Creation of Quark-gluon Plasma in Celestial
Laboratories
R. K. Thakur
*Retired Professor of Physics, School of Studies in Physics
Pt.Ravishakar Shukla University, Raipur, India
21 College Road, Choube Colony, Raipur-492001, India
Abstract
It is shown that a gravitationally collapsing black hole acts as an ultrahigh energy
particle accelerator that can accelerate particles to energies inconceivable in any ter-
restrial particle accelerator, and that when the energy E of the particles comprising
the matter in the black hole is ∼ 102 GeV or more,or equivalently the temperature
T is ∼ 1015 K or more, the entire matter in the black hole will be in the form of
quark-gluon plasma permeated by leptons.
Key words: Quark-gluon plasma, black holes, particle accelerators
PACS: 12.38 Mh, 25.75 Nq, 97.60 Lf, 04.70−s
1 Introduction
Efforts are being made to create quark-gluon plasma (QGP)in terrestrial labo-
ratories. A report released by CERN, the European Organization for Nuclear
Research, at Geneva, on February 10, 2000 said, “A series of experiments
using CERN’s lead beam have presented compelling evidence for the exis-
tence of a new state of matter 20 times denser than nuclear matter, in which
quarks instead of being bound up into more complex particles such as pro-
tons and neutrons, are liberated to roam freely“. By smashing together lead
ions at CERN’s accelerator at temperatures 100,000 times as hot as sun’s cen-
tre, i.e. at temperatures T ∼ 1.5 × 1012 K, and energy densities never before
reached in laboratory experiments, a team of 350 scientists from institutes
in 20 countries succeeded in isolating quarks from more complex particles,
e.g. protons and neutrons. However, the evidence of creation QGP at CERN
Email address: rkthakur0516@yahoo.com (R. K. Thakur).
Preprint submitted to Elsevier 10 August 2021
http://arxiv.org/abs/0704.1655v1
is indirect,involving detection of particles produced when QGP changes back
to hadrons. The production of these particles can be explained alternatively
without having to have QGP. Therefore, the evidence of the creation of QGP
at CERN is not enough and conclusive. In view of this CERN will start a
new experiment, ALICE (A Large Ion Collider Experiment), at much higher
energies available at its LHC (Large Hadron Collider). First collisions in the
LHC will occur in November 2007. A two months run in 2007, with beams
colliding at an energy of 0.9 TeV, will give the accelerator and detector teams
the opportunity to run-in their equipment, ready for a run at the full collision
energy of 14 Tev to start in spring 2008.
In the meantime, the focus of research on QGP has shifted to the Relativistic
Heavy Ion Collider (RHIC), the world’s newest and largest particle accelerator
for nuclear research, at Brookhaven National Laboratory (BNL) in Upton,
New York. RHIC’s goal is to create and study QGP by head-on collisions of
two beams of gold ions at energies 10 times those of CERN’s programme,
which ought to produce QGP with higher temperature and longer life time
thereby allowing much clear and direct observation. The programme at RHIC
started in June 2000.Researchers at RHIC generated thousands of head-on
collisions between gold ions at energies of 130 GeV creating fireballs of matter
having density hundred times greater than that of the nuclear matter and
temperature ∼ 2 × 1012 K (175 MeV in the energy scale). Fireballs were
of size ∼ 5 femtometre which lasted a few times 10−24 second. All the four
detector systems, viz., STAR, PHENIX, BRAHMS, PHOBOS, detected “jet
quenching“ and suppression of “leading particles“, highly energetic individual
particles that emerge from the nuclear fireballs in gold-gold collisions. Jet
quenching and suppression of leading particles are signs of QGP formation.
Eventually, with plenty of data in hand, all the four detector collaborations -
STAR, PHENIX, BRAHMS, PHOBOS - operating at the BNL have converged
on a consensus opinion that the fireball is a liquid of strongly interacting quarks
and gluons rather than a gas of weakly interacting quarks and gluons. More-
over, this liquid is almost a “perfect“ liquid with very low viscosity. The RHIC
findings were reported at the meeting of the American Physical Society (APS)
held during April 16-19, 2005 in Tampa, Florida in a talk delivered by Gary
Westfall. Thus, it is obvious that the existence of QGP theoretically predicted
by Quantum Chromodynamics (QCD) has been experimentally validated at
RHIC.
But the QGP created hitherto in terrestrial laboratories is ephemeral, its life-
time is, as mentioned earlier, a few times 10−24 second, presumably because
its temperature is not well above the transition temperature for transition
from the hadronic phase to the QGP phase. In addition to this, it is difficult
to maintain it even at that temperature for long enough time. However, as
shown in the sequel, in nature we have celestial laboratories in the form of
gravitationally collapsing black holes wherein QGP is created naturally; this
QGP is at much higher temperature than the transition temperature, and pre-
sumably therefore it is not ephemeral. More so, because the temperature of
the QGP created in black holes continually increases and as such it is always
above the transition temperature.
2 Gravitationally collapsing black hole as a particle accelerator
We consider a gravitationally collapsing black hole (BH). In the simplest treat-
ment (1) a BH is considered to be a spherically symmetric ball of dust with
negligible pressure, uniform density ρ = ρ(t), and at rest at t = 0. These
assumptions lead to the unique solution of the Einstein field equations, and
in the comoving co-ordinate system the metric inside the BH is given by
ds2 = dt2 − R2(t)
1− k r2
+ r2dθ2 + r2 sin2 θ dφ2
in units in which the speed of light in vacuum, c = 1, and where k = 8πGρ(0)/3
is a constant.
On neglecting mutual interactions the energy E of any one of the particles
comprising the matter in the BH is given by E2 = p2 + m2 > p2, in units
in which again c = 1, and where p is the magnitude of the 3-momentum
of the particle and m its rest mass. But p = h
, where λ is the de Broglie
wavelength of the particle and h Planck’s constant of action. Since all length
in the collapsing BH scale down in proportion to the scale factor R(t) in
equation (1), it is obvious that λ ∝ R(t). Therefore it follows that p ∝ R−1(t),
and hence p = aR−1(t), where a is the constant of proportionality. From this
it follows that E > a/R(t). Consequently, E as well as p increases continually
as R decreases. It is also obvious that E and p → ∞ as R → 0. Thus, in effect,
we have an ultrahigh energy particle accelerator, so far inconceivable in any
terrestrial laboratory, in the form of a gravitationally collapsing BH, which
can, in the absence of any physical process inhibiting the collapse, accelerate
particles to an arbitrarily high energy and momentum without any limit.
What has been concluded above can also be demonstrated alternatively, with-
out resorting to the general theory of relativity, as follows. As an object col-
lapses under self-gravitation, the inter-particle distance s between any pair of
particles in the object decreases. Obviously, the de Broglie wavelength λ of
any particle in the object is less than or equal to s, a simple consequence of
Heisenberg’s uncertainty principle. Therefore, s ≥ h
. Consequently, p ≥ h
hence E ≥ h
. Since during the gravitational collapse of an object s decreases
continually, the energy E as well as p, the magnitude of the 3-momentum of
each of the particles is the object increases continually. Moreover, from E ≥ h
and p ≥ h
it follows that E and p → ∞ as s → 0. Thus, any gravitation-
ally collapsing object in general, and a BH in particular, acts as an ultrahigh
energy particle accelerator.
It is also obvious that ρ, the density of matter in the BH, continually increases
as the BH collapses. In fact, ρ ∝ R−3, and hence ρ → ∞ as R → 0.
3 Creation of quark-gluon plasma inside gravitationally collapsing
black holes
It has been shown theoretically that when the energy E of the particles in mat-
ter is ∼ 102 GeV (s ∼ 10−16 cm ) corresponding to a temperature T ∼ 1015
K, all interactions are of the Yang-Mills type with SUc(3)×SUIW (2)×UYW (1)
gauge symmetry, where c stands for colour, IW for weak isospin, and YW for
weak hypercharge; and at this stage quark deconfinement occurs as a result
of which the matter now consists of its fundamental constituents: spin 1/2
leptons, namely, the electrons, the muons, the tau leptons, and their neu-
tirnos, which interact only through the electroweak interaction; and the spin
1/2 quarks, u(up), d(down), s(strange), c(charm), b(bottom), t(top), which
interact electroweakly as well as through the colour force generated by gluons
(2). In this context it may be noted that, as shown in section 2, the energy
E of each of the particles comprising the matter in a gravitationally collaps-
ing BH continually increases, and so does the density ρ of the matter in the
BH. During the continual collapse of a BH a stage will be reached when E
and ρ will be so large and s so small that the quarks confined in the hadrons
will be liberated from the infrared slavery and acquire asymptotic freedom,
i.e., the quark deconfinement will occur.This will happen when E ∼ 102 GeV
(s ∼ 10−16 cm) corresponding to T ∼ 1015 K. Consequently, during the con-
tinual gravitational collapse of a BH, when E ≥ 102 GeV (s ≤ 10−16 cm)
corresponding to T ≥ 1015 K, the entire matter in the BH will be in the form
QGP permeated by leptons.
One may understand what happens eventually to the matter in a gravitation-
ally collapsing BH in another way as follows. As a BH collapses continually,
gravitational energy is released continually. Since, inter alia, gravitational en-
ergy so released cannot escape the BH, it will continually heat the matter
comprising the BH. Consequently, the temperature of the matter in the BH
will increase continually. When the temperature reaches the transition tem-
perature for transition from the hadronic phase to the QGP phase, which is
predicted to be ∼ 170 MeV (∼ 1012 K) by the Lattice Gauge Theory, the
entire matter in the BH will be converted into QGP permeated by leptons.
It may be noted that in a BH the QGP will not be ephemeral like what it
has hitherto been in the case of the QGP created in terrestrial laboratories, it
will not go back to the hadronic phase, because the temperature of the matter
in the BH continually increases and, after crossing the transition temperature
for the transition from the hadronic phase to the QGP phase, it will be more
and more above the transition temperature. Consequently, once the transition
from the hadronic phase to the QGP phase occurs in a BH, there is no going
back; the entire matter in the BH will remain in the form of QGP permeated
by leptons.
4 Conclusion
From the foregoing it is obvious that a BH acts as an ultrahigh energy par-
ticle accelerator that can accelerate particles to energies inconceivable in any
terrestrial particle accelerator, and that the matter in any gravitationally col-
lapsing BH is eventually converted into QGP permeated by leptons. However,
the snag is that it is not possible to probe and study the properties of the
QGP in a BH because nothing can escape outside the event horizon of a BH.
5 Acknowledgment
The author thanks Professor S. K. Pandey, the Co-ordinator of the Refer-
ence Centre at Pt. Ravishankar Shukla University, Raipur of the University
Grants Commission’s Inter-university Centre for Astronomy and Astrophysics
at Pune. He also thanks Mr. Laxmikant Chaware and Miss Leena Madharia
for typing the manuscript.
References
[1] S. Weinberg, Gravitation and Cosmology (John Wiley & Sons, New York,
1972), 342.
[2] P. Ramond, Ann. Rev. Nucl. Part.Sc., 33 (1983) 31.
	Introduction
	Gravitationally collapsing black hole as a particle accelerator 
	Creation of quark-gluon plasma inside gravitationally collapsing black holes
	Conclusion
	Acknowledgment

  It is shown that a gravitationally collapsing black hole acts as an ultrahigh
energy particle accelerator that can accelerate particles to energies
inconceivable in any terrestrial particle accelerator, and that when the energy
E of the particles comprising the matter in the black hole is $ \sim 10^{2} $
GeV or more,or equivalently the temperature T is $ \sim 10^{15}$ K or more, the
entire matter in the black hole will be in the form of quark-gluon plasma
permeated by leptons.

Introduction
Efforts are being made to create quark-gluon plasma (QGP)in terrestrial labo-
ratories. A report released by CERN, the European Organization for Nuclear
Research, at Geneva, on February 10, 2000 said, “A series of experiments
using CERN’s lead beam have presented compelling evidence for the exis-
tence of a new state of matter 20 times denser than nuclear matter, in which
quarks instead of being bound up into more complex particles such as pro-
tons and neutrons, are liberated to roam freely“. By smashing together lead
ions at CERN’s accelerator at temperatures 100,000 times as hot as sun’s cen-
tre, i.e. at temperatures T ∼ 1.5 × 1012 K, and energy densities never before
reached in laboratory experiments, a team of 350 scientists from institutes
in 20 countries succeeded in isolating quarks from more complex particles,
e.g. protons and neutrons. However, the evidence of creation QGP at CERN
Email address: rkthakur0516@yahoo.com (R. K. Thakur).
Preprint submitted to Elsevier 10 August 2021
http://arxiv.org/abs/0704.1655v1
is indirect,involving detection of particles produced when QGP changes back
to hadrons. The production of these particles can be explained alternatively
without having to have QGP. Therefore, the evidence of the creation of QGP
at CERN is not enough and conclusive. In view of this CERN will start a
new experiment, ALICE (A Large Ion Collider Experiment), at much higher
energies available at its LHC (Large Hadron Collider). First collisions in the
LHC will occur in November 2007. A two months run in 2007, with beams
colliding at an energy of 0.9 TeV, will give the accelerator and detector teams
the opportunity to run-in their equipment, ready for a run at the full collision
energy of 14 Tev to start in spring 2008.
In the meantime, the focus of research on QGP has shifted to the Relativistic
Heavy Ion Collider (RHIC), the world’s newest and largest particle accelerator
for nuclear research, at Brookhaven National Laboratory (BNL) in Upton,
New York. RHIC’s goal is to create and study QGP by head-on collisions of
two beams of gold ions at energies 10 times those of CERN’s programme,
which ought to produce QGP with higher temperature and longer life time
thereby allowing much clear and direct observation. The programme at RHIC
started in June 2000.Researchers at RHIC generated thousands of head-on
collisions between gold ions at energies of 130 GeV creating fireballs of matter
having density hundred times greater than that of the nuclear matter and
temperature ∼ 2 × 1012 K (175 MeV in the energy scale). Fireballs were
of size ∼ 5 femtometre which lasted a few times 10−24 second. All the four
detector systems, viz., STAR, PHENIX, BRAHMS, PHOBOS, detected “jet
quenching“ and suppression of “leading particles“, highly energetic individual
particles that emerge from the nuclear fireballs in gold-gold collisions. Jet
quenching and suppression of leading particles are signs of QGP formation.
Eventually, with plenty of data in hand, all the four detector collaborations -
STAR, PHENIX, BRAHMS, PHOBOS - operating at the BNL have converged
on a consensus opinion that the fireball is a liquid of strongly interacting quarks
and gluons rather than a gas of weakly interacting quarks and gluons. More-
over, this liquid is almost a “perfect“ liquid with very low viscosity. The RHIC
findings were reported at the meeting of the American Physical Society (APS)
held during April 16-19, 2005 in Tampa, Florida in a talk delivered by Gary
Westfall. Thus, it is obvious that the existence of QGP theoretically predicted
by Quantum Chromodynamics (QCD) has been experimentally validated at
RHIC.
But the QGP created hitherto in terrestrial laboratories is ephemeral, its life-
time is, as mentioned earlier, a few times 10−24 second, presumably because
its temperature is not well above the transition temperature for transition
from the hadronic phase to the QGP phase. In addition to this, it is difficult
to maintain it even at that temperature for long enough time. However, as
shown in the sequel, in nature we have celestial laboratories in the form of
gravitationally collapsing black holes wherein QGP is created naturally; this
QGP is at much higher temperature than the transition temperature, and pre-
sumably therefore it is not ephemeral. More so, because the temperature of
the QGP created in black holes continually increases and as such it is always
above the transition temperature.
2 Gravitationally collapsing black hole as a particle accelerator
We consider a gravitationally collapsing black hole (BH). In the simplest treat-
ment (1) a BH is considered to be a spherically symmetric ball of dust with
negligible pressure, uniform density ρ = ρ(t), and at rest at t = 0. These
assumptions lead to the unique solution of the Einstein field equations, and
in the comoving co-ordinate system the metric inside the BH is given by
ds2 = dt2 − R2(t)
1− k r2
+ r2dθ2 + r2 sin2 θ dφ2
in units in which the speed of light in vacuum, c = 1, and where k = 8πGρ(0)/3
is a constant.
On neglecting mutual interactions the energy E of any one of the particles
comprising the matter in the BH is given by E2 = p2 + m2 > p2, in units
in which again c = 1, and where p is the magnitude of the 3-momentum
of the particle and m its rest mass. But p = h
, where λ is the de Broglie
wavelength of the particle and h Planck’s constant of action. Since all length
in the collapsing BH scale down in proportion to the scale factor R(t) in
equation (1), it is obvious that λ ∝ R(t). Therefore it follows that p ∝ R−1(t),
and hence p = aR−1(t), where a is the constant of proportionality. From this
it follows that E > a/R(t). Consequently, E as well as p increases continually
as R decreases. It is also obvious that E and p → ∞ as R → 0. Thus, in effect,
we have an ultrahigh energy particle accelerator, so far inconceivable in any
terrestrial laboratory, in the form of a gravitationally collapsing BH, which
can, in the absence of any physical process inhibiting the collapse, accelerate
particles to an arbitrarily high energy and momentum without any limit.
What has been concluded above can also be demonstrated alternatively, with-
out resorting to the general theory of relativity, as follows. As an object col-
lapses under self-gravitation, the inter-particle distance s between any pair of
particles in the object decreases. Obviously, the de Broglie wavelength λ of
any particle in the object is less than or equal to s, a simple consequence of
Heisenberg’s uncertainty principle. Therefore, s ≥ h
. Consequently, p ≥ h
hence E ≥ h
. Since during the gravitational collapse of an object s decreases
continually, the energy E as well as p, the magnitude of the 3-momentum of
each of the particles is the object increases continually. Moreover, from E ≥ h
and p ≥ h
it follows that E and p → ∞ as s → 0. Thus, any gravitation-
ally collapsing object in general, and a BH in particular, acts as an ultrahigh
energy particle accelerator.
It is also obvious that ρ, the density of matter in the BH, continually increases
as the BH collapses. In fact, ρ ∝ R−3, and hence ρ → ∞ as R → 0.
3 Creation of quark-gluon plasma inside gravitationally collapsing
black holes
It has been shown theoretically that when the energy E of the particles in mat-
ter is ∼ 102 GeV (s ∼ 10−16 cm ) corresponding to a temperature T ∼ 1015
K, all interactions are of the Yang-Mills type with SUc(3)×SUIW (2)×UYW (1)
gauge symmetry, where c stands for colour, IW for weak isospin, and YW for
weak hypercharge; and at this stage quark deconfinement occurs as a result
of which the matter now consists of its fundamental constituents: spin 1/2
leptons, namely, the electrons, the muons, the tau leptons, and their neu-
tirnos, which interact only through the electroweak interaction; and the spin
1/2 quarks, u(up), d(down), s(strange), c(charm), b(bottom), t(top), which
interact electroweakly as well as through the colour force generated by gluons
(2). In this context it may be noted that, as shown in section 2, the energy
E of each of the particles comprising the matter in a gravitationally collaps-
ing BH continually increases, and so does the density ρ of the matter in the
BH. During the continual collapse of a BH a stage will be reached when E
and ρ will be so large and s so small that the quarks confined in the hadrons
will be liberated from the infrared slavery and acquire asymptotic freedom,
i.e., the quark deconfinement will occur.This will happen when E ∼ 102 GeV
(s ∼ 10−16 cm) corresponding to T ∼ 1015 K. Consequently, during the con-
tinual gravitational collapse of a BH, when E ≥ 102 GeV (s ≤ 10−16 cm)
corresponding to T ≥ 1015 K, the entire matter in the BH will be in the form
QGP permeated by leptons.
One may understand what happens eventually to the matter in a gravitation-
ally collapsing BH in another way as follows. As a BH collapses continually,
gravitational energy is released continually. Since, inter alia, gravitational en-
ergy so released cannot escape the BH, it will continually heat the matter
comprising the BH. Consequently, the temperature of the matter in the BH
will increase continually. When the temperature reaches the transition tem-
perature for transition from the hadronic phase to the QGP phase, which is
predicted to be ∼ 170 MeV (∼ 1012 K) by the Lattice Gauge Theory, the
entire matter in the BH will be converted into QGP permeated by leptons.
It may be noted that in a BH the QGP will not be ephemeral like what it
has hitherto been in the case of the QGP created in terrestrial laboratories, it
will not go back to the hadronic phase, because the temperature of the matter
in the BH continually increases and, after crossing the transition temperature
for the transition from the hadronic phase to the QGP phase, it will be more
and more above the transition temperature. Consequently, once the transition
from the hadronic phase to the QGP phase occurs in a BH, there is no going
back; the entire matter in the BH will remain in the form of QGP permeated
by leptons.
4 Conclusion
From the foregoing it is obvious that a BH acts as an ultrahigh energy par-
ticle accelerator that can accelerate particles to energies inconceivable in any
terrestrial particle accelerator, and that the matter in any gravitationally col-
lapsing BH is eventually converted into QGP permeated by leptons. However,
the snag is that it is not possible to probe and study the properties of the
QGP in a BH because nothing can escape outside the event horizon of a BH.
5 Acknowledgment
The author thanks Professor S. K. Pandey, the Co-ordinator of the Refer-
ence Centre at Pt. Ravishankar Shukla University, Raipur of the University
Grants Commission’s Inter-university Centre for Astronomy and Astrophysics
at Pune. He also thanks Mr. Laxmikant Chaware and Miss Leena Madharia
for typing the manuscript.
References
[1] S. Weinberg, Gravitation and Cosmology (John Wiley & Sons, New York,
1972), 342.
[2] P. Ramond, Ann. Rev. Nucl. Part.Sc., 33 (1983) 31.
	Introduction
	Gravitationally collapsing black hole as a particle accelerator 
	Creation of quark-gluon plasma inside gravitationally collapsing black holes
	Conclusion
	Acknowledgment
