• On conformally related pp-waves

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      https://www.ias.ac.in/article/fulltext/pram/056/05/0591-0596

    • Keywords

       

      Conformal transformations; conformal Killing vectors; pp-waves

    • Abstract

       

      Brinkmann [1] has shown that conformally related distinct Ricci flat solutions are pp-waves. Brinkmann’s result has been generalized to include the conformally invariant source terms. It has been shown that [4] if gik and $$\overline g $$ik (=w−2gik; w: a scalar function), are distinct metrics having the same Einstein tensor, Gik=$$\overline G $$ik, then both represent (generalized) pp-waves and wi is a null covariantly constant vector of gik. Thus pp-waves are the only candidates which yield conformally related nontrivial solutions of Gik=Tik=$$\overline G $$ik, with Tik being conformally invariant source.

      In this paper the functional form of the conformal factor for the conformally related pp-waves/generalized pp-waves has been obtained. It has been shown that the most general pp-wave, conformally related to ds2=−2du[dvmdy=Hdu]+P−2[dy2+dz2], turns out to be (au+b)−2 ds2, where a,b are constants. Only in the special case when m=0, H=1, and P=P(y, z), the conformal factor is (au+b)−2 or (a(u+v)+b)−2.

    • Author Affiliations

       

      Varsha Daftardar-Gejji1

      1. Department of Mathematics, University of Pune, Ganeshkhind, Pune - 411 007, India
    • Dates

       
  • Pramana – Journal of Physics | News

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