Relativistic Theory of Black Holes

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1 Relativistic Theoy of Black Holes Daniele Sasso * Abstact The gavitational theoy is the most accedited theoy fo explaining black holes. In this pape we pesent a new intepetation based on the elativistic theoy that explains black holes as a consequence of the elativistic speed of depatue between the speed of celestial system and the speed of both light and quantum ays at vey high enegy, calculated with espect to the obseve. 1. Histoical intoduction to black holes The tem black hole was intoduced by Ameican physicist J.A. Wheele because eveything, inclusing the light, that went into that astonomical zone wasn t able to get out and consequently it appeaed black. In the 18 th centuy Laplace and Michell hypothesized fo the fist time the existence of a celestial body povided with a geatest mass that was able to cause an escape velocity geate than the speed of light fo which neithe light was able to esist the stongest gavitational foce geneated by the celestial body. This hypothesis got on with Newton s copuscula theoy of light but not with the wave theoy: on this account the concept of black hole was abandoned. Some month afte the publication of Geneal Relativity by Einstein (1916) the black hole was again contemplated because gavitation in GR was consideed a geometic vaiation of the space and not a foce. In 1919 Eddington on the occasion of a total sola eclipse [1] measued the deflection of light coming fom a emote sta when light passed nea the sun. He deduced that in place of the sun a geatest celestial mass should have poduced a so geat deflection of light that this once gone into the even hoizon wasn t able to get out any longe. Moe o less in the same yeas also Kal Schwazschild calculated that the black hole should have possessed a geatest mass because the calculus implied a smallest adius of the celestial body (R=2GM/cÇ) and consequently in ode to have an acceptable value of adius a vey geat mass was necessay. It is also suitable to say that lastly a few published papes have denied the existence of black holes [2]. Futue futhe expeiments will say if black holes epesent a physical eality also if aleady now thee ae many evidences in this egad. In the gavitational theoy the black hole looks like an astonomical monste that devous all what passes in the poximity of its even hoizon, the elativistic theoy intends also to popose a moe fiendly explanation of the black hole. * dgsasso@alice.it 1

2 2. Gavitational theoy Whethe in Newton s o Einstein s gavitational theoy black holes can be explained with a vey stong intensity of the gavitational field that is caused by a geatest mass. In fact in Newton s theoy the F G gavitational foce on a m mass in a point at distance fom the cente of gavity is given by F G = G M m (1) 2 whee G=6,67x10-11 Nm 2 Kg -2 is the constant of univesal gavitation and M is the mass of the celestial body geneating the gavitational field. The gavitational foce is the moe stong the moe M is geat and the moe is small. A body with m mass in ode to leave the suface of M celestial mass has to be povided with an escape foce F e =ma e with opposed diection with espect to the diection of the gavitational foce. In ode to calculate the initial minimum speed (v e escape speed) that a m mass has to possess at the distance fo leaving definitively the celestial body it has to be Being we have G M m = - m dv (2) 2 dt dv = dv d (3) dt d dt dv d = - G M (4) d dt 2 v dv = - G M d (5) 2 and v 2 = 2 G M (6) v e = 2 G M (7) Fom the (7) equation we deduce that the escape speed depends on both the distance fom the cente of gavity and the M mass of the celestial body. Fom the (6) equation, in the event of light (v=c), we find again Schwazschild s adius R = 2 G M (8) c 2 2

3 In this theoy R epesents the adius of the even hoizon because M mass is concented into a smallest volume because of the stongest gavitational field. A gaphic epesentation of black hole is given in fig.1. O R Fig.1 Gaphic epesentation of black hole in the gavitational theoy. R is the adius of the event hoizon: all what is inside cannot go out, all what passes vey nea to the hoizon (also the light) is attacted inside. The obseve is in the O point. In the gavitational theoy black hole epesents an astonomical entity whose pospective motion would have no evealing effect on its behavio. In GR the gavitational foce is eplaced with the space and time wap that is the moe stong the moe M mass is geat and consequently the behavio of black hole is equivalent to a suction effect so geat that also the light isn t able to go out. 3. Relativistic theoy Let us conside an O obseve who is in the oigin of the S efeence fame supposed at est and similaly conside a celestial body which constitutes the S efeence fame. Suppose still that S moves with V velocity in evese with espect to S. Any object launched with speed u fom the suface of the celestial body towads the S efeence fame along the conjoining line the cente of gavity of S and the O point whee the obseve is placed (fig.2), has with espect to S the vecto velocity [3][4] v = u + V (9) In concodance with intensities of V and u the following cases can happen: 1. V<u : the launched object eaches the O obseve with scala velocity v=u-v in a time d/(u-v) only if the esultant velocity v is geate than the escape speed of the celestial body v e = 2GM/R (v>v e ). 3

4 2. V=u : the launched object doesn t each the O obseve and the object staies at a constant distance fom O. 3. V>u : the launched object doesn t each the O obseve and in any case it moves away fom O with speed v=v-u (this case is epesented in fig.2). S V u u+v O S 2 2R d Fig.2 Gaphic epesentation of black hole in the elativistic theoy whee V is the speed of depatue of black hole with espect to the O obseve, u is the speed of an object launched fom the suface of black hole and u+v is the speed of the same object with espect to S. In figue the case V>u is epesented. In the gaphic the black hole is epesented by a sphee with R adius which because of vey geat distance fom the O obseve appeas like a small sphee with adius. d is the distance between the obseve and the launch point of the object. In the event of the light the u speed coincides with c. In the event of light o enegy ays emitted by the celestial body we have u=c. The following cases can happen: 1. V<c : the light eaches the O obseve with velocity v=c-v in a time d/(c-v) [4]. 2. V=c : with espect to O obseve the light has null velocity and consequently it isn t able to each the O obseve. 3. V>c : the light isn t able to each the O obseve. In the both cases 2. and 3. the celestial body behaves like a black hole. If duing its motion black hole collides with couds of cosmic dusts these behave towads the black hole like a fiction that aises by fa the tempeatue of dusts with emission of electomagnetic adiations at vey high enegy. 4. Black holes and binay stas With efeence to fig.3, supposing that V is the speed of the bynay system and that the obital speeds of the two stas ae smalle than c (v 1 <c, v 2 <c), the following cases can happen: 4

5 a. The V speed is geate than c (speed of light and speed of quantum ays at high enegy): V>c. In figue the sta binay system moves away with V speed fom the obseve, but the speed of each sta with espect to the obseve depends on the ecipocal position. In positions of figue sta1 moves away with V-v 1 speed and sta2 moves away with V+v 2 speed. In that event sta2 cetainly is a black hole while sta1 is a black hole only if V-v 1 >c. b. The V speed is equal to c: V=c. In that event sta2 is cetainly a black hole and sta1 isn t cetainly a black hole in ecipocal positions of figue. c. The V speed is smalle than c: V<c. Always with efeence to the situation in figue sta1 is an odinay sta while sta2 is a black hole if V+v 2 >c. v 2 S 2 V o 1 S 1 v 1 B o 2 O Fig.3 Gaphic epesentation of a binay sta. o 1 is the obit of sta 1 and o 2 is the obit of sta 2. B is the cente of mass of the binay sta system which moves away fom the obseve with V speed. In the situation of figue, v 1 is the appoach obital speed of the sta1 with espect to the O obseve and v 2 is the depatue obital speed of the sta2. It is inteesting to obseve that in the elativistic theoy the binay sta system has a diffeent behavio accoding to the ecipocal position between the two stas inside the binay system. Only astomical obsevations will be able to confim this behavio. The elativistic theoy hee descibed epesents an altenative way with espect to the gavitational theoy fo explaining astonomical natue and physical behavio of black holes. Refeences [1] D. Sasso, Not Linea Element, Cosmological Redshift and Deflection of Light in the Gavitational Field, vixa.og, id: , 2011 [2] S.J. Cothes, The Black Hole Catastophe, vixa.og, id: , 2011 [3] D. Sasso, Relativistic Effects of the Theoy of Refeence Fames, Physics Essays (Physicsessays.com), Vol.20, No.1, 2007 [4] D. Sasso, Is the Speed of Light Invaiant o Covaiant?, vixa.og, id: ,

Episode 401: Newton s law of universal gravitation

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