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Full-Text Articles in Cosmology, Relativity, and Gravity
Static Interaction Of Black Holes In 1+1 Dimensions, Philip Greenwood
Static Interaction Of Black Holes In 1+1 Dimensions, Philip Greenwood
Physics
We consider a version of general relativity in two spacetime dimensions, and
study a solution describing two static black holes in the presence of a cosmological
constant. We first analytically find an embedding diagram to visualize the geometry
outside the black holes. We then examine how the two black holes must be
interacting to remain static. Our main result is to show how the black holes behave
effectively like two electric charges. This charge model exhibits both attraction and
repulsion, which evidently balance and moreover are localized in different regions
of space. We also begin an investigation of the black …
Perihelion Precession In General Relativity, Charles G. Torre
Perihelion Precession In General Relativity, Charles G. Torre
Charles G. Torre
This is a Maple worksheet providing a relatively quick and informal sketch of a demonstration that general relativistic corrections to the bound Kepler orbits introduce a perihelion precession. Any decent textbook will derive this result. My analysis aligns with that found in the old text "Introduction to General Relativity", by Adler, Bazin and Schiffer. The plan of the analysis is as follows. * Model the planetary orbits as geodesics in the (exterior) Schwarzschild spacetime. * Compute the geodesic equations. * Simplify them using symmetries and first integrals. * Isolate the differential equation expressing the radial coordinate as a function of …
The Spacetime Geometry Of A Null Electromagnetic Field, Charles G. Torre
The Spacetime Geometry Of A Null Electromagnetic Field, Charles G. Torre
Charles G. Torre
We give a set of local geometric conditions on a spacetime metric which are necessary and sufficient for it to be a null electrovacuum, that is, the metric is part of a solution to the Einstein-Maxwell equations with a null electromagnetic field. These conditions are restrictions on a null congruence canonically constructed from the spacetime metric, and can involve up to five derivatives of the metric. The null electrovacuum conditions are counterparts of the Rainich conditions, which geometrically characterize non-null electrovacua. Given a spacetime satisfying the conditions for a null electrovacuum, a straightforward procedure builds the null electromagnetic field from …