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Gravitational repulsion is defined to mean that a free particle instantaneously at rest is accelerated outwards from the mass center. It is shown that there is no gravitational repulsion in the Schwarzschild spacetime, and hence that there is no acceleration to high energy via gravitational repulsion in the Schwarzschild field.

We describe the electromagnetic field of a uniformly accelerated charge in its co-moving Rindler frame. It is shown that the electrical field lines coincide with the trajectories of photons. The self force of a charged particle at rest in Rindler space, and the increase of its weight due to its charge, is calculated. The general case of an accelerated charge in Rindler space is also considered. It is shown that the electrical field inside a uniformly charged spherical shell can be used as a measure of it 4-acceleration. A result that has earlier been deduced in a different way by Fugmann and Kretzschmar is confirmed, namely that the intensity of radiation from a point charge instantaneously at rest in an accelerated frame is proportional to the square of the relative acceleration of the charge and the observer. In particular it is shown that a freely falling charge in Rindler space radiates in accordance with Larmor’s formula. In this case the radiation energy is taken from the Schott energy. The energy of the electromagnetic field is analysed from the point of view of the Hirayama-separation, which generalizes the Teitelboim-separation to non-inertial frames, of the field in a bound part and an unbound part. A detailed account, with reference to the Rindler frame, of the field energy and particle energy is given for the case of a charge entering and leaving a region with hyperbolic motion. We also consider the electromagnetic field of a uniformly accelerated charge with reference to the Milne frame, which covers a different part of spacetime than the Rindler frame. The radiating part of the electromagnetic field is found in the Milne sector of spacetime.

We give a detailed description of the energy–momentum relationships of the Bondi–Gold field. The Schott field is separated into a near field and a radiation field. The physical significance of a plane acting as a barrier for transport of energy in the field of a charge with permanent hyperbolic motion, but which lets energy through in the case of hyperbolic motion for a finite time interval, is discussed. We deduce general expressions for energy and momentum of the near field and radiation field of charges with arbitrary motion. The field reaction on the particle producing the field is calculated. The formulae are applied to the Schott field and the Bondi–Gold field.

We investigate static plane-symmetric space-times. The source of curvature in the Taub space is identified, and the modification hereof due to the presence of a conformally coupled scalar field is calculated. For a specific value of the scalar charge, the scalar field has an energy-momentum tensor of the Casimir type. In this case the source is a domain wall.

A new solution of Einstein's field equations is found. It describes a dust-filled Kantowski-Sachs universe with positive cosmological constant. The mass density of the dust is positive. This cosmological model develops from a point singularity towards an infinite barrel singularity.

The black hole model constructed by Gonzalez-Diaz, with de Sitter metric inside the horizon and Schwarzschild metric outside it, is investigated by considering a spherical region with false vacuum surrounded by ordinary vacuum. The hypersurface between the two different vacuum regions is a spherical singular layer. A static solution of the equation of motion of the junction surface exists in the limit that the “horizon positions” of the de Sitter and Schwarzschild regions approach each other. This corresponds to the Gonzalez-Diaz model. A stability analysis shows that this black hole model is dynamically unstable.

The radial motion of a free neutral test particle in the Reissner-Nordstrom space-time is studied. It is shown that when the contribution of the electrical field energy to the mass of the central body is properly taken account of, there is no repulsion of the test particle inside the inner horizon of the space-time.

Hiscock has recently found that if particles moving in nearly circular orbits at the Schwarzschild radius of a black hole, enter the hole, this would lead to a decrease in the area of the hole's horizon. I show here, within the same framework as Hiscock uses, that this is not the case.