Homogeneous, anisotropic solutions of topologically massive gravity including a cosmological constant

Abstract

I'lxact solutions l.o tin' (ic'ld (M|iial.ioiis o( 'Го|)о1о;г;1са,11у ma.ssiv(i gravity wit h a cosmological coiisl.anl. ai<' pix'scntisl. Tlics(' ai<‘ lK)mog<m<'o\is,a,iiisotro|)ic Bianchi J ’ypc VIII and l'y|x' IX mainlolds and generalize' tiu' linitc action vacniim solutions of (.opologica.ily massi\ ('gravity.We (ind tlia.t only tliose^ solutions in which two of tli(i constant scale (actors are' the' same admit a. e'.osmole)gie a.l e'.onstant.We also lind tha.t,ele'|)eniding e)ii I,he' signature' and the sign e)f I he' e e)snioleygical e'.e)nstant,the'se' se)lutie)iis |)e>int te> the e.xiste'ite:e e)f a. e ritical value' lor the te)|)ole)gical mass whie h is ele'te'rmine'd by the ce)sme)le)gie al e e)nstaid .