OK, its been a while, with no other comments or answers, so I will answer.
A: Yes. The existence of black hole horizons implies a maximum power limit in General Relativity, leading to related conjectures first posed around the time of Hogan’s 1999 paper.
Figure 1 Outgoing shell of radiation and its past appearance
Consider a process (Figure 1, Cardoso et al 2018) with a finite time $t$ which produced radiation with a total mass-energy of $E=Mc^2$ contained in a shell of thickness $R=c.t=1$. Evolve this system into the past until $R=shell radius$. For the radiation to have escaped its initial self-gravity a BH horizon cannot have been present for the ‘particle’, so:
$R ≥ 2GM/c^2$ (1)
The maximum power, or luminosity, is therefore:
$P(max)=c.F(max)= E/t=c^5/2G$ (2)
With natural units, we could assign $R$ as unit (Planck) length, $t$ is a unit (Planck) time so then $E=1/2=pc=Mc^2$ half a Planck mass-energy. The products (not the individual values), of these quantities are therefore minimum bounds in GR and quantum gravity, i.e. the uncertainty principle.
So $MR=1/2$ where $R=ℏ/2Mc=1$ being the reduced Compton radius of the ‘particle’. This was noted by Carter(1968), his Kerr-Newman solution for a charged and rotating black hole with a gyromagnetic ratio of 2 like the Dirac electron. That is, (2) also holds if the shell was charged and rotating.
(2) corresponds with the Planck acceleration $a_P$ being the maximum acceleration in quantum gravity.
$F(max)= c^4/2G=M.a_P$ (3)
(3) also agrees with Caianiello $a_c=(2Mc^3)/ℏ=a_P$
Maximum power supports the conjecture of maximum force (Gibbons) in GR, and therefore, maximum acceleration and temperature. (2) is twice the limit $F_g$ proposed by Gibbons, but of course, the local proper acceleration limit at $R$ is half $a_P$, which will also be the Hagedorn temperature in natural units, as noted by Lawrence B. Crowell.
To see this, consider the inverse square law and Figure 1. Gravitational intensity to a distant observer $I=GM/R^2 =g=1/2$ at the limit radius $R=1$. $g$ is acceleration, i.e. maximum gravitational field is $κ=1/4M= 1/2=g$. Then, from Unruh and Bekenstein:
$T= (ℏ κ)/(2πck_B )=1/4π$ (4)
$S≤ (k_B c^3 πR^2)/ℏG=π$ (5)
From (4) and (5) we can derive another limit, as per Padmanabhan
After all, the Gibbons GR force limit conjecture was for a force acting between two bodies. For example, the gravitational coupling constant, the gravitational attraction between two minimal mass-energies as above is the Gibbons (and Newtonian) limit.
$α_G=(M/m_p )^2=G (M.M)/R^2 =1/4$ (7)
The Gibbons force limit implies a local momentum flow limit, i.e. minimum mass-energy times maximum local proper acceleration $F_g=M.g$.
It also results from the entropic force $F_g R=TS$