Physical Singularity Research Articles

Phase transitions in the complex plane of physical parameters.

At low temperature, a thermodynamic system undergoes a phase transition when a physical parameter passes through a singularity point of the free energy. This corresponds to the formation of a new order. At high temperature, thermal fluctuations destroy the order. Correspondingly, the free energy is a smooth function of the physical parameter and singularities only occur at complex values of the parameter. Since a complex valued parameter is unphysical, no phase transitions are expected when the physical parameter is varied. Here we show that the quantum evolution of a system, initially in thermal equilibrium and driven by a designed interaction, is equivalent to the partition function of a complex parameter. Therefore, we can access the complex singularity points of thermodynamic functions and observe phase transitions even at high temperature. We further show that such phase transitions in the complex plane are related to topological properties of the renormalization group flows of the complex parameters. This result makes it possible to study thermodynamics in the complex plane of physical parameters.

Axiom Cosmology: A New Direction

In this work we have to deal with the axiomatization of cosmology, but it is only recently that we have hit upon a new mathematical approach to capitalize on our new set identities for the basic laws of cosmology. So our proposal of settlement is that we will propose some new laws (e.g., formation of the black hole). We introduce the concept of axiom cosmology. This principle describes the cosmology which can get freedom from the notion of the induction. We present a large-scale structure model of the universe, and this leads to successfully explanation of problem of closed universe or open universe (because from the outset it is theorem and its succinct proof). In this paper we prove that the non-singular point theorem means that a singularity cannot be mathematically defined nor physical. It allows us to overcome the mysterious, physical singularity conundrum and explain meaningful antimatter annihilations for general configurations.

Entanglement temperature in non-conformal cases

Potential reconstruction can be used to find various analytical asymptotical AdS solutions in Einstein dilation system generally. We have generated two simple solutions without physical singularity called zero temperature solutions. We also proposed a numerical way to obtain black hole solution in Einstein dilaton system with special dilaton potential. By using this method, we obtain the corresponding black hole solutions numerically and investigate the thermal stability of the black hole by comparing the free energy of thermal gas and the corresponding black hole. In two groups of non-conformal gravity solutions obtained in this paper, we find that the two thermal gas solutions are more unstable than black hole solutions respectively. Finally, we consider black hole solutions as a thermal state of zero temperature solutions to check that the first thermal dynamical law exists in entanglement system from holographic point of view.

SINGULARITY STRUCTURE OF ${\mathcal N} = 2$ SUPERSYMMETRIC YANG–MILLS THEORIES

In this paper, we consider the case where electrons, magnetic monopoles and dyons become massless. Here, we consider the [Formula: see text] supersymmetric Yang–Mills (SYM) theories with classical gauge groups with a rank r, SU(r+1), SO(2r), Sp(2r) and SO(2r+1) which are studied by Riemann surfaces called Seiberg–Witten curves. We discuss physical singularity associated with massless particles, which can be studied by geometric singularity of vanishing 1-cycles in Riemann surfaces in hyperelliptic form. We pay particular attention to the cases where mutually nonlocal states become massless (Argyres–Douglas theories), which corresponds to Riemann surfaces degenerating into cusps. We discuss nontrivial topology on the moduli space of the theory, which is reflected as monodromy associated to vanishing 1-cycles. We observe how dyon charges get changed as we move around and through singularity in moduli space.

A Non-geometric Relativistic Theory of Gravitation

A non-geometric relativistic theory of gravitation is developed by defining a semi-metric to replace the metric tensor as gravitational vector potential. The theory show that the energy-momentum tensor of the gravitational field belong to the gravitational source, gravitational radiation is contained in Einstein’s field equations that including the contribution of gravitational field, the real physical singularity in the gravitational field can be eliminated, and the dark matter in the universe is interpreted as the matter of pure gravitational field.

Siva’s Equation for Singularity of Black Holes

Classical equation for space time and matter gives the relation between a mass and the space time surrounded by its space time fluid. Mass of the basic building block of matter creation has been termed as ‘K-Suryon’. Mass of ‘K-Suryon’ has been calculated as 1.15x10-64 kgs. The density of its space time fluid is calculated as 3.32x10626 Kg/cum. Thus ‘K-Suryon’ is the most elementary mass that can exist in this universe. We know the minimum mass of anybody to become black hole is ‘Chandrasekhar’s Limit’ .For that mass we can calculate the space time fluid density. So we can find the density of space time fluid associated with it. With these calculations we have concluded that the physical singularity will not be there for a black hole. A physical singularity will exist below a critical density equal to K-Suryon where space time will not exist. It is concluded that velocity of light is reducing and space time fluid density of universe is increasing with the age of Universe. Experimental verification may be possible.

Solving the Axial Line Problem for Fast Computation of Mixed Potential Green's Functions for Cylindrically Stratified Media

An improved approach is proposed for solving the axial line problem (|ρ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">→</sup> -ρ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">→</sup> | = 0) of mixed potential Green's functions (MPGFs) in spatial domain for cylindrically stratified media. Different from the previous work, to alleviate the convergence problem of the summation of cylindrical eigenmodes in the spectral domain, two asymptotic terms with respect to <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> are extracted analytically. In this way, the higher order nonphysical singularities with respect to |ρ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">→</sup> - ρ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">→</sup> | are proven to vanish, and the lower order physical singularities can be transformed into the spatial domain completely using the Sommerfeld identity. Therefore, the remaining parts of the summation are free of singularities related to |ρ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">→</sup> - ρ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">→</sup> | and fast convergent, which can be easily transformed into closed-form spatial-domain expressions by applying the generalized pencil of function method. The present approach can be used to accurately calculate the spatial domain MPGFs over the entire cylindrical surface. Several numerical results are presented to verify the accuracy and efficiency of this approach.

Adversus Singularitates: The Ontology of Space–Time Singularities

I argue that there are no physical singularities in space–time. Singular space–time models do not belong to the ontology of the world, because of a simple reason: they are concepts, defective solutions of Einstein’s field equations. I discuss the actual implication of the so-called singularity theorems. In remarking the confusion and fog that emerge from the reification of singularities I hope to contribute to a better understanding of the possibilities and limits of the theory of general relativity.

Well-Posedness in Smooth Function Spaces for the Moving-Boundary Three-Dimensional Compressible Euler Equations in Physical Vacuum

We prove well-posedness for the three-dimensional compressible Euler equations with moving physical vacuum boundary, with an equation of state given by p(ρ) = C γ ρ γ for γ > 1. The physical vacuum singularity requires the sound speed c to go to zero as the square-root of the distance to the moving boundary, and thus creates a degenerate and characteristic hyperbolic free-boundary system wherein the density vanishes on the free-boundary, the uniform Kreiss–Lopatinskii condition is violated, and manifest derivative loss ensues. Nevertheless, we are able to establish the existence of unique solutions to this system on a short time-interval, which are smooth (in Sobolev spaces) all the way to the moving boundary, and our estimates have no derivative loss with respect to initial data. Our proof is founded on an approximation of the Euler equations by a degenerate parabolic regularization obtained from a specific choice of a degenerate artificial viscosity term, chosen to preserve as much of the geometric structure of the Euler equations as possible. We first construct solutions to this degenerate parabolic regularization using a higher-order version of Hardy’s inequality; we then establish estimates for solutions to this degenerate parabolic system which are independent of the artificial viscosity parameter. Solutions to the compressible Euler equations are found in the limit as the artificial viscosity tends to zero. Our regular solutions can be viewed as degenerate viscosity solutions. Our methodology can be applied to many other systems of degenerate and characteristic hyperbolic systems of conservation laws.

Curvature invariants, geodesics, and the strength of singularities in Bianchi-I loop quantum cosmology

We investigate the effects of the underlying quantum geometry in loop quantum cosmology on spacetime curvature invariants and the extendibility of geodesics in the Bianchi-I model for matter with a vanishing anisotropic stress. Using the effective Hamiltonian approach, we find that even though quantum geometric effects bound the energy density and expansion and shear scalars, divergences of curvature invariants are potentially possible under special conditions. However, as in the isotropic models in LQC, these do not necessarily imply a physical singularity. Analysis of geodesics and strength of such singular events, point towards a general resolution of all known types of strong singularities. We illustrate these results for the case of a perfect fluid with an arbitrary finite equation of state $w > -1$, and show that curvature invariants turn out to be bounded, leading to the absence of strong singularities. Unlike classical theory, geodesic evolution does not break down. We also discuss possible generalizations of sudden singularities which may arise at a non-vanishing volume, causing a divergence in curvature invariants. Such finite volume singularities are shown to be weak and harmless.

Emergence of a thin shell structure during collapse in isotropic coordinates

Numerical studies of gravitational collapse in isotropic coordinates have recently shown an interesting connection between the gravitational Lagrangian and black hole thermodynamics. A study of the actual spacetime was not the main focus of this work and, in particular, the rich and interesting structure of the interior has not been investigated in much detail and remains largely unknown. We elucidate its features by performing a numerical study of the spacetime in isotropic coordinates during gravitational collapse of a massless scalar field. The most salient feature to emerge is the formation of a thin shell of matter just inside the apparent horizon. The energy density and Ricci scalar peak at the shell and there is a jump discontinuity in the extrinsic curvature across the apparent horizon, the hallmark that a thin shell is present in its vicinity. At late stages of the collapse, the spacetime consists of two vacuum regions separated by the thin shell. The interior is described by an interesting collapsing isotropic universe. It tends towards a vacuum (never reaches a perfect vacuum) and there is a slight inhomogeneity in the interior that plays a crucial role in the collapse process as the areal radius tends to zero. The spacetime evolves towards a curvature (physical) singularity in the interior, both a Weyl and Ricci singularity. In the exterior, our numerical results match closely the analytical form of the Schwarzschild metric in isotropic coordinates, providing a strong test of our numerical code.

The Inert vs. the Living State of Matter: Extended Criticality, Time Geometry, Anti-Entropy – An Overview

The physical singularity of life phenomena is analyzed by means of comparison with the driving concepts of theories of the inert. We outline conceptual analogies, transferals of methodologies and theoretical instruments between physics and biology, in addition to indicating significant differences and sometimes logical dualities. In order to make biological phenomenalities intelligible, we introduce theoretical extensions to certain physical theories. In this synthetic paper, we summarize and propose a unified conceptual framework for the main conclusions drawn from work spanning a book and several articles, quoted throughout1.

Phase transitions at finite density

I discuss the analytic structure of thermodynamic quantities for complex values of thermodynamic variables within Landau theory. In particular, the singularities connected with phase transitions of second order, first order and cross over types are examined. A conformal mapping is introduced, which may be used to explore the thermodynamics of strongly interacting matter at finite values of the baryon chemical potential $\mu$ starting from lattice QCD results at $\mu^{2}\leq 0$. This method allows us to improve the convergence of a Taylor expansion about $\mu=0$ and to enhance the sensitivity to physical singularities in the complex $\mu$ plane. The technique is illustrated by an application to a second-order transition in a chiral effective model.

Obtaining one-loop gravity amplitudes using spurious singularities

The decomposition of a one-loop scattering amplitude into elementary functions with rational coefficients introduces spurious singularities which afflict individual coefficients but cancel in the complete amplitude. These cancellations create a web of interactions between the various terms. We explore the extent to which entire one-loop amplitudes can be determined from these relationships starting with a relatively small input of initial information, typically the coefficients of the scalar integral functions as these are readily determined. In the context of one-loop gravity amplitudes, of which relatively little is known, we find that some amplitudes with a small number of legs can be completely determined from their box coefficients. For increasing numbers of legs, ambiguities appear which can be determined from the physical singularity structure of the amplitude. We illustrate this with the four-point and N=1,4 five-point (super)gravity one-loop amplitudes.

Probing quantum geometry at LHC

We present an evidence, that the volumes of compactified spaces as well as the areas of black hole horizons must be quantized in Planck units. This quantization has phenomenological consequences, most dramatic being for micro black holes in the theories with TeV scale gravity that can be produced at LHC. We predict that black holes come in form of a discrete tower with well defined spacing. Instead of thermal evaporation, they decay through the sequence of spontaneous particle emissions, with each transition reducing the horizon area by strictly integer number of Planck units. Quantization of the horizons can be a crucial missing link by which the notion of the minimal length in gravity eliminates physical singularities. In case when the remnants of the black holes with the minimal possible area and mass of order few TeV are stable, they might be good candidates for the cold dark matter in the Universe.

Mediterranean saline streams in southeast Spain: What do we know?

Many Mediterranean streams in arid and semiarid areas are naturally saline systems due to the presence of evaportic rocks of Miocene or Triassic origin. Despite the fact that these aquatic ecosystems are rare in Europe, they are common in southeast of Spain. The environmental constraints of these semiarid saline streams are imposed by both geological and climatic conditions. This paper is a compilation and summary of the principal results obtained from various studies on semiarid saline streams in the Iberian southeast. Available data for these typical environments in the region covers diverse issues such as those regarding their physical and chemical features, typology, biodiversity, community structure and ecosystem functioning, as well as different ecological and evolutionary aspects of their biota (e.g. ecophysiological responses, life cycles and phylogeography). Issues concerning the conservation of these habitats, such as the main human uses, impacts, threats and their management are also summarised. Finally, topics in need of further research are provided. The current knowledge of saline streams in southeastern Spain highlights the physical and ecological singularity of these environments, and their high conservation value. Saline streams are particularly interesting due to their halotolerant/halophilic biota and high number of rare and endemic species.

Well‐posedness in smooth function spaces for moving‐boundary 1‐D compressible euler equations in physical vacuum

AbstractThe free‐boundary compressible one‐dimensional Euler equations with moving physical vacuum boundary are a system of hyperbolic conservation laws that are both characteristic and degenerate. The physical vacuum singularity (or rate of degeneracy) requires the sound speed $c^2= \gamma \rho^{ \gamma -1}$ to scale as the square root of the distance to the vacuum boundary and has attracted a great deal of attention in recent years. We establish the existence of unique solutions to this system on a short time interval, which are smooth (in Sobolev spaces) all the way to the moving boundary. The proof is founded on a new higher‐order, Hardy‐type inequality in conjunction with an approximation of the Euler equations consisting of a particular degenerate parabolic regularization. Our regular solutions can be viewed as degenerate viscosity solutions. © 2010 Wiley Periodicals, Inc.

Time-periodic solutions of the Einstein’s field equations III: physical singularities

In this paper we construct a new time-periodic solution of the vacuum Einstein’s field equations, this solution possesses physical singularities, i.e., the norm of the solution’s Riemann curvature tensor takes the infinity at some points. We show that this solution is intrinsically time-periodic and describes a time-periodic universe with the “time-periodic physical singularity”. By calculating the Weyl scalars of this solution, we investigate new physical phenomena and analyze new singularities for this universal model.

Gravitational collapse and topology change in spherically symmetric dynamical systems

A new numerical framework, based on the use of a simple first-order strongly hyperbolic evolution equations, is introduced and tested in the case of four-dimensional spherically symmetric gravitating systems. The analytic setup is chosen such that our numerical method is capable of following the time evolution even after the appearance of trapped surfaces, more importantly, until the true physical singularities are reached. Using this framework, the gravitational collapse of various gravity-matter systems is investigated, with particular attention to the evolution in trapped regions. It is verified that, in advance of the formation of these curvature singularities, trapped regions develop in all cases, thereby supporting the validity of the weak cosmic censor hypothesis of Penrose. Various upper bounds on the rate of blow-up of the Ricci and Kretschmann scalars and the Misner–Sharp mass are provided. In spite of the unboundedness of the Ricci scalar, the Einstein–Hilbert action was found to remain finite in all the investigated cases. In addition, important conceptual issues related to the phenomenon of topology changes are discussed.

A New Solution to Einstein's Field Equations

We construct a new exact solution to the vacuum Einstein field equations. This solution possesses a naked physical singularity. The norm of the Riemann curvature tensor of the solution takes infinity at some points and the solution does not have any event horizon around the singularity. A detailed analysis of this new singularity is also presented.