The notion that spacetime may emerge from entanglement between factors comprising a Hilbert space decomposition of the vacuum has been suggested by many (for example, M. Van Raamsdonk “Building up spacetime with quantum entanglement” Gen Relativ Gravit 42 (2010)).

One possible model based on this decomposition is that of a highly entangled vacuum embedded in a higher dimensional bulk. The bulk is assumed here to be disentangled from the vacuum. A large lambda assumption is also made, assigning a high value to the vacuum energy.

A consequence of disentanglement is that the Hilbert space, for the bulk is orthogonal to that supporting the vacuum. Only null vectors are common to both spaces. As zero time elapses in such null vector reference frames, no net energy can be exchanged between the bulk and vacuum i.e. energy is conserved in the vacuum.

As a BH accretes matter, spacetime quanta from the vacuum will cross the BH horizon. If the horizon acts to disentangle such quanta from the vacuum, then the high energy of vacuum entanglement can be released into the bulk. Energy conservation dictates that this energy must remain in the vacuum. It is hypothesised that this energy may take two forms:

(1) Subsequent entanglement of bulk spacetime quanta outside the BH, resulting in an expansion of the vacuum (i.e. Dark Energy); and,

(2) Bulk entrainment of gravitational energy within the BH (i.e. as Dark Matter).

Both processes may occur with no time elapsing in the vacuum.

The high incidence of supermassive BHs is consistent with positive feedback inherent in process (2). Process (1) may be testable from observations of the varying rate of cosmic expansion. There should be a positive correlation of the cosmic expansion rate with the overall rate of increase of Black Hole surface area.

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    $\begingroup$ Are the measures of growth you mention directly related to accretion by BH? If not, then recent constant expansion rate may still be consistent? Thank you. $\endgroup$
    – RalphW
    Aug 3, 2023 at 16:42
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    $\begingroup$ The growth of galaxies, AGN activity, star formation, black hole formation, etc. all show a precipitous drop since z=2 (see The Black Hole Mass Function Across Cosmic Times, Figs. 4 and 7, iopscience.iop.org/article/10.3847/1538-4357/ac34fb). But measurements of cosmological constant show it to be constant over this time period. $\endgroup$
    – eshaya
    Aug 3, 2023 at 16:52
  • $\begingroup$ A more accurate statement of the cosmic inflation rate predicted by this model is that vacuum inflation depends directly on total BH surface area (not the rate of mass accretion). BH surface area increases by absorbing vacuum spacetime, which increases the amount of entanglement energy released to the bulk. The latter drives vacuum expansion as Dark Energy. $\endgroup$
    – RalphW
    Aug 6, 2023 at 19:27
  • $\begingroup$ Your last comment is in conflict with the final paragraph of your question. $\endgroup$
    – eshaya
    Aug 6, 2023 at 20:21
  • $\begingroup$ Yes. My mistake, I'm sorry. But the model interpretation really should focus on BH surface area. $\endgroup$
    – RalphW
    Aug 6, 2023 at 21:32


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