[<< wikibooks] General Relativity/Notes to GR editors
Since I am sure I'm not the only one who will be editing this page, let's agree on some standards so that everything is cohesive.  Here are my suggestions:
1.  Certainly we should use follow the Einstein summation convention.
2.  Let's agree to use the same signature for the Minkowski metric.  I propose the 
  
    
      
        (
        −
        +
        +
        +
        )
      
    
    {\displaystyle (-+++)}
   signature, i.e., the Minkowski metric 
  
    
      
        
          η
        
      
    
    {\displaystyle \mathbf {\eta } }
   is given by 
  
    
      
        
          η
        
        (
        
          u
        
        ,
        
          v
        
        )
        =
        −
        
          u
          
            0
          
        
        
          v
          
            0
          
        
        +
        
          u
          
            1
          
        
        
          v
          
            1
          
        
        +
        
          u
          
            2
          
        
        
          v
          
            2
          
        
        +
        
          u
          
            3
          
        
        
          v
          
            3
          
        
      
    
    {\displaystyle \mathbf {\eta } (\mathbf {u} ,\mathbf {v} )=-u^{0}v^{0}+u^{1}v^{1}+u^{2}v^{2}+u^{3}v^{3}}
  .
E-mail me or edit the discussion page if you have questions or comments.
-Lathem