How to test if a metric contain close timelike curve? I read somewhere that if the space coordinate change from positive to negative then it contain close timelike curve. For example, a metric gmn=-Adt2+Bdr2+Cdθ2+Ddz2, if C is negative, then it contain close timelike curve. Is that correct? Is there any other conditions? Beside that, what is the meaning if A change from positive to negative? For example A=1-r. When r=1, A=0. What is meaning of A=0? Time stop? For r>1, A<0, what is the meaning for A<0? Is this physically possible? Thanks.