On the Static Spacetime of a Single Point Charge

Details On the Static Spacetime of a Single Point Charge On the Static Spacetime of a Single Point Charge

2010-12-07

arxiv.org/abs/1012.1400v2

Rev.Math.Phys.23:309-346,2011

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

33 pages, 2 figures, revised version, to appear in Rev. Math. Phys

Scientific paper

10.1142/S0129055X11004308

Among all electromagnetic theories which (a) are derivable from a Lagrangian, (b) satisfy the dominant energy condition, and (c) in the weak field limit coincide with classical linear electromagnetics, we identify a certain subclass with the property that the corresponding static, spherically symmetric, asymptotically flat electrovacuum spacetime metric has the mildest possible singularity at its center, namely, a conical singularity on the time axis. The electric field moreover has a point defect on the time axis, its total energy is finite, and is equal to the ADM mass of the spacetime. By an appropriate scaling of the Lagrangian, one can arrange the total mass and total charge of these spacetimes to have any chosen values. For small enough mass-to-charge ratio, these spacetimes have no horizons and no trapped null geodesics. We prove the uniqueness of these solutions in the spherically symmetric class. We conclude by performing a qualitative study of the geodesics and test-charge trajectories of these spacetimes.

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