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*A First Course in General Relativity*, section 4.5, p. 101 (in this edition), writes that

[tex]\mathrm{d}\rho-(\rho+p)\frac{\mathrm{d}n}{n}[/tex]

"depends only on rho and n." Is he saying

[tex]\mathrm{d}\rho-(\rho+p)\frac{\mathrm{d}n}{n} = f(\rho,n)[/tex]

where f : {scalar fields on spacetime} --> {1-form fields on spacetime}, and rho, n and p are such scalar fields? In the discussion that follows, are the functions A and B scalar fields on spacetime, dB being the gradient or exterior derivative of B?