The distance and neutral environment of the massive stellar cluster Westerlund 1

The goal of this study is to determine a distance to Westerlund 1 independent of the characteristics of the stellar population and to study its neutral environment, using observations of atomic hydrogen. The HI observations are taken from the Southern Galactic Plane Survey to study HI absorption in the direction of the HII region created by the members of Westerlund 1 and to investigate its environment as observed in the HI line emission. A Galactic rotation curve was derived using the recently revised values for the Galactic centre distance of $R_\odot = 7.6$ kpc, and the velocity of the Sun around the Galactic centre of $\Theta_\odot = 214$ km s$^{-1}$. The newly determined rotation model leads us to derive a distance of $3.9\pm 0.7$ kpc to Westerlund 1, consistent with a location in the Scutum-Crux Arm. Included in this estimate is a very careful investigation of possible sources of error for the Galactic rotation curve. We also report on small expanding HI features around the cluster with a maximum dynamic age of 600,000 years and a larger bubble which has a minimum dynamic age of 2.5 million years. Additionally we re-calculated the kinematic distances to nearby HII regions and supernova remnants based on our new Galaxic rotation curve. We propose that in the early stages of the development of Wd 1 a large interstellar bubble of diameter about 50 pc was created by the cluster members. This bubble has a dynamic age similar to the age of the cluster. Small expanding bubbles, with dynamical ages $\sim 0.6$ Myr are found around Wd 1, which we suggest consist of recombined material lost by cluster members through their winds.Comment: 8 pages, accepted for publication in A&

Strictly finite range forces from the signum-Gordon field: exact results in two spatial dimensions

Exact formula for the force between two identical static point charges coupled to the nonlinear scalar field of two-dimensional signum-Gordon model is obtained. Pertinent solution of the field equation is found in the form of one-dimensional integral. The force exactly vanishes when the distance between the charges exceeds certain critical value.Comment: published versio

Nambu-Goto string action with Gauss-Bonnet term

We examine the relativistic Nambu-Goto model with Gauss-Bonnet boundary term added to the action integral. The system is analysed using an invariant representation of dynamical string degrees of freedom by complex Liouville fields. The solutions of classical equations of motion for open strings are described.Comment: 9 pages, late

Three-body forces from a classical nonlinear field

Forces in the systems of two opposite sign and three identical charges coupled to the dynamical scalar field of the signum-Gordon model are investigated. Three-body force is present, and the exact formula for it is found. Flipping the sign of one of the two charges changes not only the sign but also the magnitude of the force. Both effects are due to nonlinearity of the field equation.Comment: 12 pages, 2 figure

Spinning Q-balls in the complex signum-Gordon model

Rotational excitations of compact Q-balls in the complex signum-Gordon model in 2+1 dimensions are investigated. We find that almost all such spinning Q-balls have the form of a ring of strictly finite width. In the limit of large angular momentum M_z their energy is proportional to |M_z|^(1/5).Comment: 10 page

The Jang equation, apparent horizons, and the Penrose inequality

The Jang equation in the spherically symmetric case reduces to a first order equation. This permits an easy analysis of the role apparent horizons play in the (non)existence of solutions. We demonstrate that the proposed derivation of the Penrose inequality based on the Jang equation cannot work in the spherically symmetric case. Thus it is fruitless to apply this method, as it stands, to the general case. We show also that those analytic criteria for the formation of horizons that are based on the use of the Jang equation are of limited validity for the proof of the trapped surface conjecture.Comment: minor misprints correcte

Schwarzschild horizon and the gravitational redshift formula

The gravitational redshift formula is usually derived in the geometric optics approximation. In this note we consider an exact formulation of the problem in the Schwarzschild space-time, with the intention to clarify under what conditions this redshift law is valid. It is shown that in the case of shocks the radial component of the Poynting vector can scale according to the redshift formula, under a suitable condition. If that condition is not satisfied, then the effect of the backscattering can lead to significant modifications. The obtained results imply that the energy flux of the short wavelength radiation obeys the standard gravitational redshift formula while the energy flux of long waves can scale differently, with redshifts being dependent on the frequency.Comment: Revtex, 5 p. Rewritten Sec. II, minor changes in Secs III - VII. To appear in the Classical and Quantum Gravit

Falloff of the Weyl scalars in binary black hole spacetimes

The peeling theorem of general relativity predicts that the Weyl curvature scalars Psi_n (n=0...4), when constructed from a suitable null tetrad in an asymptotically flat spacetime, fall off asymptotically as r^(n-5) along outgoing radial null geodesics. This leads to the interpretation of Psi_4 as outgoing gravitational radiation at large distances from the source. We have performed numerical simulations in full general relativity of a binary black hole inspiral and merger, and have computed the Weyl scalars in the standard tetrad used in numerical relativity. In contrast with previous results, we observe that all the Weyl scalars fall off according to the predictions of the theorem.Comment: 7 pages, 3 figures, published versio