General Relativity: An Introduction for Physicists · Problem 8.12

The gravitational field equations — Hobson, Efstathiou & Lasenby

Physics · scalar-gravity-newtonian-limit

Problem

In the scalar theory of gravity (8.30) show that, in any inertial frame, the gravitational potential Φ\Phi produced by a perfect fluid at some event PP satisfies 1c2∂2Φ∂t2−∇⃗2Φ=−4πG(ρ−3pc2),\frac{1}{c^2}\frac{\partial^2\Phi}{\partial t^2} - \vec{\nabla}^2\Phi = -4\pi G\left(\rho - \frac{3p}{c^2}\right), where ρ\rho and pp are the density and isotropic pressure as measured in the instantaneous rest frame of the fluid at PP. Hence show that the theory reduces to Newtonian gravity in the non-relativistic limit. How might a cosmological constant be included in the theory?

Related theory

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