Alex Harvey

Einstein's mistake and the cosmological constant

A brief history of the cosmological constant in the equations of general relativity is presented. Particular attention is paid to (a) a misunderstanding by Einstein of both its function as a repulsive force and new vacuum state rather than the relativistic analog of an exponential potential cutoff he thought he had introduced and to (b) a common misunderstanding of the function of the cosmological constant.

Redshifts and Killing vectors

Current approaches to physics stress the importance of conservation laws due to spacetime and internal symmetries. In special and general relativity the generators of these symmetries are known as Killing vectors. We use them for the rigorous determination of gravitational and cosmological redshifts.

A Small Puzzle from 1905

In his first relativity paper, Einstein made one erroneous prediction. Although it should have been withdrawn when he generalized the theory to include gravity, the original error has received surprisingly little attention.

Newtonian limit for a geodesic in a Schwarzschild field

In the 19th century there were many attempts to explain the advance of the perihelion of Mercury by modifying the Newtonian potential by the addition of velocity‐dependent terms. That such potentials did not give better results was due to the wrong choice of sign of the velocity term. This is demonstrated by showing that in a simple Newtonian limit for near‐circular orbits the geodesic of a mass point in a Schwarzschild field may be expressed as motion in a velocity‐dependent central potential. The sign of the velocity term is opposite to that arbitrarily assigned in the past.