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

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

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 it in 1959.

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

• Peres, Asher (1959). "Some Gravitational Waves". Phys. Rev. Lett. 3 (12): 571–572. Bibcode:1959PhRvL...3..571P. doi:10.1103/PhysRevLett.3.571. Retrieved 27 April 2013.

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