In mathematical physics, the Peres metric is defined by the proper time
d τ 2 = d t 2 − 2 f ( t + z , x , y ) ( d t + d z ) 2 − d x 2 − d y 2 − d z 2 {\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.
See also Introduction to the mathematics of general relativity Stress–energy tensor Metric tensor (general relativity)
References 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.