Why the Big Bang Model Cannot Describe the Observed Universe Having Pressure and Radiation

It has been recently shown that, since in general relativity (GR), given one time label t, one can choose any other time label t → t*= f(t), the pressure of a homogeneous and isotropic fluid is intrinsically zero (Mitra, Astrophys. Sp. Sc. 333, 351, 2011). Here we explore the physical reasons for the inevitability of this mathematical result. The essential reason is that the Weyl Postulate assumes that the test particles in a homogeneous and isotropic spacetime undergo pure geodesic motion without any collisions amongst themselves. Such an assumed absence of collisions corresponds to the absence of any intrinsic pressure. Accordingly, the “Big Bang Model” (BBM) which assumes that the cosmic fluid is not only continuous but also homogeneous and isotropic intrinsically corresponds to zero pressure and hence zero temperature. It can be seen that this result also follows from the relevant general relativistic first law of thermodynamics (Mitra, Found. Phys. 41, 1454, 2011). Therefore, the ideal BBM cannot describe the physical universe having pressure, temperature and radiation. Consequently, the physical universe may comprise matter distributed in discrete non-continuous lumpy fashion (as observed) rather than in the form of a homogeneous continuous fluid. The intrinsic absence of pressure in the “Big Bang Model” also rules out the concept of a “Dark Energy”.

Gamma/hadron segregation for a ground based imaging atmospheric Cherenkov telescope using machine learning methods: Random Forest leads

A detailed case study of γ-hadron segregation for a ground based atmo- spheric Cherenkov telescope is presented. We have evaluated and compared various supervised machine learning methods such as the Random Forest method, Artificial Neural Network, Linear Discriminant method, Naive Bayes Classifiers, Support Vector Machines as well as the conventional dynamic supercut method by simulating triggering events with the Monte Carlo method and applied the results to a Cherenkov telescope. It is demonstrated that the Random Forest method is the most sensitive machine learning method for γ-hadron segregation.

An Astrophysical Peek into Einstein’s Static Universe: No Dark Energy

It is shown that in order that the fluid pressure and acceleration are uniform and finite in Einstein’s Static Universe (ESU), , the cosmological constant, is zero. being a fundamental constant, should be same everywhere including the Friedman model. Independent proofs show that it must be so. Accordingly, the supposed acceleration of the universe and the attendant concept of “Dark Energy”(DE) could be an illusion;an artifact of explaining cosmological observations in terms of an oversimplified model which is fundamentally inappropriate. Indeed observations show that the actual universe is lumpy and inhomogeneous at the largest scales. Further in order that there is no preferred centre, such inhomogeneity might be expressed in terms of infinite hierarchial fractals. Also, the recent finding that the Friedman model intrinsically corresponds to zero pressure (and hence zero temperature) in accordance with the fact that an ideal Hubble flow implies no collision, no randomness (Mitra, Astrophys. Sp. Sc., 333,351, 2011) too shows that the Friedman model cannot represent the real universe having pressure, temperature and radiation. Dark Energy might also be an artifact of the neglect of dust absorption of distant Type 1a supernovae coupled with likely evolution of supernovae luminosities or imprecise calibration of cosmic distance ladders or other systemetic errors (White, Rep. Prog. Phys., 70, 883, 2007). In reality, observations may not rule out an inhomogeneous static universe (Ellis, Gen. Rel. Grav. 9, 87, 1978).

Kruskal Coordinates and Mass of Schwarzschild Black Holes: No Finite Mass Black Hole at All

When one presumes that the gravitational mass of a neutral massenpunkt is finite, the Schwarzschild coordinates appear to fail to describe the region within the event horizon (EH), of a Schwarzschild Black Hole (SBH). Accordingly, the Kruskal coordinates were invented to map the entire spacetime associated with the SBH. But it turns out that at the EH (Mitra, IJAA, 2012), and the radial timelike geodesic of a point particle would become null. Physically this would mean that, the EH is the true singularity, i.e., M = 0, and this zero mass BH could only be a limiting static solution which must never be exactly realized. However, since in certain cases , here we evaluate this derivative in such cases, and find that, for self-consistency, one again must have at the EH. This entire result gets clarified by noting that the integration constant appearing in the vacuum Schwarzschild solution (and not for a finite object like the Sun or a planet), is zero (Mitra, J. Math. Phys., 2009). Thus though the Schwarzschild solution for a point mass is formally correct even for a massenpunkt, such a point mass or a BH cannot be formed by physical gravitational collapse. Instead, physical gravitational collapse may result in finite hot quasistatic objects asymptotically approaching this ideal mathematical limit (Mitra & Glendenning, MNRAS Lett. 2010). Indeed “the discussion of physical behavior of black holes, classical or quantum, is only of academic interest” (Narlikar & Padmanbhan, Found. Phys. 1989).

Kruskal Dynamics for Radial Geodesics

The total spacetime manifold for a Schwarzschild black hole (BH) is believed to be described by the Kruskal coordi-nates and , where r and t are the conventional Schwarzschild radial and time coordinates re-spectively. The relationship between r and t for a test particle moving along a radial or non-radial geodesic is well known. Similarly, the expression for the vacuum Schwarzschild derivative for a geodesic, in terms of the constants of motion, is well known. However, the same is not true for the Kruskal coordinates;and, we derive here the expression for the Kruskal derivative for a radial geodesic in terms of the constants of motion. In particular, it is seen that the value of ) is regular on the Event Horizon of the Black Hole. The regular nature of the Kruskal derivative is in sharp contrast with the Schwarzschild derivative, , at the Event Horizon. We also explicitly obtain the value of the Kruskal coordinates on the Event Horizon as a function of the constant of motion for a test particle on a radial geodesic. The physical implications of this result will be discussed elsewhere.