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The positive energy theorem talks about the lower bound on the total energy/mass, like the ADM mass. To be able to define such a concept of the total energy/mass in general relativity, one needs some asymptotic region respecting a time-translational symmetry. That's the region where the gravitational potential (something like the deviation of $g_{00}$ from ...


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See L. Rodriguez and T. Yildirim, Class. Quantum Grav. 27, 155003 (2010), arXiv:1003.0026. Section 2.3 has the Schwarzschild-dS calculation. Lets define $f(r)=1-\frac{2M}{r}-\frac{r^2}{L^2}$ Radius of the horizon is given by the largest real root of f(r)=0 But of course $L\rightarrow \infty$ is still important. Once you obtain the energy momentum ...



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