The concern over mass is something which is important, for it is the IR part of the theory and has a correspondence with the UV scale. To illustrate something about this I outline the physics in some detail here
A sphere of area A will contains N = A/L_p^2 units of information. The equipartition theorem is E = (1/2)NkT, where E = mc^2, and T the Hawking Unruh temperature,
[math]
T~=~{1\over{2\pi}}{{\hbar g}\over{kc}}
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The work-energy theorem of mechanics E = ∫F*dr gives Newtonian gravity
[math]
g~=~{{Gm}\over{r^2}},
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and Newton's second law F = mg.
A surface area at the Bekenstein limit due to quantum black holes is a summation over all eigen-numbers of Planck units of area
[math]
A~=~c\sum_{i=1}^Nn_iL_p^2~=~c\sum_n A_nL_p^2,
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where n = n_1 n_2 ... n_N contributes energy E_n = cnħg/4πc. An accelerated surface is degenerate according to a partition function
[math]
Z(\beta)~=~\sum_{n=1}^\infty g(E_n)e^{-\beta E_n}.
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The average energy is
[math]
\langle E(\beta)\rangle~=~-{\partial\over{\partial\beta}}ln~Z(\beta),
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and the entropy
[math]
S(\beta)~=~k\Big(ln~Z(\beta)~-~\beta{\partial\over{\partial\beta}}ln~Z(\beta)\Big),
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from which the characteristic temperature for a phase transition of an accelerate surface is
[math]
T_c~=~{c\over{4\pi ln~2}}{{\hbar g}\over{kc}},
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where c = 2 ln2. The energy for N --> ∞ is ( |E| ) = 0 [here ( and ) used for bra-ket notation] for T \lt T_c. A critical point occurs as T --> T_c, with production of quantum black holes from the vacuum. For large N the result approximates E = NkT.
This theory then lends itself to phase transitions. I recently submitted a paper on this, but I can outline what happens from here. The stretched horizon is a place where strings which compose a black hole are "frozen" and have an effective mass. The string's mass is just its energy which is confined on the stretched horizon. The elementary analysis with the critical temperature indicates a possible phase transition, indeed a quantum critical point or phase transition. The analysis is done in a fairly straight forwards way with extremal black hole and the analysis of the spacetime near the stretched horizon. The physics for fields or strings that enter the horizon or quantum tunnel out is quantum physics with a V ~ |x| potential. This has Airy function solutions which satisfy Zamolodcikov's c = 1/2 CFT condition on massive fields. The masses correspond to the (8,1) irrep of the E_8 group.
Cheers LC
