arXiv:1303.3818v1 [physics.gen-ph] 14 Mar 2013 omrya et fTertclPyis nvo Madras of Univ Physics, Theoretical of Dept. at Formerly India, 501301, derabad htn l aetesm rqec,adta h pho- the that and frequency, same the have all photons resp.) photon the of frequency constant, b) a) a having as purpose this to for proportional behaves “mass” Grav- and Newton’s law to according itational photon, another by tracted stable. be and globe) origin,(photonic exist the occu- can including photons region of finite collection a a pying such investigate conditions and what field, under gravitational own its under times existing 1.5 at radius(SR). ballon) Schwarzschild thin the a of (like distance photons the of struc- layer thin actually Such which a spheres”, is hole. ”photonic times black called 1.5 then the to were tures equal of exactly radius is possi- Schwarzschild which are distance the orbits fixed stable black a such a at that of ble concluded influence In has the pho- under and of duration. orbit hole stable possibility long a the of forming investigated not tons has are [7] best Teo essen- at addition, are and structures unstable such con- The that tially be relativity. was general and at of exist arrived equations can conclusion field structures the such with if sistent out made find studies to the All were Geons electromagnetic. of and types gravitational two name - studied have the first investi- and have it possibility was [2-6] this gave gated region researchers who many spherical [1], Subsequently near Wheeler Geon. or J.A. by spherical conjectured a as isting STATEMENT PROBLEM INTRODUCTION: I. Globes Photonic Sustained Self On uhrtak h aaeeto SNIST of management the thanks Author NS,Jwhra nv fTc. anme,Gaksr Hy Ghatkesar, Yamnampet, Tech., of Univ. Jawaharlal SNIST, i)I hsbifsuyi ilb sue htthe that assumed be will it study brief this In (iv) ii easm htec htni rvttoal at- gravitationally light: is of photon speed each the that is assume We photon classical (iii) each of is assumptions: velocity problem following The the (ii) the of make treatment we The so (i) do to order In photons of possibility the consider paper this in We ex- radiation self-sustained a of existence possible The ewrs htncgoe,Shazcidrdu,dniyo unive of density radius, Schwarzschild globes, de 98.80 photonic average 98.62. Keywords: an 42.50, 04.20, has numbers: globe PACS frequenc photonic the a universe. such our of of that radiation photo density out large containing average turns very observed and a so universe of It the case GHZ). the of consider g radius we “photonic the Schwar example, radius Schwarzschild a the application the to within an this region corresponding As call the closely that We colle conjuncture radius the dense a to very have influence. a will gravitational of globe own treatment photonic its classical a under consider globe we paper this In 2019) April 1 (Dated: Eswaran K. b) hν/c 2 ( h and ν en Planck’s being a) c - egvnby given be n h vrg au of value average the ing osfr efssandgoeo aisR the R, radius of globe sustained density self a form tons ntevlm lmn ilb : be will element volume the in iiyo h ytmoecnso htterdu of density number R the radius ra- for Schwarzchilde the expression the that an to show dius, corresponds can globe one photonic system the the of the bility from distance radial the being r 0. centre alone, r of function that oterda iedanfo oteoii .Then O. origin the to P from velocity, drawn tangential line the radial the to lmn ilbe will element eoiycadmkn naueangle acute an making and c velocity a ,adsrone yavlm lmn i oa coor- polar (in element mass volume the a dinates), by surrounded and O, edadcnee bu h rgni xat edefine We extant. is origin gravitational the own M about its centered under and photons field of solely consisting CALCULATION OF DETAILS BRIEF II. obtained. r sgvnby: given is 0 , h etiua oc cf)o hsvlm lmn will element volume this on (c.f.) force centrifugal The twl esonta yipsn odtoso sta- of conditions imposing by that shown be will It o mgn h htn tPaemvn nadwith inward moving are P at photons the imagine Now o osdrapitPa itnerfo h centre, the from r distance a at P point a consider Now h rvttoa oc,F nti ml element small this on F, force, gravitational The ehrwt sueta htncgoe frdu R, radius of globe, photonic a that assume herewith We ( r < ob h ms”o niaiayshr fradius of sphere imaginary an of “mass” the be to ) v t 2 r = ftephotons the of ≤ c R 2 c.f / M then , ,hnetecniua oc ntephotons the on force cenrifugal the hence 2, fabakhl otisol ueradiation. pure only contains hole black a of s,bakhls akmte,dr energy , dark holes, black rse, ( = to fpoosfrigaself-sustained a forming photons of ction r v = ) ftemcoaebcgon (160.2 background microwave the of y t st hc lsl orsod othe to corresponds closely which nsity shl ais hslnigsubstance lending Thus radius. zschild m i lb hs aiscrepnsto corresponds radius whose globe nic = m ∆ F Z sinψ c ∆ v oe eso htsc dense a such that show We lobe” 0 = t 2 r = v /r σ sin 4 t Gm πr ftepoosi hsvolume this in photons the of , ν σ but , ( ν . 2 r 2 ( ψ ,wl easmdt ea be to assumed be will ), σ r ∆ r )( ν 2 M vr0to 0 over ( v hν/c r t 2 ( )( r = ) hν/c 2 c ) 2 r sin 2 2 π ψ ) rsn θdφ dθ sinθ dr dr ihrespect with , s1 as 2 ψ σ ν substitut- ; ( / r ,w see we 2, salso is ) number m (2) (1) ∆ 2

point P at an arbitrary distance r in the globe lies on an “event horizon”. The photon number density σν (r), as a m c2 c.f. = ∆ (3) function of r, of such a photonic globe is given by eq.(6). 2 r The above calculation seems to lead to an interesting The condition of stability requires thatF = c.f , hence conjecture: That the region within the Schwarzschild ra- by equating (2) and (3), we have: dius of a black hole consists of pure radiation, a stable photonic globe, sustained within itself by its own “grav- itational” field. c2 M(r)= r (4) 2G IV. APPLICATION REGARDING THE DENSITY OF Substituting for M(r), from (1), we have THE UNIVERSE

r 4 In this section, we will consider a very large photonic 2 c r σν (r) dr = r (5) globe which contains photons corresponding to 160.2 Z0 8πGhν  GHZ, the frequency of the background radiation and as- Since eq. (5) must be true for all r, we can see that sume the radius of the globe to be the radius of the uni- verse. If we start from the expression, Eq(6), for the this is not possible unless the number density, σν (r), is given by the following expression: number density of photons at frequency ν, and substitute υ ≡ νB = 160.2GHz , where νBis the frequency of the background radiation of the universe (which corresponds c4 1 to a wave length λ = 0.1872 cms), using the value of σν (r) = (6) −8 8πGhν  r2 the Gravitational constant G =6.673 10 cgs(cm-gram- second ) units and Planck’s constant h =6.626 10−27erg- It may be noted that though the number density seems sec (cgs units ) , and the value of the velocity of light to become infinite as r tends to zero, the number of pho- c = 3.0 1010 cms per sec; we see that at this frequency 4π ν 3 B tons in a very small sphere of radius ǫ will be σ (ǫ) 3 ǫ ν we can write which is finite. Now if we substitute r = R, and noting that M(R)= 62 1 M, the mass of the photonic globe, we have σνB (r)=4.55 . 10 (8) r2

2 2GM which we denote for convenience as σνB (r) = β/r , R = (7) 62 c2 where β =4.55 . 10 . Now to calculate the total number of Photons NR in- It may be noted that the rhs of (7) is nothing but the side a sphere of radius R, we need to integrate the above Scwarzchilde radius. and obtain

III. ON THE PROPERTIES OF THE PHOTONIC R 2 GLOBE NR = 4πr σνB (r) dr Z0

From the above calculation, it so turns out that the radius R of a photonic globe, eq.(7), is nothing but the =4π β R (9) Schwarzschild radius an expression for which radius was The total energy, Etotal, of radiation is then Etotal = derived by Schwarzschild in 1916, for a spherically sym- 2 metric body by using equations of general realtivity for NR.hυB,. The equivalent mass will be M = Etotal/c . Hence the average “mass density” inside this sphere will regions outside this radius. We have derived the same 4π be ρav = M/( R3). That is expression for the Schwarzchilde radius by using com- 3 pletely different arguments for regions inside this radius by considering a collection of photons and using some 3βhνB ρav = (10) assumptions detailed above. It is well known that the R2c2 event horizon for a black hole occurs at a radius equal to the Scwarzchilde radius. The physics within this radius Now if we take R as the the radius of the is not well known and can only be guessed at. Also when visible universe R=13.5 billion light years, ie. eq(4) written as r = 2GM(r)/c2, is a valid equation for R =1.2271028cms. any radius r centered around the origin, M(r) being the Substituting these valuses for R, β , νB, and c, we mass of the imaginary sphere of this radius, we see that get an average mass density for the universe as ρav = r is the Schwarzschild radius for this sphere, so every 9.869 10−30grams/cc. Which is very close to the actual 3 estimated mass density, by the WMAP.[8], as may be density of such a photonic globe is very close to the latest gathered from the following quotation in the NASA, ar- estimate of the average mass density of the universe by ticle [8]: NASAs WMAP team[7]. “WMAP determined that the universe is flat, from which it follows that the mean energy density in the uni- verse is equal to the critical density (within a 0.5% mar- VI. REFERENCES gin of error). This is equivalent to a mass density of 9.9 10−30g/cm3, which is equivalent to only 5.9 protons per cubic meter.” 1.Wheeler, J. A. (1957). “Geons” Physical Re- It is well known that only about 4 percent of the mass view 97 (2): 511. Bibcode 1955 PhRv...97..511W. of the universe consists of Baryonic matter. So, if we, (for doi:10.1103/PhysRev.97.511. a stating approximation), adopt the hypothesis that the 2.Brill, D. R.; Hartle, J. B.(1964).“Method of the universe is a photonic globe containing photons of fre- Self-Consistent in and its quency of the CMB, then the above calculations give the Application to the Gravitational Geon” Physical Re- correct average density, and obviously the correct Mass view 135 (1B): B271.Bibcode 1964 PhRv..135..271B. for the universe. However, if one considers the number doi:10.1103/PhysRev.135.B271. density of photons of frequency νB, it turns out to be 3.Louko, Jorma; Mann, Robert B.; grossly over estimated, (as can be easily calculated from Marolf,Donald(2005).“Geons with spin and the above equations) from the actual value of 400 photons charge”, Classical and Quantum 22 per cc (near earth). So here we have a situation where (7): 1451-1468. arXiv:gr-qc/0412012. Bibcode the mass and mass-density are correct but the number 2005CQGra..22.1451L.doi:10.1088/0264-9381/22/7/016. of photons estimated are far too much. So where have 4.Perry, G. P.; Cooperstock, F. I. (1999). “Sta- all the extra photons gone? It could then be conjectured bility of Gravitational and Electromagnetic Geons” that some unknown physical process has converted all Classical and 16 (6): 1889 -916. this extra radiation into dark matter and dark energy, arXiv:gr-qc/9810045. Bibcode 1999CQGra..16.1889P. thus keeping the total energy (mass) unchanged. Only doi:10.1088/0264-9381/16/6/321. further experimentation and research can resolve such is- 5.Anderson, Paul R.; Brill, Dieter R. (1997). sues. “Gravitational Geons Revisited” Physical Review D 56 (8): 4824-4833. arXiv:gr-qc/9610074. Bibcode 1997PhRvD..56.4824A. doi:10.1103/PhysRevD.56.4824. V. CONCLUSION 6.Teo, Edward (2003). ”Spherical Photon Orbits Around a Kerr Black Hole”. General Relativ- In this paper, we have considered the possibility of the ity and Gravitation 35 (11): 19091926. Bibcode existence of a stable a selfsustained photonic globe and 2003GReGr..35.1909T. doi:10.1023/A:1026286607562. have arrived at the following: (i) that such a globe must ISSN 0001-7701. have its radius equal to the Schwarzchild radius and (ii) 7.WMAP Science Team, ”Cosmology: The Study of if we consider a photonic globe which contains photons the Universe,” NASA’s Wilkinson Microwave Anisotropy of frequency equal to 160.2 GHZ and a radius equal to Probe,2013, http:map.gsfc.nasa.gov/universe/WMAP the radius of the universe then the average mass (energy) Universe.pdf, or http:map.gsfc.nasa.gov/universe/