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

Conditions for low-redshift positive apparent acceleration in smooth inhomogeneous models

It is known that a smooth LTB model cannot have a positive apparent central acceleration. Using a local Taylor expansion method we study the low-redshift conditions to obtain an apparent negative deceleration parameter $q^{app}(z)$ derived from the luminosity distance $D_L(z)$ for a central observer in a LTB space, confirming that central smoothness implies a positive central deceleration. Since observational data is only available at redshift greater than zero we find the critical values of the parameters defining a centrally smooth LTB model which give a positive apparent acceleration at $z>0$, providing a graphical representation of the conditions in the $q_0^{app},q_1^{app}$ plane, which are respectively the zero and first order terms of the central Taylor expansion of $q^{app}(z)$. We finally derive a coordinate independent expression for the apparent deceleration parameter based on the expansion of the relevant functions in red-shift rather than in the radial coordinate. We calculate $q^{app}(z)$ with two different methods to solve the null geodesic equations, one based on a local central expansion of the solution in terms of cosmic time and the other one using the exact analytical solution in terms of generalized conformal time. %The expansion of the solution in terms of cosmic time is quite useful also for other applications requiring foliation %of space-time in space-like hyper-surfaces, such as spatial averaging, which is much more difficult to study using the %analytical solution in terms of the generalized conformal time coordinate.Comment: 18 pages, 3 figures, abstract, added section with coordinate independent conditions, version accepted for publication in GR

Inverse Compton X-rays from the radio galaxy 3C 219

We report the results from a Chandra observation of the powerful nearby (z=0.1744) radio galaxy 3C 219. We find evidence for non-thermal X-ray emission from the radio lobes which fits fairly well with a combination of inverse Compton scattering of Cosmic Microwave Background radiation and of nuclear photons with the relativistic electrons in the lobes. The comparison between radio synchrotron and IC emission yields a magnetic field strength significantly lower (about a factor 3) than that calculated under minimum energy conditions; the source energetics is then dominated by the relativistic particles.Comment: 5 pages, 2 color figures, Accepted for publication in MNRAS pink page

Reflection and Transmission at the Apparent Horizon during Gravitational Collapse

We examine the wave-functionals describing the collapse of a self-gravitating dust ball in an exact quantization of the gravity-dust system. We show that ingoing (collapsing) dust shell modes outside the apparent horizon must necessarily be accompanied by outgoing modes inside the apparent horizon, whose amplitude is suppressed by the square root of the Boltzmann factor at the Hawking temperature. Likewise, ingoing modes in the interior must be accompanied by outgoing modes in the exterior, again with an amplitude suppressed by the same factor. A suitable superposition of the two solutions is necessary to conserve the dust probability flux across the apparent horizon, thus each region contains both ingoing and outgoing dust modes. If one restricts oneself to considering only the modes outside the apparent horizon then one should think of the apparent horizon as a partial reflector, the probability for a shell to reflect being given by the Boltzmann factor at the Hawking temperature determined by the mass contained within it. However, if one considers the entire wave function, the outgoing wave in the exterior is seen to be the transmission through the horizon of the interior outgoing wave that accompanies the collapsing shells. This transmission could allow information from the interior to be transferred to the exterior.Comment: 19 pages, no figures. To appear in Phys. Rev.

The spherical symmetry Black hole collapse in expanding universe

The spherical symmetry Black holes are considered in expanding background. The singularity line and the marginally trapped tube surface behavior are discussed. In particular, we address the conditions whether dynamical horizon forms for these cosmological black holes. We also discuss about the cosmological constant effect on these black hole and the redshift of the light which comes from the marginally trapped tube surface.Comment: 7 pages, 3 figures. Accepted for publication in International Journal of Modern Physics D (IJMPD). arXiv admin note: text overlap with arXiv:gr-qc/0308033 and arXiv:gr-qc/030611

Topological Quintessence

A global monopole (or other topological defect) formed during a recent phase transition with core size comparable to the present Hubble scale, could induce the observed accelerating expansion of the universe. In such a model, topological considerations trap the scalar field close to a local maximum of its potential in a cosmologically large region of space. We perform detailed numerical simulations of such an inhomogeneous dark energy system (topological quintessence) minimally coupled to gravity, in a flat background of initially homogeneous matter. We find that when the energy density of the field in the monopole core starts dominating the background density, the spacetime in the core starts to accelerate its expansion in accordance to a \Lambda CDM model with an effective inhomogeneous spherical dark energy density parameter \Omega_\Lambda(r). The matter density profile is found to respond to the global monopole profile via an anti-correlation (matter underdensity in the monopole core). Away from the monopole core, the spacetime is effectively Einstein-deSitter (\Omega_\Lambda(r_{out}) -> 0) while at the center \Omega_\Lambda(r ~ 0) is maximum. We fit the numerically obtained expansion rate at the monopole core to the Union2 data and show that the quality of fit is almost identical to that of \Lambda CDM. Finally, we discuss potential observational signatures of this class of inhomogeneous dark energy models.Comment: Accepted in Phys. Rev. D (to appear). Added observational bounds on parameters. 10 pages (two column revtex), 6 figures. The Mathematica files used to produce the figures of this study may be downloaded from http://leandros.physics.uoi.gr/topquin

CMB anisotropies seen by an off-center observer in a spherically symmetric inhomogeneous universe

The current authors have previously shown that inhomogeneous, but spherically symmetric universe models containing only matter can yield a very good fit to the SNIa data and the position of the first CMB peak. In this work we examine how far away from the center of inhomogeneity the observer can be located in these models and still fit the data well. Furthermore, we investigate whether such an off-center location can explain the observed alignment of the lowest multipoles of the CMB map. We find that the observer has to be located within a radius of 15 Mpc from the center for the induced dipole to be less than that observed by the COBE satellite. But for such small displacements from the center, the induced quadru- and octopoles turn out to be insufficiently large to explain the alignment.Comment: 8 pages (REVTeX4), 7 figures; v2: minor changes, matches published versio

B2 1144+35: A Giant Low Power Radio Galaxy with Superluminal Motion

We report on centimeter VLA and VLBI observations of the giant, low power radio galaxy 1144+35. These observations are sensitive to structures on scales from less than 1 parsec to greater than 1 megaparsec. Diffuse steep spectrum lobes on the megaparsec scale are consistent with an age of $\sim$ 10$^8$ years. On the parsec scale, a complex jet component is seen to move away from the center of activity with an apparent velocity 2.7 h$^{-1}_{50}$ c. It shows a central spine -- shear layer morphology. A faint parsec scale counterjet is detected and an intrinsic jet velocity of 0.95 c and angle to the line of sight of 25$^\circ$ are derived, consistent with an intrinsically symmetric ejection. The central spine in the parsec scale jet is expected to move at a higher velocity and a Lorentz factor $\gamma$ $\sim$ 15 has been estimated near the core.The age of this inner VLBI structure is $\sim$ 300 years. Assuming a constant angle to the line-of-sight, the jet velocity is found to decrease from 0.95 c at 20 mas (32 pc on the plane of the sky) to 0.02 c at 15 arcsec (24 kpc on the plane of the sky). These findings lend credence to the claim that (1) even the jets of low power radio galaxies start out relativistic; and (2) these jets are decelerated to subrelativistic velocities by the time they reach kiloparsec scales.Comment: 21 pages, 16 separated figures. A version with figures and table in the text is available at: ftp://terra.bo.cnr.it/papers/journals - it is a ps gzipped file, named giovannini_apr99.gz (792kb) - ApJ in pres

Living in a Void: Testing the Copernican Principle with Distant Supernovae

A fundamental presupposition of modern cosmology is the Copernican Principle; that we are not in a central, or otherwise special region of the Universe. Studies of Type Ia supernovae, together with the Copernican Principle, have led to the inference that the Universe is accelerating in its expansion. The usual explanation for this is that there must exist a `Dark Energy', to drive the acceleration. Alternatively, it could be the case that the Copernican Principle is invalid, and that the data has been interpreted within an inappropriate theoretical frame-work. If we were to live in a special place in the Universe, near the centre of a void where the local matter density is low, then the supernovae observations could be accounted for without the addition of dark energy. We show that the local redshift dependence of the luminosity distance can be used as a clear discriminant between these two paradigms. Future surveys of Type Ia supernovae that focus on a redshift range of ~0.1-0.4 will be ideally suited to test this hypothesis, and hence to observationally determine the validity of the Copernican Principle on new scales, as well as probing the degree to which dark energy must be considered a necessary ingredient in the Universe.Comment: 4 pages, 3 figures. Published versio

A Lemaitre-Tolman-Bondi cosmological wormhole

We present a new analytical solution of the Einstein field equations describing a wormhole shell of zero thickness joining two Lema{\i}tre-Tolman-Bondi universes, with no radial accretion. The material on the shell satisfies the energy conditions and, at late times, the shell becomes comoving with the dust-dominated cosmic substratum.Comment: 5 pages, latex, no figures, to appear in Phys. Rev.