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arXiv2011

On the Sackur-Tetrode equation in an expanding universe

In this work we investigate the thermodynamic properties satisfied by an expanding universe filled with a monoatomic ideal gas. We show that the equations for the energy density, entropy density and chemical potential remain the same of an ideal gas confined to a constant volume V . In particular the Sackur-Tetrode equation for the entropy of the ideal gas is also valid in the case of an expanding universe, provided that the constant value that represents the current entropy of the universe is appropriately chosen.

physics.gen-ph↗
arXiv2012

Non-linear diffusion in RD and in Hilbert Spaces, a Cylindrical/Functional Integral Study

We present a proof for the existence and uniqueness of weak solutions for a cut-off and non cut-off model of non-linear diffusion equation in finite-dimensional space RD useful for modelling flows on porous medium with saturation, turbulent advection, etc. - and subject to deterministic or stochastic (white noise) stirrings. In order to achieve such goal, we use the powerful results of compacity on functional Lp spaces (the Aubin-Lion Theorem). We use such results to write a path-integral solution for this problem. Additionally, we present the rigourous functional integral solutions for the Linear Diffussion equation defined in Infinite-Dimensional Spaces (Separable Hilbert Spaces). These further results are presented in order to be useful to understand Polymer cylindrical surfaces probability distributions and functionals on String theory.

physics.gen-ph↗
arXiv2010

Incorporating particle creation and annihilation into Bohm's Pilot Wave model

The purpose of this paper is to come up with a Pilot Wave model of quantum field theory that incorporates particle creation and annihilation without sacrificing causality. In some sense, this work echoes the work of Nikolić (I call "visibility" what he calls "effectiveness"), but in my work I choose position and visibility as beables, as opposed to field beables that are used in his.

physics.gen-ph↗
arXiv2010

A vacuum component of the Universe must evolve

The evolution of a vacuum component of the Universe is investigated in the quantum as well as the classical regimes. Probably our Universe has arisen as a vacuum fluctuation and very probably that it has had a high symmetry for Planckian parameters. Besides, vacuum energy density has to be a positive one. In the early epochs during its cooling the Universe had been losing the high symmetry by phase transitions since condensates of quantum fields carried negative contributions (78 orders) to its positive energy density. It was the period of the Universe evolution during the first parts of the first second of its life. After the last phase transition (quark-hadron) the vacuum energy `has hardened'. In this moment its energy density can be calculated using the Zeldovich's formula inserting an average value of the pseudo-Goldstone boson masses (pi-mesons) that characterizes this chromodynamical vacuum. The chiral symmetry was then lost. Dynamics of the equilibrium vacuum after its `hardness' is considered by applying the holographic conception. In this case the Universe has been losing vacuum energy (45 orders) on organization of new quantum states during 13.76 x 10^9 years. Using this conception we can get solution of the cosmological constant problem. 123 crisis orders problem may be resolved. The density of vacuum energy cannot have a constant value in principle because of the new quantum states are organized during expansion of the Universe but the equation of state vacuum w= - 1 should be naturally constant. The density of vacuum energy from z=0 up to z=10^11 is also calculated in the classical regime of the Universe evolution.

physics.gen-ph↗
arXiv2010

Trace Formulae and Spectral Statistics for Discrete Laplacians on Regular Graphs (II)

Following the derivation of the trace formulae in the first paper in this series, we establish here a connection between the spectral statistics of random regular graphs and the predictions of Random Matrix Theory (RMT). This follows from the known Poisson distribution of cycle counts in regular graphs, in the limit that the cycle periods are kept constant and the number of vertices increases indefinitely. The result is analogous to the so called "diagonal approximation" in Quantum Chaos. We also show that by assuming that the spectral correlations are given by RMT to all orders, we can compute the leading deviations from the Poisson distribution for cycle counts. We provide numerical evidence which supports this conjecture.

math-ph↗
arXiv2012

Black Holes or Frozen Stars? A Viable Theory of Gravity without Black Holes

Do observations of black hole candidates rule out alternative theories of gravity without horizon formation? This depends on the existence, viability and reasonableness of alternative theories of gravity without black holes. Here a theory of gravity without black hole horizon formation is presented. The gravitational collapse stops shortly before horizon formation and leaves a stable frozen star. In the limit $Ξ, Υ\to 0$ the Einstein equations of GR are recovered, and the frozen stars become observationally indistinguishable from GR black holes. The theory therefore provides a counterexample to recent claims that observational evidence from black hole candidates "all but requires the existence of a horizon". The theory presented here shares its equations with RTG. Nonetheless, as is shown, there remain important conceptual and physical differences. In particular, some serious problems of RTG are not present in the theory proposed here. So it can be argued that the theory is a physically viable and conceptually sound alternative to GR.

physics.gen-ph↗
arXiv2010

On the blackhole dynamic potentials

In the following paper, certain blackhole dynamic potentials have been developed definitively on the lines of classical thermodynamics. These potentials have been refined in view of the small differences in the equations of the laws of blackhole dynamics as given by Bekenstein and those of thermodynamics. Nine fundamental blackhole dynamical relations have been developed akin to the four fundamental thermodynamic relations of Maxwell. The specific heats and have been defined. For a blackhole, these quantities are negative. The equation has been obtained as an application of these fundamental relations. Time reversible processes observing constancy of surface gravity are considered and an equation connecting the internal energy of the blackhole, the additional available energy defined as the first free energy function, and the surface gravity, has been obtained. Finally as a further application of the fundamental relations, it has been proved for a homogeneous gravitational field in blackhole spacetimes that . This is dubbed as the homogeneous fluid approximation in context of the blackholes.

physics.gen-ph↗
arXiv2010

Charged Black Holes and Constraints on Baryon Asymmetry

The no-hair theorem, which postulates that all black holes can be completely characterized by only three externally observable parameters: mass, electric charge, and angular momentum, sets constraints on both the maximal angular momentum and maximal electric charge. In this work, we would explore the consequence of these for the formation of primordial black holes in the early universe and also the formation of black holes due to collapse of dark matter configurations and how this could be used to probe the conditions in the very early universe and constrain the epoch when baryon asymmetry was established.

physics.gen-ph↗
arXiv2010

General Transformations of Space and Time according to Aether Theory

Assuming the existence of a preferred aether frame and the anisotropy of the one-way speed of light in platforms different from the aether frame, we derive the space and time transformations relative to bodies moving in any direction of space and not only in the direction of the common x-axis of the co-ordinate systems under consideration. Taking for granted length contraction and clock retardation, we show that the experimental space-time transformations result from measurement distortions due to the fact that the length of the rods and the frequency of the clocks, used for the measure, do not have a constant value as a result of their motion through the aether, and because the standard synchronization procedures are affected by a synchronism discrepancy effect. When the motion of bodies is aligned along the common x-axis, the transformations assume the same mathematical form as the conventional transformations. However, their meaning is quite different because they have been derived on the basis of very different assumptions, and they arise from the measurement distortions mentioned above. Therefore they conceal hidden variables which are the true transformations.

physics.gen-ph↗
arXiv2010

Universal Velocity and Universal Force

In his monumental discoveries, the driving force for Einstein was, I believe, consistency of concept and principle rather than conflict with experiment. Following this Einsteinian dictum, we would first argue that homogeneity (universal character) of space and time characterizes 'no force' (absence of force) and leads to existence of a universal velocity while inhomogeneity (again a universal property) characterizes curved spacetime and presence of a universal force which is present everywhere and always. The former gives rise to Special Relativity while the latter to General Relativity.

physics.gen-ph↗
arXiv2010

The second law of blackhole dynamics

In this paper, the non-generalized or restricted second law blackhole dynamics as given by Bekenstein in the beginning is restated, with a rigid proof, in a different form akin to the statement of the second law of thermodynamics given by Clausius. The various physical possibilities and implications of this statement are discussed therein. This paper is a mere venture into the restricted second law of blackhole dynamics pertaining to blackholes emitting Hawking radiation. The paper thus considers a didactically interesting reformulation of the second law of blackhole thermodynamics after some revisions.

physics.gen-ph↗
arXiv2010

Compensational Gravity Fundamentals and an Application: The Cycling Universe

Compensational gravity, which is regarded as a fundamental theory, is an advanced version of semiclassical gravity. It is a construction which extends the Einstein equation. Along with the energy-momentum tensor, the extended Einstein equation includes the compensation tensor, or compenson. The latter compensates for the energy-momentum tensor insufficiency, which consists in the discontinuity in time (due to quantum state reduction) and in space (due to sharp cutoff), as well as in an anomaly (nonrealistic state equation and nonzero divergence). The compenson is a primary object, for which equations are formulated. Specifically, purely dark objects may or may not exist. The dynamics of compensational gravity gives rise naturally to the cosmological constant, or dark energy and to dark matter: The compenson versus particle dark matter. On the basis of the dynamics, a cycling model of the closed universe is constructed.

physics.gen-ph↗
arXiv2010

Self-force and radial fall: new integration method for the Zerilli wave equation

We establish the jump conditions for the wavefunction and its derivatives through the formal solutions of the wave equation. These conditions respond to the requirement of continuity of the perturbations at the position of the particle and they are given for any mode at first order. Using these jump conditions, we then propose a new method for computing the radiated waveform without direct integration of the source term. We consider this approach potentially applicable to generic orbits.

gr-qc↗
arXiv2010

Black Hole Entropy Prediction without Immirzi Parameter

In our earlier paper "Corrections to the Bekenstein-Hawking entropy and the Hawking radiation spectrum", arXiv:0910.2755, we provided two concrete numerical evidences for the new area spectrum based on the Einstein-Kaufman pseudo tensor as opposed to the Ashtekar variables: namely, the reproduction of the Bekenstein-Hawking entropy without fixing Immirzi parameter and the reproduction of the Hawking radiation spectrum. In this article, we provide another concrete, numerical evidence for this new area spectrum; there was a constant in our earlier article, which was inversely proportional to the density of state, and which we could not fix a priori. Nevertheless, in our earlier article, we obtained this constant to be around 172~173 by fitting it to the Planck radiation spectrum. In this article, we calculate this value using another method. We obtain 172.87...which implies consistency.

physics.gen-ph↗
arXiv2010

Another possible interplay between gravitation and cosmology

I describe here some features of a non-geometrical approach to quantum gravity which leads to another picture of ties of gravitation and cosmology. The role of taking into account the effect of time dilation of the standard cosmological model is considered. It is shown that the correction for no time dilation leads to a good accordance of Supernovae 1a data and predictions of the considered model. The distributions of stretch factor values of Supernovae 1a for the cases of time dilation and no time dilation are discussed.

physics.gen-ph↗
arXiv2011

A model of possible gravitational confinement of fast light particles

According to special relativity and the equivalence principle, the Newtonian gravitational force between two particles with relativistic velocities increases significantly with velocity and in fact becomes unbound as the latter approaches c. One may thus construct a deterministic model of three fast rotating light particles which uses gravitation as the attractive force, special relativity, the weak equivalence principle and introduces angular momentum quantization as in the Bohr model of the H atom. The model shows the existence of stable rotational states corresponding to highly relativistic particle velocities with radii in the fm range. When the rest masses of the three light particles is in the mass range of neutrinos (~0.1 eV/c^2), then surprisingly the rest masses and Compton wavelengths of these rotational states are found to correspond to those of baryons and in fact the masses (~1 GeV/c^2) reproduce quite well the light baryon mass spectrum. Interestingly the model also predicts a lower limit for the lifetime of the baryons which is consistent with their measured lifetimes and yields a good approximation for their magnetic moments. It thus appears that this deterministic Bohr-type approach to subatomic phenomena, i.e. a classical special relativistic treatment coupled with the de Broglie wavelength expression to seek conformity with quantum mechanics, may be a useful zeroth-order model to explore some quantum gravity problems.

physics.gen-ph↗
arXiv2014

On a Broken Formal Symmetry between Kinetic and Gravitational Energy

Historically, the discovery of symmetries has played an important role in the progress of our fundamental understanding of nature. This paper will demonstrate that there exists in Newtonian theory in a spherical gravitational field a formal symmetry between the kinetic (KE) and gravitational potential energy (GPE) of a test mass. Put differently, there exists a way of expressing GPE such that the form of the mathematical expression remains invariant under an interchange of KE and GPE. When extended to relativity by a suitable assumption, it leads to a framework that bridges the general relativistic and Newtonian conceptions of gravitational energy, even though the symmetry is broken except in the infinitesimal limit. Recognizing this symmetry at infinitesimal scales makes it possible to write a relativistic equation of an individual graviton, the properties of which under under one interpretation may be unexpected.

physics.gen-ph↗