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.

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

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

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

The Tolman Surface Brightness Test for the Reality of the Expansion. II. The Effect of the Point-Spread Function and Galaxy Ellipticity on the Derived Photometric Parameters

To complete the Tolman surface brightness test on the reality of the expansion of the Universe, we need to measure accurately the surface brightness profiles of the high-redshift galaxy sample. We, therefore, investigate the effects of various sizes of point-spread-functions composed of telescope diffraction, CCD pixel resolutions, and ground-based seeing on the measurements of mean surface brightness. We have done the calculations using two synthetic galaxies of effective radii of 0.70" and 0.25" with point-spread functions of 0.1, 0.3, and 0.9 arcseconds. We have also compared actual observations of three high-redshift galaxies in the cluster Cl 1324 + 3011 (z = 0.76) made both with the Keck telescopes in seeing of about 0.9" and with HST which has a PSF that is approximately ten times smaller. The conclusion is that HST data can be used as far into the galaxy image as a Petrosian metric radius of eta = 1.3 magnitudes, whereas the ground-based data will have systematic errors of up to 2.9 magnitudes in the mean surface brightness at eta values of less than 2.2 magnitudes. In the final section, we compare the differences in derived average surface brightness for nearly circular galaxy images compared with highly flattened images. The comparison is made by using the two reduction procedures of (1) integrating the profile curves using circular apertures, and (2) approximating an ``equivalent circular'' galaxy that is highly elongated by using an ``effective'' radius of sqrt{ab}, where a and b are the semi-major and semi-minor axis, respectively, of the best-fitting ellipse. The conclusion is that the two methods of reduction give nearly identical results and that either method can be used to analyze the low and high-redshift galaxy samples used in the Tolman test.Comment: 15 pages, 9 figures; accepted for publication in Astronomical Journa

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

Inter-frequency Bias Estimation for the GPS Monitor Station Network

The inter-frequency bias (IFB) is present in all dual frequency combinations of GPS pseudorange and carrier phase observables. It is caused by the path dependent signal delays in both the satellite and receiver. That delay can be directly measured for a space vehicle prior to launch, or for a ground based receiver prior to its being used in the field. However the bias is known to drift, and monitoring the delay estimate by direct measurement is time consuming for ground based receivers and impossible for deployed space vehicles. Hansen (2002) examined the observability of IFB through a global model of ionosphere total electron content (TEC). Variation in the receiver portion of the IFB can also be observed in receivers with antennae in a zero-baseline configuration. This is referred to as an inter-receiver bias (IRB). In this study a Kalman filter is formulated to observe IFBs and IRBs. Process noise is used to allow the filter to track changes in the IFBs and IRBs. The filter also implements constraints to reflect the fact that a given IRB is not linearly independent of the IFBs. Because the receivers are distributed on a global scale, the Kalman filter requires a globally observable phenomenon by which to tie the IFBs. In this case ionosphere delay provides such a phenomenon. The filter was applied to observations collected by GPS monitor stations that comprise the National Geospatial- Intelligence Agency Monitor Station Network (MSN). Each monitor station contains two geodetic quality receivers in a zero-baseline configuration and continuously collects GPS observations. The GPS observations collected by this network are used to produce both precise ephemeris and the broadcast ephemeris. GPS observations made through the network are incorporated into the GPS Master Control Station (MCS) Kalman filter of the Operational Control System (OCS) (Wiley, 2006). The Kalman filter in the OCS estimates the orbital parameters that are transmitted via the navigation message. If estimated effectively, knowledge of the receiver portion of the IFB can aid in achieving better ionosphere models. IFBs are made observable using a global ionosphere delay model. A ninth order spherical harmonic model derived by Y.C. Chao (1997) was used in this study for ionosphere delay. Chao used this spherical harmonic model to capture ionospheric variations that occurred over a smaller global region in his IFB estimation process. In this study a similar model was used but was verified using observations that span a global coverage. The receiver portion of the IFB is observed precisely using the IRB. In this study error terms were introduced into the Kalman filter design to realign the IRB estimates to the IFB estimates produced for each of the two receivers in a zero baseline configuration. For a nominal epoch of measurement, there were 198 noisy measurements used each epoch to generate twelve monitor station specific IRBs. The IRB estimates showed small, decimeter level dynamic variation over the period of a day. The quality of the IFB estimate directly affects the quality of the ionospheric model formed during the estimation process. Results verify that the filter is operating properly. The ionosphere model, though simple, demonstrates that the total electron content (TEC) peaks during local noon and is at a minimum during local night. IRB estimates are roughly constant over time and have a magnitude of less than 2.5 meters. Similar estimates are formed for the IFBs, however when processing one day of observations, the IFB estimates are less stable than those of the IRBs. Future effort will involve tuning the filter, and establishing criteria for its convergence

T-spheres as a limit of Lemaitre-Tolman-Bondi solutions

In the Tolman model there exist two quite different branches of solutions - generic Lemaitre-Tolman-Bondi (LTB) ones and T-spheres as a special case. We show that, nonetheless, T-spheres can be obtained as a limit of the class of LTB solutions having no origin and extending to infinity with the areal radius approaching constant. It is shown that all singularities of T-models are inherited from those of corresponding LBT solutions. In doing so, the disc type singularity of a T-sphere is the analog of shell-crossing.Comment: 6 pages. 1 Reference added. To appear in Phys. Rev.