Does the Principle of Equivalence Prohibit Trapped Surfaces from Forming in the General Relativistic Collapse Process?

It has recently been shown that time-like spherical collapse of a physical fluid in General Relativity does not permit formation of trapped surfaces. This result followed from the fact that the formation of a trapped surface in a physical fluid would cause the time-like world lines of the collapsing fluid to become null at the would-be trapped surface, thus violating the Principle of Equivalence in General Theory of Relativity (GTR). For the case of the spherical collapse of a physical fluid, the no trapped surface condition 2GM(r, t)/R(r, t) c ²<1 was found to be required to be satisfied in all regions of spacetime, where R(r, t) is the invariant circumference variable, r is a co-moving radial coordinate and M(r, t) is the gravitational mass confined within the radius r. The above result was obtained by treating the problem from the viewpoint of an internal co-moving observer at radius r. The boundary of the fluid at r _s=R _s(r _s, t) must also behave in a similar manner, and an external stationary observer should be able to obtain a similar no trapped surface relationship. Accordingly, we generalize this analysis by studying the problem of a time-like collapsing radiating plasma from the point of view of the exterior stationary observer. We find the Principle of Equivalence implies that the physical surface surrounding the plasma must obey 1/(1+z _s)>0, where z _s is the surface red shift seen by a zero-angular momentum observer. When this condition is applied to the first integral of the time-time component of the Einstein equation, it leads to the no trapped surface condition 2GM(r _s, t)/R(r _s, t) c ²<1 consistent with the condition obtained above for the interior co-moving metric. The Principle of Equivalence enforces the no trapped surface condition by constraining the physics of the general relativistic radiation transfer process in a manner that requires it to establish and maintain an Eddington limited secular equilibrium on the dynamics of the collapsing radiating surface so as to always keep the physical surface of the collapsing object outside of its Schwarzschild radius. The important physical implication of the no trapped surface condition is that galactic black hole candidates GBHC do not possess event horizons and hence do possess intrinsic magnetic fields. In this context the spectral characteristics of galactic black hole candidates offer strong evidence that their central nuclei are highly red-shifted Magnetospheric Eternally Collapsing Objects (MECO) within the framework of General Relativity.     

Gelfand Pairs with Coherent States

The notion of solvable Gelfand pairs (K,N) (K is a compact Lie group acting on N, a solvable connected and simply connected Lie group) is due to Benson, Jenkins and Ratcliff. Thanks to the localization lemma, they came back to the case where K is a connected subgroup of U(n) acting on N = Hn, the 2n + 1-dimensional Heisenberg group. They gave a geometrical condition for such a pair: (K,Hn) is a Gelfand pair if and only if the intersection of each coadjoint orbit of G = K Hn with (Lie K) contains at most one integral K-orbit. Using coherent states, we define here a generating function of multiplicity m for each in K^. m is holomorphic on D(0,1), m (r) = n = 0 an rn, an and limr 1 m (r) = mtp (, W) (W is the generic representation of Hn naturally extended to K). (K,Hn) is thus a Gelfand pair if and only if limr 1 m 1. We prove here that if m is a non homogeneous function, then there is at least two K-orbits in the intersection of the generic coadjoint orbit associated to with (Lie K).     

Current distributions in a two-dimensional random-resistor network

The current and logarithm-of-the-current distributionsn(i) andn(ln i) on bond diluted two-dimensional random-resistor networks at the percolation threshold are studied by a modified transfer matrix method. Thek th moment (–9k8) of n(ln i) i.e., ln i&^k, is found to scale with the linear sizeL as (InL)^(k). The exponents (k) are not inconsistent with the recent theoretical prediction (k)=k, with deviations which may be attributed to severe finitesize effects. For small currents, ln n(y)–, yielding information on the threshold below which the multifractality of (i) breaks down. Our numerical results for the moments of the currents are consistent with other available results.     

A new experimental approach to Mach's principle and relativistic graviation

As noted many years ago by Sciama, and more recently by Nordtvedt, Lorentz invariant (relativistic) gravitation at linear order involves a vector potential that is required to properly account for large inertial effects as well as the correct prediction of the classical tests of general relativity theory (GRT). It is pointed out that the linear-order vector aspect of the gravitational potential makes possible a simple, powerful and inexpensive technique for testing the predictions of GRT and associated issues. An experiment using this technique gives preliminary results that, to order of magnitude, corroborate GRT.1. If one demands a theory that satisfies Mach's Principle irrespective of the particular value of _c, one must go to a theory that contains GRT with critical cosmic matter density as a special case. Such a theory (an Einstein-Cartan theory with teleparallelism) has been developed by Treder [2].2. Equation (4) here is Nordtvedt's Eq. (14), in Ref. 3, with GRT PPN parameters chosen.3. The exact value of this correction factor that depends on the way in which energy is distributed between field and sources in turn depends on how the source term for the gravitational field equations is constructed. At least two different source terms that give correct predictions for the various tests of GRT exist. In this connection see Peters [4]. This ambiguity does not mean that it is impossible in principle to determine how energy is distributed between sources and field. Indeed, if one posits the existence of critical cosmic matter density, this experiment can decide the issue.     

Distance and the conventionality of simultaneity in special relativity

The conventionality of simultaneity within inertial frames is presented in a general formalism that clarifies the relationship of spatial measures to the choice of simultaneity. A number of claims that such measures undermine the conventional nature of simultaneity are presented and shown to be unfounded. In particular, a recent claim by Coleman and Korte [9] that such measures empirically establish a unique simultaneity relationship is shown to be in error. In addition, the general formalism enables the empirical status of simultaneity within an inertial frame to be clarified by presenting the choice of simultaneity as a gauge choice.1. Recent introductions to the literature have been given by Redhead [35], Ungar [47], Havas [21], and Vetharaniam and Stedman [48].2. The conventionalist position is by no means a uniform one, and in particular, it is worth noting an important distinction exemplified in the respective positions of Reichenbach and Grünbaum. For Reichenbach [37, p. 144f.] we have no empirical access to the one-way speed of light due to the nature of light as a first signal, and the conventionality comes from our absence ofknowledge about the one-way speed of light. For Grünbaum the one-way speed of light is actually objectively undetermined, and the physical attributes that sustain a speed in a given direction are non-existent. See, for example, [16, p. 87] and [17, p. 352]. Discussions of the differences between the positions of Reichenbach and Grünbaum may be found in [14] and [35]. Naturally, one may adhere to a position espoused by Reichenbach without the added ontological commitment of Grünbaum.3. Our is equivalent to (1 - 2), where is the symbol introduced by Reichenbach and customarily used in the discussions of the conventionality of simultaneity.4. An exposition of this argument may be found in the recent text by Lucas and Hodgson [28].5. Schrödinger [42, p. 78] has aptly labeled this quantity the distance of simultaneity.6. Examples of previous uses space-dependent synchrony parameters may be found in studies by Clifton [8], Havas [21], Anderson and Stedman [1], and Stedman [43; 44, § 2].7. This approach has been reviewed by Basri in [4] and [3].8. A number of faulty assessments of the empirical status of the conventionality of simultaneity may be similarly traced at least in part to overly simplistic assumptions on the nature of as Havas [21] and Clifton [8], for example, have had occasion to point out.9. See, for example, [1]. Kinematic formula relating other quantities in a treatment of STR without the standard convention on the one-way speed of light were first derived by Winnie [53].10. In comparison to other space dependent treatments of the synchrony parameter, ourh is analogous to defined by Clifton in Eq. (15) of [8], and equivalent to -f defined by Havas in Eq. (A1) of [21] and to defined in Eq. (6) of our earlier treatment in [1]. We take this opportunity to mention that the irrotational property ofh was inadvertently referred to as solenoidal in this work.11. Equation (26) is equivalent to Møller's expression in § 8.8 of [32] for the speed of light in terms of the metric components where our-h _i is equivalent to Møller's _i (g _i0)/ .12. Note as well, the expression of this operation in standard texts on STR by Rindler [38, pp. 27–28] and Mermin [30, p. 79] respectively: To measure the rod's length in any inertial frame in which it moves longitudinally, its end-point must be observed simultaneously... and, ...a measurement of the length of a moving meter stick involves determining how far apart the two ends areat the same time. In the same context of determining the length of moving rods, Mermin [30, p. 185] proposes that the sense of length entailing the concept of being determined at simultaneous times is inherent in the notion of rods: ...it is precisely the lines of constant time that determine whatA orB means by the stick. For the notion of the stick includes implicitly the assumption that all the points of matter making up the stick exist at the same moment.13. In many ways the claim that the special properties of proper lengths with Einstein synchronization undermines the conventionality of simultaneity is analogous to the claim that the correspondence of the slow-clock transport method of synchronization with that of Einstein synchronization provides an empirical determination of synchronization. The use of clock transport as a means for synchronization was discussed by Reichenbach [37, p. 133f], while the proposal that slow transport of clocks provides a unique form of synchronization was first argued for by Eddington [10]. Arguments that it undermines any significant sense of the conventionality in the one-way speed of light have been given by Ellis and Bowman [13] with responses by Grünbaum [19] and Salmon [41, 40].14. Coleman and Korte [9, pp. 423–425] claim their method is free from any assumptions on the one-way speed of light; however, they assume that is a constant 3-vector.15. Reichenbach explicitly mentioned in [36, § 43] that a condition equivalent to Eq. (13) is a sufficient condition for a constant roundtrip speed of light.16. The remarks of one of the referees have served to alert us to the need to emphasize both of these points.17. The manner in which gravity may be viewed as a gauge theory has been the subject of considerable discussion (see, for example, the discussion in [23] and [24]). We note that the manner in which we are takingh as a potential differs from the sense in which the Christoffel symbols as affine connections may be seen to play a role of gauge potentials in GTR.18. A discussion of the significance of Weyl's work and the importance of the round-trip measurements may be found in works by Yang [56] and Mills [31].19. In the context only of time orthogonal coordinates, an example of the fiber structure we are imposing on space and time may be found in [26, p. 71f]. Again we note that in a more general treatment, where the Christoffel symbols are considered as connections, the fiber structure instead consists of a bundle of linear frames of Riemannian spacetime (see, for example, the presentations in [46] and [23]).20. Our position is not unlike Göckeler and Schücker's [15, p. 75] claim that Einstein's particular choice of coordinates in GTR masks the general gauge structure of the theory.     

Equivalence Principle and the Principle of Local Lorentz Invariance

In this paper we scrutinize the so called Principle of Local Lorentz Invariance (PLLI) that many authors claim to follow from the Equivalence Principle. Using rigourous mathematics, we introduce in the General Theory of Relativity two classes of reference frames (PIRFs and LLRFs) which as natural generalizations of the concept of the inertial reference frames of the Special Relativity Theory. We show that it is the class of the LLRFs that is associated with the PLLI. Next we give a definition of physically equivalent reference frames. Then, we prove that there are models of General Relativity Theory (in particular on a Friedmann universe) where the PLLI is false. However our finding is not in contradiction with the many experimental claims vindicating the PLLI, because theses experiments do not have enough accuracy to detect the effect we found. We prove moreover that PIRFs are not physically equivalent.     

Determination of rf electric field strengths in deuterium from satellite structure of Balmer lines

In a linear magnetoplasma withn _e5×10¹⁸ m^–3 microwaves with frequencyf=34.8 GHz and powerP100 kW were focussed with a quasi-optical horn-lens system. The profiles of the deuterium lines D, D, and D were recorded from the focus. The profiles show a satellite structure which is generated by the rf electric field. Beside the first order satellites which can be resolved from the main line, even second order satellites were detectable. Comparing the satellites' intensities with theory it is possible to determine the electric field strength in the focus. Due to a sensitive dependence of the satellites' intensities upon the polarization direction one can also determine an unknown polarization direction.     

Onset of superconductivity at 107K in YBa2Cu3O7 − δ at high pressure

Electrical resistivity measurements under pressure have been carried out on the high-temperature superconductor YBa₂Cu₃O_{7 –} as a function of temperature T between 1 and 300 K at various pressures between 8 kbar and 149 kbar. The superconducting transition temperature T_c increases almost linearly with pressure at the rate dT_c/dP - 0.13 K/kbar. The onset of T_c, defined as the temperature at which(T) drops to 90% of its extrapolated normal state value, increases from 95 K at 8 kbar to 107 K at 149 kbar. These results suggest that higher pressures will yield yet higher values of T_c.     

Construction of the faithful irreducible representation for the subgroupG contained inS 7

Every element in the transitive subgroupG of order 42 contained in the symmetric group of degree 7 is expressed as an ordered product of powers of the basic permutationsg ₂ (1234567) andg ₈ (1) (243756). The only faithful irreducible representation forG is then given explicitly in terms of the six-dimensional matricesD(g ₂ ) andD(g ₈ ), obtained here with the aid of a simple computational algorithm.     

On the nilpotent * - Fourier transform

LetG be a nilpotent Lie group. The adapted nilpotent Fourier transform was introduced by D. Arnal and J. C. Cortet,:L(G) C (V,L(^2d )), whereL(G) is the Schwartz space ofG andV × ^2k is aG-invariant Zariski open set ing ^* the dual of the Lie algebra ofG. We prove the surjectivity of this transformation, which allows us to extend it to distribution spaces.     

Singular measures without restrictive intervals

For the transformationT:[0,1][0,1] defined byT(x)=x(1–x) with 04, a is shown to exist for whichT has no restrictive intervals, hence is sensitive to initial conditions, but for which no finite absolutely continuous invariant measure exists forT.Supported by the U.S. Army Research Office through the Mathematical Sciences Institute of Cornell University     

Self-avoiding walks in quenched random environments

The self-avoiding walk in a quenched random environment is studied using real-space and field-theoretic renormalization and Flory arguments. These methods indicate that the system is described, ford _c =4, and, for large disorder ford>d _c , by a strong disorder fixed point corresponding to a glass state in which the polymer is confined to the lowest energy path. This fixed point is characterized by scaling laws for the size of the walk,LN ^p withN the number of steps, and the fluctuations in the free energy,fL ^p. The bound 1/-d/2 is obtained. Exact results on hierarchical lattices yield> _pure and suggests that this inequality holds ford=2 and 3, although= _pure cannot be excluded, particularly ford=2. Ford>d _c there is a transition between strong and weak disorder phases at which= _pure. The strong-disorder fixed point for SAWs on percolation clusters is discussed. The analogy with directed walks is emphasized.     

Multiple harmonic conversion of pulsed CO2 laser radiation in Tl3AsSe3

The nonlinear material Tl₃AsSe₃ is used to convert pulsed 9.6 m CO₂ laser radiation into its second, third, fourth and fifth harmonic. Internal (external) conversion efficiencies of 28, 14(6.7), 3.6(3.1), and 0.5(0.3)% from the pump fundamental are achieved in 4.8, 3.2, 2.4, and 1.9 m generation respectively.     

On classical models of Spin

We discuss two classical situations that lead to probabilities characteristic for systems with spin-1/2. (a) Pitowsky model: It is demonstrated that the definition of spin functions does not imply which circle (a parallel or a great circle) on the sphere should be taken as a probability space in calculation of conditional probabilities. Pitowsky's choice of parallels must be formulated as an assumption about the model. It is shown that the model explicitly avoiding this difficulty is possible and no contradiction with the Bell Theorem is found. The modification is based on a new pathological decomposition of the sphere and belongs to a class of hidden variable theories with undetected signals. (b) Aerts model: We show the importance of the polarization effect of the measurements for the sake of obtaining a non-Kolmogorovian probability model. It is also shown that the conditioning by a change of state leads in general to the non-Kolmogorovian probability calculus.2. For example, let _{Cw,z xCw,z}µ_c ({y C _w,z S ₊|(x,y) /2})=µ _c(C _w,z S ₊)= 1/2µ _c(C _w,z). Pitowsky spheres with white points distributed onC _w,z in this way exist. The proof is exactly analogous to this of Theorem 1 in [1]. Then (**) = 1 -/, if one takesC _w,z as the probability space. This example seems very instructive.3. If the chargeq falls down on some point then it clearly has not fallen down on another one. Having given a result of a measurement we cannot, within the model with polarization, talk in a sensible way about its alternative: We can think either aboutsuccessive measurements (then the Bell inequality is not derivable) or ask What would have happened if..., but then we deal with a different problem (in Aerts' terminology [2b] this is anobservation) and obtain again Eq. (8) (there is no complementarity but there is no model of spin either).     

Measurements of charged kaon semileptonic decay branching fractions K±→π0μ±ν and K±→π0e±ν and their ratio

In an earlier paper [1], the background for K_e3 was over estimated due to an erroneous calculation of the electron identification efficiency. The correct ratios of the partial widths involving this channel are and . Assuming the PDG value [2] for the K_2π branching ratio, the measured branching fraction of Br (K_e3) continues to exceed the current PDG value [2]. The extracted value of |V_us|f₊(0) is in agreement with the CKM unitary prediction; thus, our conclusions in [1] do not change. The online version of the original article can be found at     

The dependence of susceptibility on the high-frequency field at ferromagnetic resonance

The dependence of the uniform precession amplitude and susceptibility at ferromagnetic resonance on the high-frequency fieldh is discussed on the basis of an equation for the energy balance and classical equations for the spin wave amplitudes. The dependence (h) is first determined in the lowest non-linear approximation. According to these calculations, the initial decline of the susceptibility differs from Schlömann's quadratic law. The influence of other nonlinear interactions between spin wavesk0 is then discussed on a certain special assumption of the type of two-magnon scattering. It is shown that such interactions can lead to the appearance of a maximum in the h.f. field dependence of the uniform precession amplitude.     

Modelling of electron stream discharge

Particle-in-cell Monte Carlo code is used to simulate gas discharge initiated by a high current (I _e10kA) middle energy ( _e10keV) hot ( _e1 keV) electron stream. The generation of such an overthermal electron stream has been clearly demonstrated at the experimental REBEX facility during the relativistic electron beam-plasma interaction. When the electron beam (represented by1000 macroparticles) is injected into the drift tube filled by neutral gas (hydrogen,p=13.3–133 Pa) two different stages are observed. During the initial stage the arising Virtual Cathode (VC) is filled by hydrogen ions. The VC disappears when the quasineutrality of ionized gas is achieved. Then the severe exponential growth of electron and ion component of ionized gas is observed.List of symbols x distance from the left electrode [m] - t time [s] - v _x ,v _y velocity components [m/s] - g4(x) potential [Volt] - g4 _1/2(t) middle potential [Volt] - E(x) electric field [Volt/m] - Q _wall wall charge [C/m.m] - I current [C/s] - _tot total energy [J] - N number of macroparticles - f() energy distribution of electron macroparticles at the left electrode, is kinetic energy of macroparticle [eV]. Presented at 17^th Symposium Plasma Physics and Technology, Prague, June 13–16, 1995.     

Some properties of an “aesthetic” field theory

We continue our study of the Lorentz-invariant field theory based on the equations _jk;l ⁱ =0 and g_ij;k=0. To first order in a perturbation expansion, we find _jk;l ⁱ =0 reduces to the wave equation. In orders higher than the first, we find that _jk;l ⁱ =0 cannot be linearized. We also find that the simple wave-type equation g^ij2g/xⁱx^j=0 is contained in the theory when an appropriate choice is made for the parameters at the origin point.     

F-Information, a Unitless Variant of Fisher Information

A new information matrix [F] with elements F _mn = (y _m - a _m )(y _n - a n) ( ln p(y | a)/a _m ) ( ln p(y | a)/a _n ) is analyzed. The PDF p(y | a) is the usual likelihood law. [F] differs from the Fisher information matrix by the presence of the first two factors in the given expectation. These factors make F _mn unitless, in contrast with the Fisher information. This lack of units allows F _mn values from entirely different phenomena to be compared as, for example, Shannon information values can be compared. Each element F _mn defines an error inequality analogous to the Cramer-Rao inequality. In the scalar case F _mn F, for a normal p(y|a) law F = 3, while for an exponential law F = 9. A variational principle F = min (called FMIN) allows an unknown PDF p(x) to be estimated in the presence of weak information. Under certain conditions F obeys a Boltzmann F-theorem F/t 0, indicating that F is a physical entropy. Finally, the trace of [F] may be used as the scalar information quantity in an information-based principle for deriving distribution laws p of physics.     

Hyperbolic initial-boundary-value problem for magnetic flux compression by plane liners

Based on the (relativistic) Maxwell equations with displacement current E/t, the initial-boundary-value problem for the compression of an initially homogeneous magnetic fieldB={0,B(x,t),0} between a fixed liner atx=0 and a detonation-driven liner atx=s(t) is solved analytically. By homogenizing the boundary conditions at the moving boundary, the transient electromagnetic fields are shown to be a superposition of quasistatic elliptic (E/t=0) and hyperbolic (E/t0) wave solutions. The wave equation is solved by a Fourier expansion in time-dependent eigenfunctionsf _n =f _n [nx/s(t)] for the variable region 0xs(t), where the Fourier amplitudes _n (t) are determined by coupled differential equations of second order. It is concluded that the conventional elliptic flux compression theories (E/t=0) hold approximately for nonrelativistic liner speeds , whereas the hyperbolic theory (E/t0) is valid for arbitrary liner speeds .