We show that black holes can be made of light by adding gravity to the discussion of AlvarezDominguez et al. arXiv2405.02389 PRL 130 041401 2024.
['General Relativity and Quantum Cosmology', 'Astrophysics - Cosmology and Nongalactic Astrophysics']
Comment on No Black Holes from Light arXiv2405.02389
{"Comment on 'No Black Holes from Light', PRL130, 041401 (2024)": "Abraham Loeb 1, ∗  \n1 Department of Astronomy, Harvard University, 60 Garden Street, Cambridge, MA 02138, USA (Dated: August 22, 2024)  \nWe show that black holes can be made of light by adding gravity to the discussion of AlvarezDominguez et al. [PRL 130 , 041401 (2024)].  \nRecently, Alvarez-Dominguez et al. published a paper titled: 'No Black Holes from Light' [1]. The authors did their calculations in the Minkowski metric, ignoring gravity. Here we demonstrate that gravity changes their conclusions.  \nEarly in the history of the Universe, the cosmic energy budget was dominated by radiation composed of photons and relativistic particles, including electron-positron pairs, neutrinos of all flavors, µ and τ leptons and antileptons, W+, W -and Z bosons, and a plasma of quarks and gluons of all types in thermal equilibrium. The Universe expanded slowly enough for these particles to reach thermodynamic equilibrium in the first 10-microseconds after the Big-Bang. In this thermal state, the process considered by the authors - pair creation by vacuum polarization, also known as the Schwinger effect [2], was balanced by the reverse process of pair annihilation, not only for electron-positron pairs but for all particle-antiparticle pairs. The existence of relativistic particles, in addition to photons in thermal equilibrium, only changes the effective number of degrees of freedom in the energy density of the radiation field at a given temperature [3] that shapes the evolution of spacetime under gravity through the associated energy-momentum tensor.  \nEinstein's equations of General Relativity imply that an expanding spherical region in the early Universe, filled with radiation in thermal equilibrium of an energy density above the critical value, 3 H 2 / 8 πG , where H ( t ) is the Hubble parameter at time t , would collapse to a black hole [4, 5]. If the overdensity is of order unity on the Hubble scale, c/H , the collapse occurs on a timescale of order a few t . The spherical region, whose interior is described by the Friedmann-Lemaire-Robertson-Walker spacetime, could have a sharp outer boundary and be surrounded by vacuum. In that case, the spacetime outside of this boundary would be described by the Schwarzschild solution for a black hole with a mass M equal to the total mass-energy enclosed within the finite sphere. Applying Birkhoff's and Israel's theorems [6] to the sphericallysymmetric spacetime interior to the boundary, implies that it follows the evolution of a closed Universe that eventually collapses to a singularity within a finite time in a Big Crunch. This final state would be a black hole, described by the full Schwarzschild spacetime.  \nIt is well known that in order to create a black hole, one needs to concentrate a mass M within a Schwarzschild radius of ∼ 2 GM/c 2 , as formulated by the so-called 'Hoop  \nConjecture'[7]. Any choice of black hole mass, M , or the equivalent radiation energy E = Mc 2 , translates to the radius of the progenitor region that will collapse to make the black hole.  \nThe radius of the cosmic horizon at a time of ∼ 10 µ s after the Big-Bang was ∼ 3 km. The radiation temperature at that time was 150 MeV= 294 m e c 2 , with an equivalent mass density of ∼ 2 × 10 16 g cm -3 . It is possible to create a Schwarzschild black hole with the mass of the Sun by concentrating a thermal radiation bath at this temperature of total energy E = 1 . 8 x 10 47 Joules within a spherical region smaller than 3 km.  \nFinally, we note that black hole creation out of light does not demand a radiation field of extreme intensity. If we were to fill the present-day universe with a thermal blackbody radiation at room temperature, ∼ 300K, no electron-positron pairs would be produced by the Schwinger mechanism of the associated infrared photons. However, the radiation energy density would exceed the critical value for collapse to a black hole singularity by a factor of ∼ 3 × 10 4 . Currently, we do not live inside the event horizon a black hole because the actual temperature of the cosmic microwave background, 2.73 K, is 110 times smaller, making the radiation field sub-critical by a factor of ∼ 5 × 10 3 .  \nIn conclusion, black holes can be made out of light. In fact, it is possible that dark matter is primordial black holes in the asteroid-mass range of ∼ 10 17 -10 22 g [8, 9]. If that is the case, most of the matter in today's Universe was created by the collapse of thermal radiation into black holes in the first 10 picoseconds after the Big Bang. But even today, giant black holes could be created by concentrating low-energy photons in a large enough volume of space.  \nAcknowledgments - This work was supported in part by the Black Hole Initiative which is funded by JTF and GBMF.  \n- [3] E. W. Kolb, D. Hooper, and M. Turner, Particle Cosmology and Astrophysics (2024).\n- [4] B. J. Carr and S. W. Hawking, Black holes in the early Universe, MNRAS 168 , 399 (1974).\n- [5] B. J. Carr and A. M. Green, The History of Primordial Black Holes, arXiv e-prints , arXiv:2406.05736 (2024), arXiv:2406.05736 [astro-ph.CO].\n- [6] W. Israel, Event Horizons in Static Vacuum Space-Times, Physical Review 164 , 1776 (1967).\n- [7] R. Schoen and S. T. Yau, The existence of  \n- a black hole due to condensation of matter, 90\n- Communications in Mathematical Physics , 575 (1983). [8] B. Carr and F. Kuhnel, Primordial Black Holes as Dark Matter Candidates, arXiv e-prints , arXiv:2110.02821 (2021), arXiv:2110.02821 [astro-ph.CO].\n- [9] A. M. Green, Primordial black holes as a dark matter candidate -a brief overview, Nuclear Physics B 1003 , 116494 (2024), arXiv:2402.15211 [astro-ph.CO]."}