The Universal Terminal Burst of Geometric Black-Hole
Evaporation:
Light-Curve Shape, Standard Energy, and the Inverted Burst
Population
Raghu Kulkarni
SSMTheory Group, IDrive Inc., Calabasas, CA 91302, USA raghu@idrive.com
August 20, 2026
Abstract
A published companion derives a geometric evaporation channel for black holes: lattice surface
tension gives a lifetime τ ∝ M
2
, unsuppressed below the code coherence length ξ ∼ 1 fm and
exponentially frozen above it, with a survival cutoff at M
cut
≃ 10
16.5
g. This paper works out
what that law makes observable. Because every dying hole must pass through the horizon scale
ξ, the final phase is universal: it starts at the fixed mass M
ξ
= ξc
2
/2G ≃ 6.7 × 10
14
g, releases
the fixed energy E
b
= M
ξ
c
2
≃ 6 × 10
35
erg, lasts τ
b
∼ 0.1 ms up to the companion’s stated
O(1) coefficient, and follows a fixed light curve, L ∝ (τ −t)
−1/2
, against Hawking’s (τ −t)
−2/3
.
The energy radiated in the final interval ∆t scales as ∆t
1/2
against Hawking’s ∆t
1/3
. The
burst population is inverted relative to the standard picture: the classic Hawking bursters near
5 × 10
14
g died before recombination under this channel, so the geometric law predicts the
absence of their present-day bursts and diffuse emission, with today’s bursts supplied only by
holes at the cutoff edge. The channel’s particle content is open, so the gamma-ray band of the
burst is not predicted here; its total energy, duration, profile, and source population are. Each is
falsifiable: one confirmed present-day burst with the Hawking profile, from the standard mass,
would rule the channel out.
1 Introduction
Primordial black holes below about 10
17
g are constrained through Hawking evaporation [1, 2]:
holes of initial mass M
⋆
≃ 5 ×10
14
g have lifetimes equal to the age of the Universe and should be
dying today in bursts of GeV–TeV gamma rays. Dedicated searches exist and are active. HAWC
bounds the local burst rate density at 3400 pc
−3
yr
−1
[4]; H.E.S.S. [5] and LHAASO [6] report
comparable programs; Fermi-LAT searches for the associated steady emission [7]; and the expected
burst light curves under the Standard Model are worked out in Ref. [3]. All of it assumes the
semiclassical rate, τ
Hawk
∝ M
3
.
A published companion derives a second channel [10]. In the Selection–Stitch Model [9], a black
hole is a vacancy in a face-centered-cubic lattice, and the intact lattice exerts a surface tension on
the vacancy boundary. The boundary recedes by curvature-driven re-stitching, giving τ ∝ M
2
. A
code-distance threshold freezes the channel exponentially once the horizon exceeds the coherence
length ξ ∼ 1 fm, which produces a sharp survival cutoff at M
cut
≃ 10
16.5
g and maps each sub-cutoff
mass to the cosmological epoch of its death. The companion states the law, the cutoff, and the
epoch map, all with an overall coefficient uncertain at O(1).
1
This paper derives the burst phenomenology that law implies. The results are of two kinds.
The first is a universality statement: every geometric death, whenever it occurs, ends the same
way, because every shrinking hole must pass through the scale ξ where the unsuppressed channel
takes over. The terminal burst has a fixed starting mass, a fixed total energy, a fixed duration up
to the companion’s O(1), and a fixed light-curve shape. The second is a population statement: the
geometric law removes the standard burst population entirely and replaces it with a different one.
Both kinds are falsifiable with instruments now running.
2 The universal terminal phase
The unsuppressed channel operates for horizon radius R
H
≲ ξ, that is, below
M
ξ
=
ξc
2
2G
≃ 6.7 × 10
14
g. (1)
Above M
ξ
the channel is code-frozen and the hole shrinks slowly (or, for M ≫ M
cut
, effectively
not at all); below M
ξ
it evaporates at the unsuppressed τ ∝ M
2
rate. Every dying hole therefore
funnels through the same gate, and the final phase is the same for all of them. [derived, from the
companion’s two-parameter law]
Three universal numbers follow. The total energy of the terminal burst is
E
b
= M
ξ
c
2
≃ 6 × 10
35
erg, (2)
independent of the hole’s initial mass. The duration is τ
b
= κM
2
ξ
∼ 0.1 ms, where κ is fixed by
the companion’s anchor (an effective lifetime of 1.1 ms at 10
15
g, with its stated e
R
H
/ξ
suppression
removed) and carries the companion’s O(1) uncertainty. The mean luminosity is E
b
/τ
b
∼ 5×10
32
W.
A geometric terminal burst is a standard event: same energy, same duration, same shape, every
time. [derived; coefficient O(1) inherited]
3 Light curve and energetics
The law τ = κM
2
gives dM/dt = −1/(2κM), so
M(t) = M
ξ
p
1 − t/τ
b
, L(t) = c
2
dM
dt
=
E
b
2τ
b
1 −
t
τ
b
−1/2
. (3)
The light curve diverges with exponent −1/2 in the remaining lifetime. Hawking evaporation,
τ ∝ M
3
, gives M ∝ (τ −t)
1/3
and L ∝ (τ −t)
−2/3
: a steeper terminal rise. Equivalently, the energy
emitted in the final interval ∆t scales as
E(< ∆t) ∝ ∆t
1/2
(geometric) vs. ∆t
1/3
(Hawking) : (4)
the geometric burst is front-loaded relative to a Hawking burst of the same remaining lifetime —
more of its energy arrives early, less in the final spike. Figures 1 and 2 show both laws. These
exponents are properties of the lifetime scaling alone and carry no O(1) uncertainty. [derived]
2
10
3
10
2
10
1
10
0
remaining lifetime (
t
)/
b
10
0
10
1
10
2
luminosity (normalized)
geometric:
L
(
t
)
1/2
Hawking:
L
(
t
)
2/3
Figure 1: Terminal light curves, normalized at one burst duration of remaining lifetime. The
geometric channel rises with exponent −1/2; Hawking with −2/3. The shapes are coefficient-free
discriminators.
10
4
10
3
10
2
10
1
10
0
final interval
t
/
b
10
2
10
1
10
0
E
( <
t
)/
E
b
universal total
E
b
=
M c
2
6 × 10
35
erg
geometric:
E
( <
t
)
t
1/2
Hawking:
E
( <
t
)
t
1/3
Figure 2: Energy emitted in the final interval ∆t, in units of the universal total E
b
. The geometric
burst approaches its fixed total as ∆t
1/2
; a Hawking burst as ∆t
1/3
, with no universal total.
4 What is and is not predicted about the emission
The companion specifies the carriers: each severed bond releases its dangling-pair energy, and
the emission is lattice excitations near the bond scale — non-thermal by construction, with no
presumption of a Planck spectrum [10]. How those excitations convert to Standard-Model particles
is not derived there and is not derived here. The honest split is therefore this. Predicted: the
3
total energy (Eq. 2), the duration, the light-curve exponent (Eq. 3), and the front-loaded energetics
(Eq. 4). Not predicted: the photon band and spectrum of the burst. A search can test the predicted
quantities in any band where a counterpart is found; the number of photons scales as E
b
/⟨E
γ
⟩ for
whatever mean photon energy ⟨E
γ
⟩ the conversion supplies. [the split itself is the claim; carrier
conversion open]
4.1 Reach of current instruments
The universal energy makes the reach computable per band, conditional only on where the conver-
sion deposits it (Table 1). If a fraction of order one emerges at TeV energies, a water-Cherenkov
array of effective area 10
5
m
2
collects about 300 photons from 100 pc and a few from 1 kpc — all
inside 0.1 ms. A sub-millisecond TeV multiplet has no known astrophysical source and negligible
chance coincidence in so short a window, so even a handful of clustered photons is significant. Exist-
ing burst searches bin at 0.2–10 s [4, 5, 6]; a dedicated sub-millisecond window is a template change,
not new hardware. At keV–MeV, an all-sky monitor with fluence threshold 10
−7
–10
−8
erg cm
−2
reaches 0.2–0.7 kpc. [conditional on the band; the horizon scaling d ∝
√
E
b
is derived]
Two further consequences. Because E
b
is fixed, a detected burst is a standard candle: its
fluence gives its distance, d =
p
E
b
/4πF , a self-consistency check no mass-dependent Hawking burst
provides. And the burst occupies empty phase space: no known transient combines ∼ 10
35.8
erg
with ∼ 0.1 ms in the gamma-ray sky. At radio wavelengths that duration and energy brush the
territory of galactic magnetar radio bursts; whether any fraction converts coherently is part of the
open carrier question and is flagged here only as a search consideration. [standard candle derived;
the radio remark speculative]
band instrument class horizon signature in 0.1 ms
TeV water-Cherenkov, 10
5
m
2
∼ 0.3–1 kpc 3–300 photon multiplet
GeV pair-conversion, ∼ 1 m
2
∼ 0.1 kpc few-photon cluster
keV–MeV all-sky monitor, 10
−7 .. −8
erg cm
−2
0.2–0.7 kpc single sub-ms spike
Table 1: Reach for the universal burst, per assumed conversion band; each row is conditional on
the open carrier question, while the E
b
powering all rows is derived.
5 The inverted burst population
Under the geometric law the standard burst population does not exist. The companion’s epoch
map [10] places the death of each sub-cutoff mass: holes near the classic M
⋆
≃ 5 × 10
14
g evap-
orated before big-bang nucleosynthesis; the whole range up to 2.2 × 10
16
g died before or around
recombination. Two consequences follow (Fig. 3).
First, an absence. The present-day bursts and the diffuse gamma-ray background expected
from the ∼ 10
15
g population under Hawking evaporation [2, 8] are predicted not to exist: their
sources are gone. Existing burst-search nulls [4, 5, 6] are therefore consistent with the geometric
channel by default, and any confirmed detection of a present-day burst with Hawking’s profile, at
the standard mass scale, falsifies the channel outright.
Second, a replacement. The holes dying today are those at the cutoff edge, near M
cut
≃ 10
16.5
g,
whose code-suppressed lifetimes equal the age of the Universe. Their deaths end in the same
universal terminal burst of
§
2 — the slow suppressed phase is invisible; the observable event is
the final 0.1 ms. The rate of such bursts is set by the PBH mass function at the cutoff edge
4
and is not predicted here; what is predicted is that any present-day PBH burst has the universal
energy, duration, and profile, whatever its rate. [population map derived from the companion; rate
conditional on the mass function]
10
14
10
15
10
16
10
17
PBH mass (g)
thermalized
before BBN
BBN /
photodissoc.
CMB -dist.
y
-dist.recomb. today
M
cut
: bursting today (geometric)
M
: Hawking bursters (long gone here)
Where each mass dies under the geometric channel
Figure 3: The inverted population. Under the geometric channel each sub-cutoff mass dies at the
epoch shown; the classic Hawking bursters (red dashed) are long gone, and the only present-day
bursters sit at the cutoff edge (blue). Band boundaries from the companion’s epoch map [10].
6 Discriminators and falsifiers
Table 2 collects the differences. The falsifiers, each sharp: (F1) a confirmed present-day burst with
light-curve exponent −2/3 and Hawking’s mass-dependent energetics, at the standard M
⋆
scale,
falsifies the geometric channel and with it the companion’s evaporation law. (F2) a confirmed de-
tection of the Hawking diffuse background from the 10
15
–10
16
g population falsifies the epoch map.
(F3) a confirmed present-day PBH burst whose total energy or duration departs from Eqs. (2) and
the 0.1 ms scale by far more than the stated O(1) falsifies the universality statement. Conversely,
a burst with exponent −1/2, front-loaded energetics, and the standard energy would be strong
evidence for the channel.
Hawking geometric (this work)
lifetime law τ ∝ M
3
τ ∝ M
2
, code-frozen above ξ
light-curve exponent −2/3 −1/2
energy in final ∆t ∝ ∆t
1/3
∝ ∆t
1/2
burst energy mass-dependent universal, E
b
≃ 6 × 10
35
erg
burst duration spectrum-dependent universal, ∼ 0.1 ms ×O(1)
who bursts today M
⋆
≃ 5 × 10
14
g cutoff edge, ≃ 10
16.5
g
diffuse background present absent below 2.2 × 10
16
g
spectrum quasi-thermal, computed open (carrier conversion)
Table 2: The two channels’ burst phenomenology. Exponent rows are coefficient-free.
5
7 Limitations
Four, stated as in the companion series. (L1) Every duration and rate inherits the companion’s
O(1) coefficient; the exponents and the total energy do not. (L2) The transition at ξ is treated as
sharp; the companion’s exponential suppression smooths it over a factor of order one in mass, inside
the stated uncertainty. (L3) The conversion of bond-scale lattice excitations to Standard-Model
particles is open, so no photon spectrum is claimed; falsifier F3 tests the bolometric quantities only
where a counterpart is identified. (L4) The burst rate today depends on the unknown PBH mass
function at the cutoff edge; the universality of the burst does not.
Declarations
Funding. Not applicable.
Availability of data and material. All numbers and the three figures are produced by one
script, pbh burst.py, archived as pbh burst scripts.zip with the series’ verification suites at
github.com/raghu91302/ssmtheory.
Competing interests. The author declares no competing interests.
Authors’ contributions. Not applicable (single author).
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