Physical Singularity Research Articles

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.

Are loop quantum cosmos never singular?

A unified treatment of all known types of singularities for flat, isotropic and homogeneous spacetimes in the framework of loop quantum cosmology (LQC) is presented. These include bangs, crunches and all future singularities. Using effective spacetime description we perform a model-independent general analysis of the properties of curvature, behavior of geodesics and strength of singularities. For illustration purposes a phenomenological model based analysis is also performed. We show that all values of the scale factor at which a strong singularity may occur are excluded from the effective loop quantum spacetime. Further, if the evolution leads to either a vanishing or divergent scale factor then the loop quantum universe is asymptotically deSitter in that regime. We also show that there exists a class of sudden extremal events, which includes a recently discussed possibility, for which the curvature or its derivatives will always diverge. Such events however turn out to be harmless weak curvature singularities beyond which geodesics can be extended. Our results point toward a generic resolution of physical singularities in LQC.

Well‐posedness for compressible Euler equations with physical vacuum singularity

AbstractAn important problem in the theory of compressible gas flows is to understand the singular behavior of vacuum states. The main difficulty lies in the fact that the system becomes degenerate at the vacuum boundary, where the characteristic speeds u ± c coincide and have unbounded spatial derivative since c behaves like x1/2 close to the boundary. In this paper, we overcome this difficulty by presenting a new formulation and new energy spaces. We establish the local‐in‐time well‐posedness of one‐dimensional compressible Euler equations for isentropic flows with the physical vacuum singularity in some spaces adapted to the singularity. © 2009 Wiley Periodicals, Inc.

Fisher zeros in the Kallen–Lehmann approach to 3D Ising model

The distribution of the Fisher zeros in the Kallen–Lehmann approach to three-dimensional Ising model is studied. It is argued that the presence of a non-trivial angle (a cusp) in the distribution of zeros in the complex temperatures plane near the physical singularity is realized through a strong breaking of the 2D Ising self-duality. Remarkably, the realization of the cusp in the Fisher distribution ultimately leads to an improvement of the results of the Kallen–Lehmann ansatz. In fact, excellent agreement with Monte Carlo predictions both at high and at low temperatures is observed. Besides, agreement between both approaches is found for the predictions of the critical exponent α and of the universal amplitude ratio Δ=A+/A−, within the 3.5% and 7% of the Monte Carlo predictions, respectively.

The Archaic Universe: Big Bang, Cosmological Term and the Quantum Origin of Time in Projective Cosmology

This article proposes some cosmological reflections at the qualitative and conjectural level, suggested by the Fantappié-Arcidiacono projective relativity theory. The difference will firstly be discussed between two types of singularity in this theory: geometric (de Sitter horizon) and physical (big bang, big crunch). The reasons for the existence of geometric singularities are deeply rooted in the principle of inertia and in the principle of relativity, while physical singularities are associated with the creation or destruction of matter.In this framework, quantum mechanics is introduced through a particular interpretation of Bohm’s holomovement. Finally, a possible mechanism is discussed for the genesis of the cosmological term. No form of inflation appears in the scenario described.

Study on Path Planning for Industrial Robots in Free-Form Surfaces Polishing

Expected path of polishing tool is one of the most essential needs for movement scheduling and movement controlling of polishing robot in free-form surfaces polishing. By analyzing the expected movement and position of polishing tool and based on the traditional movement scheduling methods, this paper carries out systematic research works on contour-parallel-machining tool path planning method and direction-parallel-machining tool path planning method for polishing tool paths figuring out. Compared with contour-parallel-machining tool path planning method, the direction-parallel-machining tool path planning method needs one less number of degree of freedom and is much easier to avoid physical interventions and mechanic singularity, so it is an improved one.

Homotopy Approach to Quantum Gravity

Gravity may be a quantum-space-time effect. General relativity is quantized by small generic changes in its commutation relations that make its Lie algebras simple on all levels, positing extra variables frozen by self-organization as needed. This quantizes space-time coordinates as well as fields and eliminates physical singularities. Fermi statistics and sl (nℝ) Lie algebras are assumed for all levels. Spin 1/2 is taken to be anomalous, arising from vacuum organization; the spin-statistics relation is incorporated. The gravitational field is quartic in Fermi variables. Einstein’s non-commutativity of parallel transport emerges as a vestige of Heisenberg’s quantum non-commutativity near the classical limit.

Martin David Kruskal

Martin David Kruskal

Nonlinear Formation-Keeping and Mooring Control of Multiple Autonomous Underwater Vehicles

This paper deals with the nonlinear formation-keeping and mooring control of multiple autonomous underwater vehicles (AUVs) in chained form. The AUV formation under consideration is constrained by the desired separations and orientations of follower AUVs with respect to a time-varying leader AUV. First, a time-varying, smooth feedback control law for the formation-keeping of multiple nonholonomic AUVs is presented by taking advantage of the Lyapunov direct method. Its asymptotical convergence to a desired formation trajectory prescribed by a leader-follower pair is guaranteed. Second, a time-varying, smooth feedback control law with asymptotic stability is designed to collaboratively moor the follower AUV to its desired docking position and orientation with respect to the leader by using the integrator backstepping method. Third, the realization problems of physical AUV system and singularity avoidance are investigated for applying the aforementioned control laws to a real formation system of AUVs. Finally, simulation results are provided to illustrate the effectiveness of the proposed control laws

ON THE SUPERSTRING BLACK HOLE

The effective Lagrangian for the heterotic superstring theory of Gross et al. contains higher-derivative gravitational terms [Formula: see text], n ≥ 2, which become important at large curvatures. This leads to a natural realization of the limiting-curvature hypothesis of Frolov et al., which was formulated to describe the interior of black holes. Assuming a purely geometrical, four-dimensional Schwarzschild black hole, for which all matter fields are zero, this interior consists of two regions: a shell of effective energy-density ρ immediately beyond the event horizon at r+ = 2M, due to the back reaction of the [Formula: see text] on the Schwarzschild metric, extending inward to a transition radius r0 ≈ M⅓, where the shell signature (- + - -) reverts to the exterior Lorentzian form (+ - - -), and an innermost core tending asymptotically to anti-de Sitter space as r → 0. The total mass-energy content of the hole M can be expressed in terms of the effective energy–momentum tensor Sij as the Nordström mass [Formula: see text], since the space–time is static and free of physical singularities. The conjecture that ρ N (r) is positive in the shell, which is necessary for the contribution to M N to be positive, is shown to be true for the term [Formula: see text], due to the unrenormalized [Formula: see text]. The corresponding "potential" energy–momentum tensor calculated in the Schwarzschild background is isotropic in the region r0 ≪ r ≪ r+, where [Formula: see text], while the dominant "kinetic" contribution is [Formula: see text], so that [Formula: see text].

On the theory of gravitationally-frozen superdense and supermassive objects

The black hole paradigm (BHP) is based on an implicit assumption that the collapse occurs quickly not only on proper times of falling particles, but on world time also, and that information about that is retarded only. According to general relativity (GR) in a static field there is a global simultaneity of events, the proper times are slowed down with respect to world time absolutely and these facts are confirmed experimentally by clocks long-term located at different heights. Therefore, the basic assumption of BHP is incompatible with GR, the collapse occurs not quickly, but it needs in really infinity world time. For a falling particle at any finite world time moment its corresponding proper time moment is insufficient for reaching the gravitational radius of the source. As the result, in GR real horizons and physical singularities do not exist, the black holes never be formed. Instead of the black holes GR predicts the gravitationally-frozen states of matter in superdense and supermassive objects. Particles inside of any compact object are frozen by the strong gravitational field so that the time dilation is finite, but maximal at the center and minimal on the surface. In cosmology this fact solves the problem of an initial singularity, in astrophysics allows one to construct a theory of superdense stars, quasars and AGN, in particle physics leads to the ultraviolet finiteness of quantum fields, including quantum gravity. PACS: 95.30.Sf, 97.60.Lf, 98.35.Jk, 98.54.-h, 98.80.-k, 04.60.-m

Challenging the Paradigm of Singularity Excision in Gravitational Collapse

A paradigm deeply rooted in modern numerical relativity calculations prescribes the removal of those regions of the computational domain where a physical singularity may develop. We here challenge this paradigm by performing three-dimensional simulations of the collapse of uniformly rotating stars to black holes without excision. We show that this choice, combined with suitable gauge conditions and the use of minute numerical dissipation, improves dramatically the long-term stability of the evolutions. In turn, this allows for the calculation of the waveforms well beyond what was previously possible, providing information on the black-hole ringing and setting a new mark on the present knowledge of the gravitational-wave emission from the stellar collapse to a rotating black hole.

An explanation of the peculiar behavior of TSDC peaks at Tg: a simple model of entropy relaxation

Thermally stimulated depolarization current (TSDC) signals measured in polymers at the glass transition Tg often exhibit intricate shapes that much depend on the thermal history and on the non-stationary condition used during experiments. This peculiar behavior is frequently explained in terms of a physical singularity of the molecular motions. We show that this singularity, i.e. unexpected values for activation energy and pre-exponential factor, obtained around Tg, result from the misuse of the Arrhenius law for treating the experimental data obtained in non-stationary experimental conditions. A simple model using time dependent configurational entropy for the material evolution and using a single Debye relaxation for the dielectric relaxation process is therefore proposed to explain the experimental behavior. The influence of the heating rate and of a non-Debye relaxation on the TSDC signal is also studied and clearly shows that the peculiar behavior of TSDC peaks can originate from the conjugated effects of entropy relaxation and non-Debye response

An explanation of the peculiar behavior of TSDC peaks at Tg: a simple model of entropy relaxation

Thermally stimulated depolarization current (TSDC) signals measured in polymers at the glass transition T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g</sub> often exhibit intricate shapes that much depend on the thermal history and on the non-stationary condition used during experiments. This peculiar behavior is frequently explained in terms of a physical singularity of the molecular motions. We show that this singularity, i.e. unexpected values for activation energy and pre-exponential factor, obtained around T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g</sub> , result from the misuse of the Arrhenius law for treating the experimental data obtained in non-stationary experimental conditions. A simple model using time dependent configurational entropy for the material evolution and using a single Debye relaxation for the dielectric relaxation process is therefore proposed to explain the experimental behavior. The influence of the heating rate and of a non-Debye relaxation on the TSDC signal is also studied and clearly shows that the peculiar behavior of TSDC peaks can originate from the conjugated effects of entropy relaxation and non-Debye response

Numerical generation and grid controls of boundary‐fitted conformal grids in multiply connected regions

AbstractBased on the study of grid generation methods in a simply connected region (Int. J. Numer. Meth. Engng 1997; 40:343), with the aid of a new transformation from a multiply connected region to a simply connected domain, the grid generation in a multiply connected domain is carried out in this paper. 2‐D conformal and orthogonal grids are generated in a multiply connected region, mostly involving a multiple‐blocks method developed in the present study. To avoid grid distortion on the degenerated boundary caused by physical singularities, controls of grids through specified points are implemented, without losing the conformal properties. Further applications of this grids‐controlling technique for points inside the region, the nested grids, and the multiple‐blocks method are introduced and discussed comprehensively. Numerical examples are taken to demonstrate the validity and applicability of the theorems. Copyright © 2006 John Wiley &amp; Sons, Ltd.

Hydraulic jump as a white hole

In the geometry of the circular hydraulic jump, the velocity of the liquid in the interior region exceeds the speed of capillary-gravity waves (ripplons), whose spectrum is `relativistic' in the shallow water limit. The velocity flow is radial and outward, and thus the relativistic ripplons cannot propagating into the interior region. In terms of the effective 2+1 dimensional Painleve-Gullstrand metric appropriate for the propagating ripplons, the interior region imitates the white hole. The hydraulic jump represents the physical singularity at the white-hole horizon. The instability of the vacuum in the ergoregion inside the circular hydraulic jump and its observation in recent experiments on superfluid 4He by E. Rolley, C. Guthmann, M.S. Pettersen and C. Chevallier in physics/0508200 are discussed.

Two-loop superstrings V Gauge slice independence of the N-point function

A systematic construction of superstring scattering amplitudes for N massless NS bosons to two loop order is given, based on the projection of supermoduli space onto superperiod matrices used earlier for the superstring measure in the first four papers of this series. The one important new difficulty arising for the N-point amplitudes is the fact that the projection onto superperiod matrices introduces corrections to the chiral vertex operators for massless NS bosons which are not pure ( 1 , 0 ) differential forms. However, it is proved that the chiral amplitudes are closed differential forms, and transform by exact differentials on the worldsheet under changes of gauge slices. Holomorphic amplitudes and independence of left from right movers are recaptured after the extraction of terms which are Dolbeault exact in one insertion point, and de Rham closed in the remaining points. This allows a construction of GSO projected, integrated superstring scattering amplitudes which are independent of the choice of gauge slices and have only physical kinematical singularities.

Physics of the interior of a spherical, charged black hole with a scalar field

We analyze the physics of nonlinear gravitational processes inside a spherical charged black hole perturbed by a self-gravitating massless scalar field. For this purpose we created an appropriate numerical code. Throughout the paper, in addition to investigation of the properties of the mathematical singularities where some curvature scalars are equal to infinity, we analyze the properties of the physical singularities where the Kretschmann curvature scalar is equal to the Planckian value. Using a homogeneous approximation we analyze the properties of the spacetime near a spacelike singularity in spacetimes influenced by different matter contents, namely, a scalar field, pressureless dust and matter with ultrarelativistic isotropic pressure. We also carry out full nonlinear analyses of the scalar field and geometry of spacetime inside black holes by means of an appropriate numerical code with adaptive mesh refinement capabilities. We use this code to investigate the nonlinear effects of gravitational focusing, mass inflation, matter squeeze, and these effects dependence on the initial boundary conditions. It is demonstrated that the position of the physical singularity inside a black hole is quite different from the positions of the mathematical singularities. In the case of the existence of a strong outgoing flux of the scalar field inside a black hole it is possible to have the existence of two null singularities and one central $r=0$ singularity simultaneously.

A simple model of entropy relaxation for explaining effective activation energy behavior below the glass transition temperature

Strong changes in relaxation rates observed at the glass transition region are frequently explained in terms of a physical singularity of the molecular motions. We show that the unexpected trends and values for activation energy and preexponential factor of the relaxation time tau, obtained at the glass transition from the analysis of the thermally stimulated current signal, result from the use of the Arrhenius law for treating the experimental data obtained in nonstationary experimental conditions. We then demonstrate that a simple model of structural relaxation based on a time dependent configurational entropy and Adam-Gibbs relaxation time is sufficient to explain the experimental behavior, without invoking a kinetic singularity at the glass transition region. The pronounced variation of the effective activation energy appears as a dynamic signature of entropy relaxation that governs the change of relaxation time in nonstationary conditions. A connection is demonstrated between the peak of apparent activation energy measured in nonequilibrium dielectric techniques, with the overshoot of the dynamic specific heat that is obtained in calorimetry techniques.

ON THE EXISTENCE OF TURNING POINTS IN d-DIMENSIONAL SCHWARZSCHILD–De SITTER AND ANTI-De SITTER SPACETIMES

We investigate the motion of a test particle in a d-dimensional, spherically symmetric and static spacetime supported by a mass M plus a Λ-term. The motion is strongly dependent on the sign of Λ. In Schwarzschild–de Sitter (SdS) space–time (Λ&gt;0), besides the physical singularity at r=0 there are cases with two horizons and two turning points, one horizon and one turning point and the complete absence of horizon and turning points. For Schwarzschild–Anti de Sitter (SAdS) spacetime (Λ&lt;0) the horizon coordinate is associated to an unique turning point.