Wolfgang Rindler

Kruskal space and the uniformly accelerated frame.

The striking formal similarities between the diagram of Kruskal space in general relativity and that of the uniformly accelerated rigid rod in special relativity are shown to be the result of certain physical similarities.

Contribution of the cosmological constant to the relativistic bending of light revisited

We study the effect of the cosmological constant

A new independent limit on the cosmological constant/dark energy from the relativistic bending of light by Galaxies and clusters of Galaxies

\ensuremath{\Lambda}

Rotating coordinates as tools for calculating circular geodesics and gyroscopic precession

on the bending of light by a concentrated spherically symmetric mass. Contrarily to previous claims, we show that, when the Schwarzschild-de Sitter geometry is taken into account,

Length Contraction Paradox

\ensuremath{\Lambda}

More on lensing by a cosmological constant

does indeed contribute to the bending.

The relevance of the cosmological constant for lensing

We derive new limits on the value of the cosmological constant, A, based on the Einstein bending of light by systems where the lens is a distant galaxy or a cluster of galaxies. We use an amended lens equation in which the contribution of A to the Einstein deflection angle is taken into account and use observations of Einstein radii around several lens systems. We use in our calculations a Schwarzschild-de Sitter vacuole exactly matched into a Friedmann-Robertson-Walker background and show that a A-contribution term appears in the deflection angle within the lens equation. We find that the contribution of the A-term to the bending angle is larger than the second-order term for many lens systems. Using these observations of bending angles, we derive new limits on the value of A. These limits constitute the best observational upper bound on A after cosmological constraints and are only two orders of magnitude away from the value determined by those cosmological constraints.

The Lense-Thirring effect exposed as anti-Machian

If an axially symmetric stationary metric is given in standard form (i.e. in coordinates adapted to the symmetries) the transformationφ→φ′ =φ-ωt (ω=constant) of the azimuthal angle leads to another such standard form. The spatial latticeL′ corresponding to the latter rotates at angular velocityω relative to the latticeL of the former. For the standard form of a stationary metric there are simple formulae giving the four-acceleration of a given lattice point and the rotation of a gyroscope at a given lattice point. Applying these formulae toL′, we find the condition for circular paths about the axis inL to be 4-geodesic, and also the precession of gyroscopes along circular paths which are not necessarily geodesic. Among other examples we re-obtain the complete geodesic structure of the Gödel universe, and the gyroscopic precessions associated with the names of Thomas, Fokker and de Sitter, and Schiff.

Energy conservation as the basis of relativistic mechanics. II.

A certain man walks very fast—so fast that the relativistic length contraction makes him very thin. In the street he has to pass over a grid. A man standing at the grid fully expects the fast thin man to fall into the grid. Yet to the fast man the grid is much narrower even than to the stationary man, and he certainly does not expect to fall in. Which is correct? The answer hinges on the relativity of rigidity.

Visual horizons in world-models

The question of whether or not the cosmological constant affects the bending of light around a concentrated mass has been the subject of some recent papers. We present here a simple, specific and transparent example where A bending clearly takes place, and where it is clearly neither a coordinate effect nor an aberration effect. We then show that in some recent works using perturbation theory the A contribution was missed because of initial too stringent smallness assumptions. Namely, our method has been to insert a Kottler (Schwarzschild with A) vacuole into a Friedmann universe, and to calculate the total bending within the vacuole. We assume that no more bending occurs outside. It is important to observe that while the mass contribution to the bending takes place mainly quite near the lens, the A bending continues throughout the vacuole. Thus, if one deliberately restricts ones search for A bending to the immediate neighbourhood of the lens, one will not find it. Lastly, we show that the A bending also follows from standard Weyl focusing, and so again, it cannot be a coordinate effect.