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The Book im reading about general relativity says that energy unit in GR are kg, so until i know the units of energy in the SI are Joules (J) $$ 1 J = 1 kg \frac{m^2}{s^2} $$ the books says i need to use these convertion rules $$ 1 s = 3 \times 10^{8} m $$ and $$ 1 m= \frac{1}{3\times10^8 s} $$ but if i use the last two equation in the first only i get $$ 1 J = \frac{1kg}{81 \times 10^{32}s^{2}m^{2}} $$ what im doing wrong?

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closed as off-topic by AccidentalFourierTransform, heather, Gert, Jon Custer, user36790 Nov 26 '16 at 17:05

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    $\begingroup$ use one of the equations, not both! $\endgroup$ – AccidentalFourierTransform Nov 25 '16 at 18:19
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    $\begingroup$ You have evidently misread the location os s in the 3rd equation you write. Is it consistent with the second? $\endgroup$ – Cosmas Zachos Nov 25 '16 at 18:40
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When doing calculations in general relativity we don't distinguish between matter and energy. Instead we treat them as the same thing related by Einstein's famous equation $E=mc^2$. So if you're trying to turn a mass in $kg$ into an energy in $J$ just multiply it by $c^2$ in SI units i.e. $299792458^2$.

Likewise, if you're trying to trun an energy in $J$ into a mass in $kg$ just divide by $299792458^2$.

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