Relativity and the Nature of Spacetime, Vesselin Petkov, Springer, 2009, ISBN 978-3-642-01952-4, Chapter: 7
The property of charge invariance follows from the vanishing divergence of the charge-current four-vector \( j^\mu=(c\rho,{\vec j}) \) , with \( \partial_\mu j^\mu=0. \)

In mathematical physics, the Peres metric is defined by the proper time

\( {d \tau}^{2} = dt^2 - 2f\, (t+z,\,x,\,y) (dt+dz)^2-dx^2-dy^2-dz^2 \)

for any arbitrary function f. If f is a harmonic function with respect to x and y, then the corresponding Peres metric satisfies the Einstein field equations in vacuum. Such a metric is often studied in the context of gravitational waves. The metric is named for Israeli physicist Asher Peres, who first defined the metric in 1959.
See also

Introduction to the mathematics of general relativity
Stress–energy tensor
Metric tensor (general relativity)


Peres, Asher (1959). "Some Gravitational Waves". Phys. Rev. Lett. 3: 571–572. Bibcode:1959PhRvL...3..571P. doi:10.1103/PhysRevLett.3.571. Retrieved 27 April 2013.

Black hole complementarity
de Sitter space

1 Exact solutions
2 Black hole uniqueness
3 See also

Physics Encyclopedia

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