More complete discussion of the time-dependence of the non-static line element for the universe

In a previous article,(1) I have shown that a continuous transformation of matter into radiation, occurring throughout the universe, as postulated by the astrophysicists, would necessitate a nonstatic line element for the universe, and have shown that the non-static character thus introduced might provide an explanation of the red shift in the light from the extra-galactic nebulae. In the present article, I wish to discuss the form of dependence of the line element on the time more completely than was possible on the previous occasion. This is a matter of considerable importance, since changes in the approximations which must be introduced to obtain a usable result affect to quite a different extent the expressions for the relation between red shift and distance and for the rate of annihilation of matter. Indeed, the possibility arises of slight changes from the treatment previously given which would leave the theoretical relation between red shift and distance still approximately linear, as observationally found, and yet produce a very considerable change in the calculated rate for the annihilation of matter

Concept development of a tendon arm manipulator and anthropomorphic robotic hand

AMETEK/ORED inhouse research and development efforts leading toward a next-generation robotic manipulator arm and end-effector technology is summarized. Manipulator arm development has been directed toward a multiple-degree-of-freedom, flexible, tendon-driven concept referred to here as a Tendon Arm Manipulator (TAM). End-effector development has been directed toward a three-fingered, dextrous, tendon-driven, anthropomorphic configuration which is referred to as an Anthropomorphic Robotic Hand (ARH). Key technology issues are identified for both concepts

Gravitational collapse and black hole evolution: do holographic black holes eventually "anti-evaporate"?

We study the gravitational collapse of compact objects in the Brane-World. We begin by arguing that the regularity of the five-dimensional geodesics does not allow the energy-momentum tensor of matter on the brane to have (step-like) discontinuities, which are instead admitted in the four-dimensional General Relativistic case, and compact sources must therefore have an atmosphere. Under the simplifying assumption that matter is a spherically symmetric cloud of dust without dissipation, we can find the conditions for which the collapsing star generically ``evaporates'' and approaches the Hawking behavior as the (apparent) horizon is being formed. Subsequently, the apparent horizon evolves into the atmosphere and the back-reaction on the brane metric reduces the evaporation, which continues until the effective energy of the star vanishes. This occurs at a finite radius, and the star afterwards re-expands and ``anti-evaporates''. We clarify that the Israel junction conditions across the brane (holographically related to the matter trace anomaly) and the projection of the Weyl tensor on the brane (holographically interpreted as the quantum back-reaction on the brane metric) contribute to the total energy as, respectively, an ``anti-evaporation'' and an ``evaporation'' term. Concluding, we comment on the possible effects of dissipation and obtain a new stringent bound for the brane tension.Comment: 18 pages in RevTeX4 style, 11 eps figures included. Discussion on the contribution of dissipation and clarifications added, version accepted for publication in Prog. Theor. Phys. Vol. 114, No.

Stability of the Einstein static universe in presence of vacuum energy

The Einstein static universe has played a central role in a number of emergent scenarios recently put forward to deal with the singular origin of the standard cosmological model. Here we study the existence and stability of the Einstein static solution in presence of vacuum energy corresponding to conformally-invariant fields. We show that the presence of vacuum energy stabilizes this solution by changing it to a centre equilibrium point, which is cyclically stable. This allows non-singular emergent cosmological models to be constructed in which initially the universe oscillates indefinitely about an initial Einstein static solution and is thus past eternal.Comment: Some references adde

On a common misunderstanding of the Birkhoff theorem and light deflection calculation: generalized Shapiro delay and its possible laboratory test

In Newtonian gravity (NG) it is known that the gravitational field anywhere inside a spherically symmetric distribution of mass is determined only by the enclosed mass. This is also widely believed to be true in general relativity (GR), and the Birkhoff theorem is often invoked to support this analogy between NG and GR. Here we show that such an understanding of the Birkhoff theorem is incorrect and leads to erroneous calculations of light deflection and delay time through matter. The correct metric, matching continuously to the location of an external observer, is determined both by the enclosed mass and mass distribution outside. The effect of the outside mass is to make the interior clock run slower, i.e., a slower speed of light for external observer. We also discuss the relations and differences between NG and GR, in light of the results we obtained in this Lettework. Finally we discuss the Generalized Shapiro delay, caused by the outside mass, and its possible laboratory test.Comment: 12 pages, 4 figures, invited talk in the 2nd Galileo-Xu Guangqi Meeing, Italy, 2011, IJMPD in pres

Symmetry relations in chemical kinetics arising from microscopic reversibility

It is shown that the kinetics of time-reversible chemical reactions having the same equilibrium constant but different initial conditions are closely related to one another by a directly measurable symmetry relation analogous to chemical detailed balance. In contrast to detailed balance, however, this relation does not require knowledge of the elementary steps that underlie the reaction, and remains valid in regimes where the concept of rate constants is ill-defined, such as at very short times and in the presence of low activation barriers. Numerical simulations of a model of isomerization in solution are provided to illustrate the symmetry under such conditions, and potential applications in protein folding-unfolding are pointed out.Comment: 4 pages, 1 figure, accepted to Phys Rev Let

Entropy of Contracting Universe in Cyclic Cosmology

Following up a recent proposal \cite{BF} for a cyclic model based on phantom dark energy, we examine the content of the contracting universe (cu) and its entropy $S_{cu}$. We find that beyond dark energy the universe contains on average zero or at most a single photon which if present immediately after turnaround has infinitesimally energy which subsequently blue shifts to produce $e^+e^-$ pairs. These statements are independent of the equation of state $\omega = p/\rho$ of dark energy provided $\omega < -1$. Thus $S_{cu} = 0$ and if observations confirm $\omega < -1$ the entropy problem is solved. We discuss the absence of a theoretical lower bound on $\phi = |\omega + 1|$, then describe an anthropic fine tuning argument that renders unlikely extremely small $\phi$. The present bound $\phi \lesssim 0.1$ already implies a time until turnaround of $(t_T - t_0) \gtrsim 100$ Gy.Comment: 5 pages late

Cyclic Universe and Infinite Past

We address two questions about the past for infinitely cyclic cosmology. The first is whether it can contain an infinite length null geodesic into the past in view of the Borde-Guth-Vilenkin (BGV) "no-go" theorem, The second is whether, given that a small fraction of spawned universes fail to cycle, there is an adequate probability for a successful universe after an infinite time. We give positive answers to both questions then show that in infinite cyclicity the total number of universes has been infinite for an arbitrarily long time.Comment: 7 pages. Clarification in discussion of infinite pas

Phantom Energy Accretion onto Black Holes in Cyclic Universe

Black holes pose a serious problem in the cyclic or oscillating cosmology. It is speculated that, in the cyclic universe with phantom turnarounds, black holes will be torn apart by the phantom energy before turnaround before they can create any problems. In this paper, using the mechanism of the phantom accretion onto black holes, we find that black holes do not disappear before the phantom turnaround. But the remanent black holes will not cause any problems due to the Hawking evaporation.Comment: 8 pages, no figure; typographical errors are correcte