Which method relies on bending spacetime to map a cluster's total mass?

Gravitational lensing

Gravitational lensing provides perhaps the most accurate method for determining the total mass of a galaxy cluster, relying directly on Einstein’s theory of General Relativity. Massive objects warp the fabric of spacetime around them. When light from extremely distant background galaxies passes near a foreground cluster, this warped spacetime bends the light rays, causing observable distortions such as magnification, shearing, or multiple images of the background source. By meticulously analyzing the degree of this distortion, scientists can create a precise map of the total mass distribution, revealing the location and extent of the underlying dark matter halo, offering a measurement independent of the cluster's dynamical state or gas temperature.