Hubble's law and faster than light expansion speeds

Naively applying Hubble's law to a sufficiently distant object gives a receding velocity larger than the speed of light. By discussing a very similar situation in special relativity, we argue that Hubble's law is meaningful only for nearby objects with non-relativistic receding speeds. To support this claim, we note that in a curved spacetime manifold it is not possible to directly compare tangent vectors at different points, and thus there is no natural definition of relative velocity between two spatially separated objects in cosmology. We clarify the geometrical meaning of the Hubble's receding speed v by showing that in a Friedmann-Robertson-Walker spacetime if the four-velocity vector of a comoving object is parallel-transported along the straight line in flat comoving coordinates to the position of a second comoving object, then v/c actually becomes the rapidity of the local Lorentz transformation, which maps the fixed four-velocity vector to the transported one.Comment: 5 pages, 2 figures, to appear in Am. J. Phy

Prompt Photon Identification in the ALICE Experiment: The Isolation Cut Method

Submitted for publication in NIMThe ALICE experiment at LHC will detect and identify prompt photons and light neutral mesons with the PHOS and EMCal detectors. Charged particles will be detected and identified by the central tracking system. In this paper, a method to identify prompt photons and to separate them from the background of hadrons and decay photons in PHOS with the help of isolation cuts is presented

Removing non-stationary, non-harmonic external interference from gravitational wave interferometer data

We describe a procedure to identify and remove a class of non-stationary and non-harmonic interference lines from gravitational wave interferometer data. These lines appear to be associated with the external electricity main supply, but their amplitudes are non-stationary and they do not appear at harmonics of the fundamental supply frequency. We find an empirical model able to represent coherently all the non-harmonic lines we have found in the power spectrum, in terms of an assumed reference signal of the primary supply input signal. If this signal is not available then it can be reconstructed from the same data by making use of the coherent line removal algorithm that we have described elsewhere. All these lines are broadened by frequency changes of the supply signal, and they corrupt significant frequency ranges of the power spectrum. The physical process that generates this interference is so far unknown, but it is highly non-linear and non-stationary. Using our model, we cancel the interference in the time domain by an adaptive procedure that should work regardless of the source of the primary interference. We have applied the method to laser interferometer data from the Glasgow prototype detector, where all the features we describe in this paper were observed. The algorithm has been tuned in such a way that the entire series of wide lines corresponding to the electrical interference are removed, leaving the spectrum clean enough to detect signals previously masked by them. Single-line signals buried in the interference can be recovered with at least 75 % of their original signal amplitude.Comment: 14 pages, 5 figures, Revtex, psfi

Relativistic r-modes in Slowly Rotating Neutron Stars: Numerical Analysis in the Cowling Approximation

We investigate the properties of relativistic $r$-modes of slowly rotating neutron stars by using a relativistic version of the Cowling approximation. In our formalism, we take into account the influence of the Coriolis like force on the stellar oscillations, but ignore the effects of the centrifugal like force. For three neutron star models, we calculated the fundamental $r$-modes with $l'=m=2$ and 3. We found that the oscillation frequency $\bar\sigma$ of the fundamental $r$-mode is in a good approximation given by $\bar\sigma\approx \kappa_0 \Omega$, where $\bar\sigma$ is defined in the corotating frame at the spatial infinity, and $\Omega$ is the angular frequency of rotation of the star. The proportional coefficient $\kappa_0$ is only weakly dependent on $\Omega$, but it strongly depends on the relativistic parameter $GM/c^2R$, where $M$ and $R$ are the mass and the radius of the star. All the fundamental $r$-modes with $l'=m$ computed in this study are discrete modes with distinct regular eigenfunctions, and they all fall in the continuous part of the frequency spectrum associated with Kojima's equation (Kojima 1998). These relativistic $r$-modes are obtained by including the effects of rotation higher than the first order of $\Omega$ so that the buoyant force plays a role, the situation of which is quite similar to that for the Newtonian $r$-modes.Comment: 22 pages, 8 figures, accepted for publication in Ap

Nonlinear Gravitational Waves: Their Form and Effects

A gravitational wave must be nonlinear to be able to transport its own source, that is, energy and momentum. A physical gravitational wave, therefore, cannot be represented by a solution to a linear wave equation. Relying on this property, the second-order solution describing such physical waves is obtained. The effects they produce on free particles are found to consist of nonlinear oscillations along the direction of propagation.Comment: 15 pages, no figures. v2: presentation changes aiming at clarifying the text; matches published versio

The Stability of an Isentropic Model for a Gaseous Relativistic Star

We show that the isentropic subclass of Buchdahl's exact solution for a gaseous relativistic star is stable and gravitationally bound for all values of the compactness ratio $u [\equiv (M/R)$, where $M$ is the total mass and $R$ is the radius of the configuration in geometrized units] in the range, $0 < u \leq 0.20$, corresponding to the {\em regular} behaviour of the solution. This result is in agreement with the expectation and opposite to the earlier claim found in the literature.Comment: 9 pages (including 1 table); accepted for publication in GR

Quantum cosmological perfect fluid models

Perfect fluid Friedmann-Robertson-Walker quantum cosmological models for an arbitrary barotropic equation of state $p = \alpha\rho$ are constructed using Schutz's variational formalism. In this approach the notion of time can be recovered. By superposition of stationary states, finite-norm wave-packet solutions to the Wheeler-DeWitt equation are found. The behaviour of the scale factor is studied by applying the many-worlds and the ontological interpretations of quantum mechanics. Singularity-free models are obtained for $\alpha \alpha > - 1$.Comment: Latex file, 12 pages. New paragraphs in the Introduction and Conclusion, and other minor corrections in the text and in some formulas. Accepted for publication in General Relativity and Gravitatio