Black-hole (Planck)

Planck-unit Black-hole universe

A Planck-unit Black-hole universe defines the universe superstructure in terms of discrete Planck-units and is applicable to Simulation Hypothesis programming that use digital time where time is measured in discrete units of Planck time (the universe simulation clock-rate).

A base structure, a discrete and indivisible Planck micro black-hole is assigned the Planck-units [1], forming the scaffolding for particle substructures.

Universe time tage is defined by incremental additions of these Planck micro black-holes to the sum Planck Black-hole universe, as such for any chosen unit of simulation (Planck) time tage, there can be calculated the equivalent cosmic microwave background parameters [2].

In this table tage = 0.428 1061 units of Planck time;

cosmic microwave background parameters; calculated vs observed
Parameter Calculated Observed
Age (billions of years) 14.624 13.8
Age (units of Planck time) 0.428 1061
Mass density 0.21 x 10-26 kg.m-3 0.24 x 10-26 kg.m-3
Radiation energy density 0.417 x 10-13 kg.m-1.s-2 0.417 x 10-13 kg.m-1.s-2
Hubble constant 66.86 km/s/Mpc 67 (ESA's Planck satellite 2013)
CMB temperature 2.727K 2.7255K
CMB peak frequency 160.2GHz 160.2GHz
Entropy CEH 2.3 x 10122kB 2.6 x 10122kB[3]
Casimir length 0.42mm

Mass densityEdit

For each increment to time tage, to the Planck Black-hole is added a Planck micro black-hole comprising a unit of Planck time tp, Planck mass mP and Planck (spherical) volume (Planck length = lp), such that we can then calculate the mass, volume and so mass density of the sum Black-hole for any chosen unit of time, (tsec if the age of the Black-hole is measured in seconds).


Gravitation constant G as Planck units;


From the Friedman equation; replacing p with the above mass density formula, √(λ) reduces to the radius of the universe;



Measured in terms of Planck temperature = TP;


The mass/volume formula uses tage2, the temperature formula uses √(tage). We may therefore eliminate the age variable tage and combine both formulas into a single constant of proportionality that resembles the radiation density constant.


Radiation energy densityEdit

From Stefan Boltzmann constant σSB


Casimir formulaEdit

The Casimir force per unit area for idealized, perfectly conducting plates with vacuum between them; F = force, A = plate area, dc 2 lp = distance between plates in units of Planck length


if dc = 2 π √tage then the Casimir force equates to the radiation energy density.


A radiation energy density pressure of 1Pa gives tage = 0.8743 1054 tp (2987 years), Casimir length = 189.89nm and temperature TBH = 6034 K.

Hubble constantEdit

1 Mpc = 3.08567758 x 1022.


Black body peak frequencyEdit




Cosmological constantEdit

Riess and Perlmutter using Type 1a supernovae to show that the universe is accelerating. This discovery provided the first direct evidence that Ω is non-zero giving the cosmological constant as ~ 1071 years;

  units of Planck time;

This remarkable discovery has highlighted the question of why Ω has this unusually small value. So far, no explanations have been offered for the proximity of Ω to 1/tuniv2 ~ 1.6 x 10-122, where tuniv ~ 8 x 1060 is the present expansion age of the universe in Planck time units. Attempts to explain why Ω ~ 1/tuniv2 have relied upon ensembles of possible universes, in which all possible values of Ω are found [4] .

The maximum temperature Tmax would be when tage = 1. What is of equal importance is the minimum possible temperature Tmin - that temperature 1 Planck unit above absolute zero, this temperature would signify the limit of expansion (the black hole could expand no further). For example, taking the inverse of Planck temperature;


This then gives us a value for the final age in units of Planck time (about 0.35 x 1073 yrs);


The mid way point (Tuniverse = 1K) would be when (about 108.77 billion years);



External linksEdit


  1. Macleod, Malcolm J. "Programming Planck units from a virtual electron; a Simulation Hypothesis". Eur. Phys. J. Plus 113: 278. 22 March 2018. doi:10.1140/epjp/i2018-12094-x. 
  2. Macleod, Malcolm; "Programming relativity and gravity in a Planck unit Simulation Hypothesis". RG. 26 March 2020. doi:10.13140/RG.2.2.31308.16004. 
  4. J. Barrow, D. J. Shaw; The Value of the Cosmological Constant, arXiv:1105.3105v1 [gr-qc] 16 May 2011