Does the energy density of space create cause gravitational attraction beyond what would be computed from an object's mass alone?

Question

I am starting from the assumption that the gravitational warping of spacetime increases its volume, so a spherical region of space with a fixed surface area would be able to fit a larger number of telephone booths inside it if it contained a large mass than it would without the mass. John Rennie's answer to this question: When a massive object warps the space around it, does the amount of space expand? and some of the answers to this question: Does curved spacetime change the volume of the space? give me the impression that gravitational warping does increase volume, but some of the other answers I have seen suggest otherwise.

A second assumption I am using is that energy exerts a gravitational pull and empty space has some intrinsic energy embedded within it. I am basing this on what I have read about kugelblitz backholes, and the vacuum energy of space.

So, when we examine a region of space defined by a surface area around a large mass, does that region have more gravity than what would be attributed to the mass alone due to the relatively larger volume of space inside the region created by the mass's warping of spacetime?

Answer 1

Does the energy density of space create cause gravitational attraction beyond what would be computed from an object's mass alone?

No. A positive cosmological constant (equivalent to positive dark energy) reduces gravitational attraction. It has a repulsive effect.

From the deSitter-Schwarzschild metric, the Newtonian potential of a mass $M$ in the presence of a cosmological constant $\Lambda$ is

$$\varphi=-\frac{M}{r}-\frac{\Lambda r^2}{6}$$

and the gravitational field is

$$-\nabla\varphi=\left(-\frac{M}{r^2}+\frac{\Lambda r}{3}\right)\hat r$$

in geometrical units where $G=c=1$.

At the surface of the Earth, the cosmological constant reduces gravitational acceleration by the unmeasurable amount of about $1$ part in $10^{30}$.

The repulsive effect of the cosmological constant / dark energy is what is causing the observed acceleration of the expansion of the universe, according to the current Lambda-CDM model of cosmology.

In General Relativity, both energy density and pressure cause spacetime curvature. Lorentz invariance requires a positive energy density of the vacuum to be accompanied by a negative pressure of the vacuum. The antigravity of the negative pressure dominates the gravity of the positive energy density, causing repulsion.