Analytical Study on the Sunyaev-Zeldovich Effect for Clusters of Galaxies. II. comparison of covariant formalisms

Satoshi Nozawa, Yasuharu Kohyama, Naoki Itoh

We study a covariant formalism for the Sunyaev-Zeldovich effects developed in the previous papers by the present authors, and derive analytic expressions for the redistribution fun…