Physics Letters B 739 (2014) 405–409
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Physics Letters B
www.elsevier.com/locate/physletb
Planck star phenomenology
Aurélien Barrau
a,∗
, Carlo Rovelli
b,c
a
Laboratoire de Physique Subatomique et de Cosmologie, Université Grenoble-Alpes, CNRS–IN2P3, 53, avenue des Martyrs, 38026 Grenoble cedex, France
b
Aix Marseille Université, CNRS, CPT, UMR 7332, 13288 Marseille, France
c
Université de Toulon, CNRS, CPT, UMR 7332, 83957 La Garde, France
a r t i c l e i n f o a b s t r a c t
Article history:
Received
13 October 2014
Received
in revised form 7 November 2014
Accepted
12 November 2014
Available
online 15 November 2014
Editor: S.
Dodelson
It is possible that black holes hide a core of Planckian density, sustained by quantum-gravitational
pressure. As a black hole evaporates, the core remembers the initial mass and the final explosion occurs
at macroscopic scale. We investigate possible phenomenological consequences of this idea. Under several
rough assumptions, we estimate that up to several short gamma-ray bursts per day, around 10 MeV, with
isotropic distribution, can be expected coming from a region of a few hundred light years around us.
© 2014 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/3.0/). Funded by SCOAP
3
.
1. The model
Recently, a new possible consequence of quantum gravity has
been suggested [1]. The idea is grounded in a robust result of loop
cosmology [2]: when matter reaches Planck density, quantum grav-
ity
generates pressure sufficient to counterbalance weight. For a
black hole, this implies that matter’s collapse can be stopped be-
fore
the central singularity is formed: the event horizon is replaced
by a “trapping” horizon [3] which resembles the standard horizon
locally, but from which matter can eventually bounce out. Because
of the huge time dilation inside the gravitational potential well of
the star, the bounce is seen in extreme slow motion from the out-
side,
appearing as a nearly stationary black hole. The core, called
“Planck star”, retains memory of the initial collapsed mass m
i
(be-
cause
there is no reason for the metric of the core to be fully
determined by the area of the external evaporating horizon) and
the final exploding object depends on m
i
and is much larger than
Planckian [1]. The process is illustrated by the conformal diagram
in Fig. 1.
In
particular, primordial black holes exploding today may pro-
duce
a distinctive signal. The observability of a quantum gravita-
tional
phenomenon is made possible by the amplification due to
the large ratio of the black hole lifetime (Hubble time t
H
) over the
Planck time [4].
If
this scenario is realized in nature, can the final explosion of
a primordial Planck star be observed? This is the question we in-
vestigate
here.
*
Corresponding author.
E-mail
addresses: Aurelien.Barrau@cern.ch (A. Barrau), rovelli@cpt.univ-mrs.fr
(C. Rovelli).
Fig. 1. Penrose diagram of a collapsing star. The dotted line is the external boundary
of the star. The shaded area is the region where quantum gravity plays an important
role. The dark line represents the two trapping horizons: the external evaporating
one, and the internal expanding one. The lowest light-line is where the horizon of
the black hole would be without evaporation. P is where the explosion happens.
The thin arrows indicate the Hawking radiation. The thick arrow is the signal stud-
ied
in this paper.
2. Dynamics
As a first step, we evaluate the energy of the particles emit-
ted
by the explosion of a primordial Planck star. Let m
f
= am
i
be
the final mass reached by the black hole before the dissipation of
the horizon (at the point P in Fig. 1). In [1], an argument based
on information conservation was given, pointing to the preferred
value
http://dx.doi.org/10.1016/j.physletb.2014.11.020
0370-2693/
© 2014 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/3.0/). Funded by
SCOAP
3
.