of reahing the speed of light. Etering past the event horizon is like traveling at greater than the speed of light. The singularity at the enter of the event horizon is omparable to traveling at infinite speed. Another analogy of reahing an event horizon, is stopping the passage of time. Traveling past the event horizon is analogous to reversing the passage of time, and the singularity at the enter is like infinitely fast negative passage of time. The event horizon an also be ompared to the absolute zero of temperature, or zero Kelvin, whih annot be attained aording to the Third law of thermodynamis. The singularity at the enter is like infinite negative Kelvin of temperature. TABLE I ANALOGIES IN PHYSICS FOR EVENT HORIZON AND SINGULARITY AT CENTER Blak hole Event horizon Singularity Temperature Absolute zero, 0 K - Speial Relativity Speed of light veloity Passage of time Stopping Time -, time Volume Volume zero - volume X. MULTIPLE EVENT HORIZONS Most of the literature desribes the event horizon as a unique membrane or sphere of Shwarzhild radius GM/ around a singularity. The same result is obtained by ombining Newtonian and Relativisti mehanis by equating the potential and kineti energies of a body of mass m [6]. However this radius is only derived from of a body at zero veloity in far-away spae. This fixed radius GM/ is now shown to be not-so-fixed as numerous ontraditions arise. Body Shot from Outer Spae A body shot with signifiant veloity, V, from far-away spae, will attain the speed of light before it reahes the Shwarzhild event horizon (figure 4). To an outside observer, it's view would beome infinitely weakened and red-shifted right before reahing the event horizon. This implies the absurdity that this is the new event horizon for this body, lying outside the Shwarzhild radius. Fig. 4. Expanded and dereased event horizons of bodies with a faraway veloity, or dropped from lose by Considering reversibility, so as to reah a finite veloity V in outer spae, projetile must be shot from this new event horizon. A highly simplisti solution an be found by ombining Newtonian and Einsteinian physis. Equating the potential and kineti energies, we an find the new event horizon R (similar to the alulation of the regular Shwarzshild radius). mv + R = GMm = R GM v m The simplisti assumption is that a body at the speed of light has a finite kineti energy. The larger event horizon implies that speeding bodies from far-away spae are more likely to be trapped by blak holes, whih is ounter-intuitive (Figure 5). It is also ounter-intuitive that a body shot at lose to the veloity of light from far-away spae would enounter and be trapped by a greatly expanded event horizon. GMm/R = 0.5 m The flaw above of ourse is the assumption of finite energy of the body at the speed of light April 0 IJENS

6 International Journal of Engineering & Tehnology IJET-IJENS Vol: No: 0 6 orbit around the blak hole, going in and out of the Shwarzhild event horizon (Figure 7). Fig. 5. Speeding projetile more likely to be aptured by a larger event horizon, whih is ounter-intuitive A body shot (with veloity V) from distant spae would enter its own event horizon outside the regular event horizon, and find matter areting outside the regular event horizon., whih is again absurd. Another absurdity would be to have two bodies (at different veloities) entering side by side (figure 6). One would have entered its own event horizon, before the other reahed the regular event horizon. Fig. 7. A body given a small tangential thrust from just outside the regular event horizon going into an orbit going in and out of the event horizon. Another body dropped from just outside the new smaller event horizon, would find an event horizon that is even smaller. This thought experiment an be extended until the event horizon has radius lose to zero. Clearly, the event horizon an range from muh below the onventional Shwarzhild radius to muh larger than it. These absurdities, raise doubts about the very existene of the event horizon. Fig. 6. Absurdity of two bodies o-existing, one inside its own event horizon, and the other outside its own event horizon Body Dropped from lose to the event horizon. In the same way, we onsider a body dropped from height D (by a traveler) at zero veloity from near the event horizon. This body would reah the veloity of light after rossing the regular event horizon. Equating the hange in the potential energy with the kineti energy, a simplisti value of the radius R of the new event horizon is found. GMm - R R = GMm = D GM GM D m Bodies dropped from lose to the event horizon will enounter a new smaller event horizon (Figure 4). A body given a slight tangential veloity may find itself going into a near-elliptial Light and the Observer As in above ase of falling matter, the Shwarzhild radius is only valid for light, whih has just zero strength, and zero frequeny in far away spae. The Shwarzhild radius is not valid for light with finite energy in faraway spae, and for zero energy waves near the event horizon. Light with finite energy and frequeny in far away spae would find itself reahing infinite frequeny before reahing the Shwarzhild event horizon. This would define the new enlarged event horizon for this light. Similarly, light with low frequeny and energy lose to the event horizon would reah infinite frequeny well inside the Shwarzhild event horizon, and find its own event horizon to have shrunk to a smaller radius. An observer in far away spae would see or sense the event horizon to be at the Shwarzhild radius. The observer sees and senses the event horizon through the gravitational lensing effet. An observer approahing the blak hole would see/sense the event horizon to be getting smaller (figure 8). In the limiting ase of observer being just outside the Shwarzhild radius, the new event horizon-b would appear signifiantly smaller. Interestingly, the observer an slowly go inside the Shwarzhild radius, and approah the new event horizon-b, only to see and sense a third event horizon-c. This an be progressively ontinued until the newest event horizon April 0 IJENS

7 International Journal of Engineering & Tehnology IJET-IJENS Vol: No: 0 7 is lose to zero. One again, it is seen that the event horizon an range from zero to very large. Fig. 9. A rotating blak hole with imperfet harge and mass distribution, radiating energy into an external oil. Fig. 8. Approahing observer sees or senses progressively smaller event horizons XI. ROTATING BLACK HOLE A rotating blak hole with imperfet struture and harge distribution would learly radiate gravitational and eletromagneti waves outside the event horizon. A stationary observer outside the event horizon would sense the variations, or even harvest the transmitted energy. As blak holes are said to have a singularity at the enter, we onsider dereasing the radius of a ollapsing star towards singularity. It should be noted that the approahing singularity does not imply that mass and harge imperfetions will disappear. Instead, the inreasing rotational speed may imply that the radiated energy may inrease. A rotating blak hole with strutural imperfetions, would ause a variation of the gravitational fores ating outside. This fits the definition of gravitational waves radiated outside the event horizon. Energy, together with information on the strutural imperfetions are being sent outside. Based on the view that harge and gravitation an be sensed from outside, an eletrostati and gravitational field exists outside of the event horizon. A rotating blak hole with imperfet struture and harge distribution would ause hanges in the eletrostati and gravitational field outside of the event horizon. This implies energy loss by gravitational waves being sent outside the event horizon. By definition, and aording to Maxwell s equations, a hanging eletrostati field would also reate a hanging magneti field outside of the event horizon. These hanging eletrostati and magneti fields, are the very definition of eletromagneti waves. A rotating blak hole would radiate energy through eletromagneti waves. A blak hole approahing singularity and rotating at say 3x0 4 revolutions per seond would radiate eletromagneti waves at the frequeny of light, visible to a distant observer (!). We now show that a shrinking blak hole may radiate inreasing energy as it approahes singularity. The radiated energy may atually keep inreasing indefinitely. To illustrate this indefinite inrease, we onsider a blak hole is approahing singularity of zero volume and infinite density at the enter. We let mass, radius, and angular veloity be M, R, and respetively. For ease in alulations, Newtonian mehanis is applied, with the law of onservation of angular momentum: ω. 5 where K is a onstant. MR = ω. 5 = K /R MR = onstant We assume the eletrostati field owing to imperfet harge distribution, varies sinusoidally outside the event horizon, with the max at φ m φ=φ msin ωt. A oil of wire plaed outside the event horizon for harvesting the energy (figure ), would give emf : e α Ndφ/dt e = K N(d/dt)φ msin ωt. = K Nωφ mos ωt If the emf were to allow a urrent to flow through a resistor, the urrent would equal i = K Nωφ mos ωt The average power dissipated would equal P avg = K N ω φ m Assuming the number of turns in the oil of wire is, the equation is of the form P avg = K ω φ m We assume that as the radius approahes zero, the imperfetions of mass and harge distribution remain, neither dereasing, nor inreasing. We assume that the maximum flux dereases in diret proportion to the radius April 0 IJENS

8 International Journal of Engineering & Tehnology IJET-IJENS Vol: No: K K P avg = K (K3R) = R The above implies that with the radius R approahing zero, or singularity, the power radiated as eletromagneti and gravitational waves will keep inreasing in inverse proportion to the square of the radius. In the limiting ase of zero radius, the radiated power will be infinite. The power transmitted outside will tend to redistribute the matter and harge on and in the blak hole, and would also ause the rotation to slow down over time. The impliation is that the onditions outside the blak hole will affet the ondition inside the blak hole. With a blak hole of finite size and imperfet mass and harge distribution, a traveler irling the event horizon, would be able to gather information about the mass and harge distributions, violating the ondition that blak holes are defined only by their mass, harge, and angular momentum. Blak hole with perfet mass and harge distribution We now onsider the ase of a blak hole with a entral nearsingularity that has perfet harge and mass distribution. Just like the blak hole has a gravitational and eletrostati effet on a massive body outside the event horizon, the massive outside body will have an effet on the near-singularity. If this outside body has irregular harge and mass distribution and is rotating at the high speed arising out of ollapse, it will ause the near-singularity, to have imperfet harge and mass distribution. This effet of the outside body on the blak hole is also somewhat absurd. XII. ALTERNATIVES TO EVENT HORIZON The only alternative to the ontraditions desribed in this paper is that the event horizon is never really reated, regardless of how ompat the star beomes. A highly simplisti option is proposed here. It avoids the reation of the ontraditory event horizon, by taking the relativisti kineti energy, instead of the Newtonian kineti energy, for alulating the esape veloity. Equating it to the potential energy we get. GMm m [ ] v R For a given esape veloity, the radius an be found R = GM v K R K 3 For a given radius, the esape veloity an be found: GM v = R 0.5 In the above, it is seen that for a finite radius, the singularity of esape veloity equaling light is avoided. The above only for illustration of avoiding the event horizon. It is somewhat naïve, as it does not take into aount other elements of general relativity. XIII. CONCLUSION The solution of Einstein s field equations in extreme gravity is found to have so many ontraditions, the blak hole itself is suspet. Attempts over the last hundred years to reonile the blak hole with other known physis only leads to further ontraditions with other laws of physis. This also raises questions about whether the blak hole solution of the field equations are trivial, with little basis in reality. The event horizon still has numerous unresolved ontraditions, and is only valid for a body with zero veloity in far away spae. The radius of the horizon is less for a body tossed in from lose to the event horizon, and greater for a body with a finite veloity in far away spae. A traveler would see a progressively diminishing event horizon, while approahing the blak hole. The reasons given in modern physis, for why the Big Bang did not degenerate into a blak hole are also not very onvining. The urrently held view that an outside observer would never see a body enter the event horizon, implies that to the outside world, no blak hole has ever been reated or will be reated. As a rotating blak hole ollapses towards singularity, assuming strutural and harge distribution imperfetions, even more energy should be radiated as gravitational and eletromagneti waves. 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