Galaxy cluster hydrostatic bias in Kottler spacetime
  We calculate the relativistic corrections to hydrostatic X-ray masses for
galaxy clusters in Kottler spacetime, which is the spherically symmetric
solution to Einstein's equations in General relativity endowed with a
cosmological constant. The hydrostatic masses for clusters (calculated assuming
Newtonian gravity) have been found to be underestimated compared to lensing
masses, and this discrepancy is known as hydrostatic mass bias. Since the
relativistic hydrostatic X-ray masses are automatically lower than lensing
masses, under the edifice of Kottler metric, we check if the hydrostatic mass
bias problem gets alleviated using this {\it ansatz}. We consider a sample of
18 galaxy clusters for this pilot test. We find that the ratio of X-ray to
lensing mass is close to unity even in Kottler spacetime. Therefore, the effect
of relativistic corrections to hydrostatic X-ray masses for galaxy clusters is
negligible.
