Gurcharn Singh Sandhu

Sir, I am interested in your work keep in touch, just reading the attached. pls send me more of your fundamental works.

1) Eu is just putting false belief in the world, just giving noble prices, since 1980, very few discoveries rewarded they deserved rest is for assumptions, clearly monopoly politics, and their is no authority in science. This is because how they will account for the huge grant spent? It help to put pressure on govt.

2) keep the brain working don't be hurt by such monopoly, entire Eu is sleeping, so it is opportunity for rest to work.

thankyou

dinesh

Sorry, may be I am too ignorant on the subject of Black Hole. I have never heard that BHs have been proven to be non-existent. I only know that Stephen Hawking spent his whole life working on the physics of BH.

Furthermore LIGO has just discovered gravitational waves from BHs, and physicists were honored by Nobel prize for that reason.

Good and valid points. I support you.

Even if black holes were indeed proved to be non-existent, the experimental facts discovered by LIGO would be unaffected. It would not be the experimental search that would need to be abandoned, but the interpretation would require modification. The LIGO project would in fact become even more fascinating, since we would not understand the origin of the source any more.

Of course, it remains to see whether you have indeed proved this, or anything. What I could see was a jumble of unconnected and unproved assertions, leading nowhere, and published in a journal that nominally sends its articles for refereeing but will, in fact, pretty much accept anything.

Probably Black Holes, which have a fairly simple mathematical origin, may yet survive your remarks.

Black holes (BHs) are the fates of stars having supersolar masses

The gravitational waves are generated due to their collisions

Nonexistence of BHs is questionable

Dear Leyvraz,

I am sorry, I thought that 'all Science and Engineering Graduates can easily follow and understand the analysis, logic and conclusions of this paper'. From your remarks I find that even for highly qualified scientists, understanding why 'Black Holes are a mathematical fantasy, not a physical reality' appears to be a tough job. Therefore, I am now elaborating the first part of my paper and request you to kindly confirm which one of the following is the correct derivation of the Gravitational Red-shift.

Under Newtonian theory of gravitation, only matter particles are the sources of gravitation field and only matter particles experience gravitational attraction. However, under GR all forms of matter and energy, including the energy of electromagnetic field, contribute towards the production of gravitation field. Hence, under GR the electromagnetic energy of photons does get influenced by the gravitational field just like the mass of matter particles. That is, under GR a photon of frequency f does experience gravitational attraction towards a massive body of mass M, in proportion to the photon energy hf or its equivalent dynamic mass hf/c2 and hence experience red-shift while escaping from the gravitation field of M.

In GR the quantitative relations for computing the magnitude of gravitational red-shift are based on the well-known concepts of gravitational potential. The gravitational potential (V) at a given location is the gravitational potential energy per unit mass. Thus, at a distance r from the center of a spherically symmetric body of mass M, the gravitational force Fg on a body of mass m is given by,

Fg(r) = -GMm/r2 .... (1)

The gravitational potential V as the gravitational potential energy per unit mass is obtained by integration of Fg(r),

V(r) = -GM/r .... (2)

It is important to note that during integration of gravitational force, M and m remain constant and can be taken out of the integral sign. Normally, when a small body of mass m is brought to a location of gravitational potential V(r) its potential energy will be given by m.V(r), implying thereby that a gravitational interaction energy of m.V(r) has been released from the combined gravitational field of the two bodies and converted to kinetic energy (T) of the interacting bodies. Conservation of energy ensures that the sum of the kinetic and potential energies remains constant at all points in the gravitational field. Therefore, if a test body of mass m with kinetic energy T0 moves from body surface radius R0 with gravitational potential V(R0) to a location r2 with gravitational potential V(r2) then the new kinetic energy T2 at location r2 will be given by the energy conservation relation,

T0 + m.V(R0) = T2 + m.V(r2) .... (3)

Considering location r2 to be at infinite distance from the center of the gravitating body, where the gravitational potential V(r2) reduces to zero by equation (2), we get the escape energy T2 as,

T2 = T0 + m.V(R0) .... (4)

A. Red-shift Derivation based on Potential Energy Concept

Let us replace the test body of mass m with a photon of frequency f0 at location R0. The total energy T0 for this photon will be hf0 and the dynamic mass or the 'effective mass' of the photon will be given by hf0/c2. Then from equations (2) and (4), the escape energy T2 = hf2 and the ratio of escape frequency f2 to the emission frequency f0 of the photon will be given by,

f2/f0 = 1- GM/(c2.R0) = 1 - Rs/(2.R0) .... (5)

where Rs = 2GM/c2 is the Schwarzschild radius.

Equation (5) represents the standard gravitational red-shift formula under the so called weak-field conditions. However, under strong gravitation field conditions, equation (5) is modified by the Schwarzschild metric coefficient as follows.

f2/f0 = Sqrt(1 - Rs/R0) .... (6)

When the gravitating body is so compact that its surface radius R0 is equal to (or less than) the Schwarzschild radius Rs then the right-hand side of equation (6) will vanish leading to zero energy or zero value of frequency f2 of the escaped photon. That precisely is the condition of a Black Hole from where no photon can escape.

However, there is one major flaw in this derivation. The gravitational potential V as the gravitational potential energy per unit mass is obtained by treating the test mass m as constant during integration of gravitational force from infinity to R0. But when we replace m with equivalent dynamic mass hf/c2 of a photon, this dynamic mass hf/c2 or the photon frequency f does not remain constant during integration of gravitational force from infinity to R0. That is, it is wrong to use gravitational potential V(r) for computing the change in energy hf of a photon while bringing it from infinity to location r or vice versa.

B. Red-shift Derivation based on Gravitational Force Concept

Let us consider the gravitational attraction experienced by a photon of frequency f, energy E=hf and dynamic equivalent mass m=hf/c2, in the gravitational field of a massive, spherically symmetric body of mass M. From equation (1), the gravitational force Fg acting on a photon of dynamic equivalent mass hf/c2 located at distance r from the center of the gravitating body is given by,

Fg(r) = -(hGM/c2).f/r2 .... (7)

When a photon moves against this gravitational force Fg from a location with smaller radius r to a bigger radius R, it will lose some of its energy to the gravitational field and its frequency f will get reduced. Hence, during the motion of the photon from r to R, its frequency f will not remain constant but will keep decreasing steadily, unlike the mass m of a test body in equations (1) and (2). A small increment of energy dE, lost by the photon in moving from r to r+dr against Fg is given by,

dE = h.df = Fg(r).dr = -(hGM/c2).(f.dr/r2) .... (8)

Or df/f = -(GM/c2).(dr/r2) .... (9)

Integrating equation (9) between limits r=R0 to infinity with corresponding f=f0 to f2, we get,

f2/f0 = exp(-GM/(c2.R0)) = exp(-Rs/2R0) .... (10)

Equation (10) shows that the escape frequency of any photon emitted from a gravitating body of finite mass M and finite R0 can never vanish. That is, light photons cannot be trapped by any finite mass Black Hole. Hence it stands proved that for a gravitating body of any finite mass M and finite R0, there is absolutely no Black Hole effect.

The error in standard derivation of gravitational red-shift as presented in equations (5) and (6) is essentially rooted in the wrong use of standard gravitational potential, derived with a test body of constant mass m and used for the red-shift analysis of a photon of variable energy in the gravitation field.

For comparison, equations (5), (6) and (10) have been plotted with x=Rs/R0 along X-axis and the exit frequency ratio y=f2/f0 along Y-axis. For most stellar bodies,Rs/R0 varies between 10-6 to 10-4 in which case all three curves give almost the same result.

Article Black Holes are a Mathematical Fantasy, not a Physical Reality