Peres metric explained

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

{d \tau} ^{2} = dt ^{2} - 2 f(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 it in 1959.

See also

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

References

• Peres . Asher . 1959 . Some Gravitational Waves . . 3 . 12 . 571–572 . 10.1103/PhysRevLett.3.571 . 27 April 2013. 1959PhRvL...3..571P .