The theory of gravitational lensing is reviewed from a spacetime perspective, without quasi-Newtonian approximations More precisely, the review covers all aspects of gravitational lensing where light propagation is described in terms of lightlike geodesics of a metric of Lorentzian signature It includes the basic equations and the relevant techniques for calculating the position, the shape, and the brightness of images in an arbitrary general-relativistic spacetime It also includes general theorems on the classification of caustics, on criteria for multiple imaging, and on the possible number of images The general results are illustrated with examples of spacetimes where the lensing features can be explicitly calculated, including the Schwarzschild spacetime, the Kerr spacetime, the spacetime of a straight string, plane gravitational waves, and others

https://link.springer.com/content/pdf/10.12942%2Flrr-2004-9.pdf

Gravitational Lensing from a Spacetime Perspective

The theory of gravitational lensing is reviewed from a spacetime perspective, without quasi-Newtonian approximations. More precisely, the review covers all aspects of gravitational lensing where light propagation is described in terms of lightlike geodesics of a metric of Lorentzian signature. It includes the basic equations and the relevant techniques for calculating the position, the shape, and the brightness of images in an arbitrary general-relativistic spacetime. It also includes general theorems on the classification of caustics, on criteria for multiple imaging, and on the possible number of images. The general results are illustrated with examples of spacetimes where the lensing features can be explicitly calculated, including the Schwarzschild spacetime, the Kerr spacetime, the spacetime of a straight string, plane gravitational waves, and others.

On event horizons in static vacuum spacetimes

Interior solutions for a static, axially symmetric family of solutions of Einstein's equations are described. The interior solutions correspond to spatially bound matter and are properly matched to an exterior vacuum solution. The family of solutions discussed include the Schwarzschild solution as a special case. A general method is exhibited for transforming any spherically symmetric interior solution to an interior for the other members of the family of solutions. The energy density remains positive for at least a finite range of the parameter that describes the family of solutions. Two solutions are explicitly exhibited. One is transformed from the constant density Schwarzschild interior solution and one from the Adler interior solution. The first solution would be expected to be unstable under adiabatic perturbations of the matter, the second would be expected to be stable.

An interior solution for the gamma metric

Preface Introduction A general characterisation of the subject A synopsis of notations of Riemannian geometry The Noether theorem: space-time invariance The Noether densities transformation laws Reference frames calculus The monad formalism and its place in the description of reference frames in relativistic physics Reference frames algebra Geometry of congruences. Acceleration, rotation, expansion and shear of a reference frame Differential operations and identities of the monad formalism Equations of motion of test particles The electric field strength and magnetic displacement vectors Monad description of the motion of a test charged mass in gravitational and electromagnetic fields Motion of photons, the redshift and Doppler effects The dragging phenomenon Dragging in circular equatorial orbits in the Kerr space-time An orbit shift in the TaubNUT space-time Dragging in the space-time of a pencil of light Other dragging effects More general gravitoelectromagnetic and gravitoelectric phenomena The Maxwell field equations The four-dimensional Maxwell equations The electromagnetic stress-energy tensor and its monad decomposition Monad representation of Maxwells equations A charged fluid without electric field An Einstein-Maxwell field with kinematic magnetic charges The Einstein field equations The four-dimensional Einstein equations Monad representation of Einsteins equations The geodesic deviation equation and a new level of analogy between gravitation and electromagnetism New quasi-Maxwellian equations of the gravitational field Remarks on classification of intrinsic gravitational fields Example of the Taub-NUT field Example of the spinning pencil-of-light field Gravitational fields of the G..odel universe Perfect fluids Introductive remarks Rank 2 and 3 fields Free rank 2 field Free rank 3 field Rotating fluids Special relativistic theory Additional remarks Mechanics versus field theory Canonical approach to field theory Canonical formalism and quantisation Concluding remarks References Index.

J. Porter

Papers

Methods of Local and Global Differential Geometry in General Relativity