3. Shifting the cosmological constant to the right side and interpret it as a source. One way of interpreting the cosmological constant \(\Lambda\) is to bring it to the RHS of the Einstein equation and treat it as a piece of energy-momentum tensor \(R_{\mu\nu} - \frac{1}{2}g_{\mu\nu}R + \Lambda g_{\mu\nu} = \frac{8\pi G}{c^4}T_{\mu\nu}\) (41) \(R_{\mu\nu} - \frac{1}{2}g_{\mu\nu}R = \frac{8\pi G}{c^4}T_{\mu\nu} - \Lambda g_{\mu\nu}\) (42) \(R_{\mu\nu} - \frac{1}{2}g_{\mu\nu}R = \frac{8\pi G}{c^4}T_{\mu\nu} + \frac{8\pi G}{c^4}T_{\mu\nu}^{(\Lambda)}\) (43) Simply write out \(T_{\mu\nu}^{(\Lambda)}\) explicitly.
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