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Having looked at this question online, multiple sources overwhelmingly support the statement that 'Gravity results from the curvature of space-time due to mass-energy'. However, discussions on the H-Bar (See here in the chat logs) have led to me doubting this.

So, is the above statement correct, or not? If not, then can it be corrected, or should it be completely disregarded? I cannot see how the curvature of space-time and gravity cannot be related, as gravity and curvature are both linked to the mass of an object. For example, a black hole results in massive curvature of space-time, and the gravitational forces are also massive.

Qmechanic
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Noah P
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1 Answers1

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Gravitational force, and electromagnetic force for that matter, are both described accurately by curvature theories. The Einstein Field Equations are described by the following:

$G_{ab} +\Lambda g_{ab}= \frac{8\pi G}{c^4} T_{ab}$

In this equation, $T_{ab}$ is the stress-energy tensor which describes the motion and state of matter in a frame where the shape of the space is described by the metric tensor $g_{ab}$ and $\Lambda$ is the cosmological constant. $G_{ab}$ is called the Einstein Tensor and is defined as

$G_{ab} = R_{ab} - \frac{1}{2}g_{ab}R$

Where $R_{ab}$ is the Ricci curvature tensor and $R$ is the scalar curvature.

The above Field Equations are really a set of equations. Each matching index in the tensors presented gives another equation. One such solution is

$\nabla^2\Phi = 4\pi G\rho -\Lambda c^2$,

Which is Poisson's equation and describes the Laplacian of gravitational potential with the addition of the cosmological constant for description of large scale gravitational mechanics. Further exercises can be done to derive the basic Newtonian theory.

hebetudinous
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