# Primordial black hole

Primordial black holes are a hypothetical type of black hole that formed soon after the Big Bang. In the early universe, high densities and inhomogeneous conditions could have led sufficiently dense regions to undergo gravitational collapse, forming black holes. Yakov Borisovich Zel'dovich and Igor Dmitriyevich Novikov in 1966[1] first proposed the existence of such black holes. The theory behind their origins was first studied in depth by Stephen Hawking in 1971.[2] Since primordial black holes did not form from stellar gravitational collapse, their masses can be far below stellar mass (c. 2×1030 kg). Hawking calculated that primordial black holes could weigh as little as 10−8 kg, about the weight of a human ovum.

## Theoretical history

Depending on the model, primordial black holes could have initial masses ranging from 10−8 kg (the so-called Planck relics) to more than thousands of solar masses. However, primordial black holes with a mass lower than 1011 kg would have evaporated due to Hawking radiation in a time much shorter than the age of the Universe, so they would not have survived to the present. Primordial black holes are non-baryonic[3] and as such are plausible dark matter candidates.[4][5][6][7] Primordial black holes are also good candidates for being the seeds of the supermassive black holes at the center of massive galaxies, as well as of intermediate-mass black holes.[8]

Primordial black holes belong to the class of massive compact halo objects (MACHOs). They are naturally a good dark matter candidate: they are (nearly) collision-less and stable (if sufficiently massive), they have non-relativistic velocities, and they form very early in the history of the Universe (typically less than one second after the Big Bang). Nevertheless, tight limits on their abundance have been set up from various astrophysical and cosmological observations, so that it is now excluded that they contribute significantly to dark matter over most of the plausible mass range.

In March 2016, one month after the announcement of the detection by Advanced LIGO/VIRGO of gravitational waves emitted by the merging of two 30 solar mass black holes (about 6×1031 kg), three groups of researchers proposed independently that the detected black holes had a primordial origin.[9][10][11][12] Two of the groups found that the merging rates inferred by LIGO are consistent with a scenario in which all the dark matter is made of primordial black holes, if a non-negligible fraction of them are somehow clustered within halos such as faint dwarf galaxies or globular clusters, as expected by the standard theory of cosmic structure formation. The third group claimed that these merging rates are incompatible with an all-dark-matter scenario and that primordial black holes could only contribute to less than one percent of the total dark matter. The unexpected large mass of the black holes detected by LIGO has strongly revived interest in primordial black holes with masses in the range of 1 to 100 solar masses. It is however still debated whether this range is excluded or not by other observations, such as the absence of micro-lensing of stars, the cosmic microwave background anisotropies, the size of faint dwarf galaxies, and the absence of correlation between X-ray and radio sources towards the galactic center.

In May 2016, Alexander Kashlinsky suggested that the observed spatial correlations in the unresolved gamma-ray and X-ray background radiations could be due to primordial black holes with similar masses, if their abundance is comparable to that of dark matter.[13]

In April 2019 a study was published suggesting this hypothesis may be a dead end. An international team of researchers has put a theory speculated by the late Stephen Hawking to its most rigorous test to date, and their results have ruled out the possibility that primordial black holes smaller than a tenth of a millimeter make up most of dark matter (journal reference from the article).

## Formation

Primordial black holes could have formed in the very early Universe (less than one second after the Big Bang), during the so-called radiation dominated era. The essential ingredient for the formation of a primordial black hole is a fluctuation in the density of the Universe, inducing its gravitational collapse. One typically requires density contrasts ${\displaystyle \delta \rho /\rho \sim 0.1}$  (where ${\displaystyle \rho }$  is the density of the Universe) to form a black hole.[14] There are several mechanisms able to produce such inhomogeneities in the context of cosmic inflation (in hybrid inflation models, for example axion inflation), reheating, or cosmological phase transitions.

## Observational limits and detection strategies

A variety of observations have been interpreted to place limits on the abundance and mass of primordial black holes:

• Lifetime, Hawking radiation and gamma-rays: One way to detect primordial black holes, or to constrain their mass and abundance, is by their Hawking radiation. Stephen Hawking theorized in 1974 that large numbers of such smaller primordial black holes might exist in the Milky Way in our galaxy's halo region. All black holes are theorized to emit Hawking radiation at a rate inversely proportional to their mass. Since this emission further decreases their mass, black holes with very small mass would experience runaway evaporation, creating a massive burst of radiation at the final phase, equivalent to a hydrogen bomb yielding millions of megatons of explosive force.[15] A regular black hole (of about 3 solar masses) cannot lose all of its mass within the current age of the universe (they would take about 1069 years to do so, even without any matter falling in). However, since primordial black holes are not formed by stellar core collapse, they may be of any size. A black hole with a mass of about 1011 kg would have a lifetime about equal to the age of the universe. If such low-mass black holes were created in sufficient number in the Big Bang, we should be able to observe explosions by some of those that are relatively nearby in our own Milky Way galaxy. NASA's Fermi Gamma-ray Space Telescope satellite, launched in June 2008, was designed in part to search for such evaporating primordial black holes. Fermi data set up the limit that less than one percent of dark matter could be made of primordial black holes with masses up to 1013 kg. Evaporating primordial black holes would have also had an impact on the Big Bang nucleosynthesis and change the abundances of light elements in the Universe. However, if theoretical Hawking radiation does not actually exist, such primordial black holes would be extremely difficult, if not impossible, to detect in space due to their small size and lack of large gravitational influence.
• Lensing of gamma-ray bursts: Compact objects can induce a change in the luminosity of gamma-ray bursts when passing close to their line-of-sight, through the gravitational lensing effect. The Fermi Gamma-Ray Burst Monitor experiment found that primordial black holes cannot contribute importantly to the dark matter within the mass range 5 x 1014 – 1017 kg.[16]
• Capture of primordial black holes by neutron stars: If primordial black holes with masses between 1015 kg and 1022 kg had abundances comparable to that of dark matter, neutron stars in globular clusters should have captured some of them, leading to the rapid destruction of the star.[17] The observation of neutron stars in globular clusters can thus be used to set a limit on primordial black hole abundance.
• Micro-lensing of stars: If a primordial black hole passes between us and a distant star, it induces a magnification of these stars due to the gravitational lensing effect. By monitoring the magnitude of stars in the Magellanic Clouds, the EROS and MACHO surveys have put a limit on the abundance of primordial black holes in the range 1023 – 1031 kg. According to these surveys, primordial black holes within this range cannot constitute an important fraction of the dark matter.[18][19] However, these limits are model-dependent. It has been also argued that if primordial black holes are regrouped in dense halos, the micro-lensing constraints are then naturally evaded.[20]
• Micro-lensing of Ia supernovae: Primordial black holes with masses larger than 1028 kg would magnify distant type Ia supernova (or any other standard candle of known luminosity) due to gravitational lensing. These effects would be apparent if primordial black holes were a significant contribution to the dark matter density, which is constrained by current data sets.[21][22]
• Temperature anisotropies in the cosmic microwave background: Accretion of matter onto primordial black holes in the early Universe should lead to energy injection in the medium that affects the recombination history of the Universe. This effect induces signatures in the statistical distribution of the cosmic microwave background (CMB) anisotropies. The Planck observations of the CMB exclude that primordial black holes with masses in the range 100 – 104 solar masses contribute importantly to the dark matter,[23] at least in the simplest conservative model. It is still debated whether the constraints are stronger or weaker in more realistic or complex scenarios.

At the time of the detection by LIGO of the gravitational waves emitted during the final coalescence of two 30 solar mass black holes, the mass range between 10 and 100 solar masses was still only poorly constrained. Since then, new observations have been claimed to close this window, at least for models in which the primordial black holes have all the same mass:

• from the absence of X-ray and optical correlations in point sources observed in the direction of the galactic center.[24]
• from the dynamical heating of dwarf galaxies[25]
• from the observation of a central star cluster in the Eridanus II dwarf galaxy (but these constraints can be relaxed if Eridanus II owns a central intermediate mass black hole, which is suggested by some observations).[26] If primordial black holes exhibit a broad mass distribution, those constraints could nevertheless still be evaded.
• from the gravitational micro-lensing of distant quasars by closer galaxies, allowing only 20% of the galactic matter to be in the form of compact objects with stellar masses, a value consistent with the expected stellar population.[27]
• from micro-lensing of distant stars by galaxy clusters, suggesting that the fraction of dark matter in the form of primordial black holes with masses comparable to those found by LIGO must be less than 10%.[28]

In the future, new limits will be set up by various observations:

• The Square Kilometre Array (SKA) radio telescope will probe the effects of primordial black holes on the reionization history of the Universe, due to energy injection into the intergalactic medium, induced by matter accretion onto primordial black holes.[29]
• LIGO, VIRGO and future gravitational waves detectors will detect new black hole merging events, from which one could reconstruct the mass distribution of primordial black holes.[30] These detectors could allow distinguishing unambiguously between primordial or stellar origins if merging events involving black holes with a mass lower than 1.4 solar mass are detected. Another way would be to measure the large orbital eccentricity of primordial black hole binaries.[31]
• Gravitational wave detectors, such as the Laser Interferometer Space Antenna (LISA) and pulsar timing arrays will also probe the stochastic background of gravitational waves emitted by primordial black hole binaries, when they are still orbiting relatively far from each other.[32]
• New detections of faint dwarf galaxies, and the observations of their central star cluster, could be used to test the hypothesis that these dark matter-dominated structures contain primordial black holes in abundance.
• Monitoring star positions and velocities within the Milky Way could be used to detect the influence of a nearby primordial black hole.
• It has been suggested[33][34] that a small black hole passing through the Earth would produce a detectable acoustic signal. Because of its tiny diameter, large mass compared to a nucleon, and relatively high speed, such primordial black holes would simply transit Earth virtually unimpeded with only a few impacts on nucleons, exiting the planet with no ill effects.
• Another way to detect primordial black holes could be by watching for ripples on the surfaces of stars. If the black hole passed through a star, its density would cause observable vibrations.[35][36]
• Monitoring quasars in the microwave wavelength and detection of the wave optics feature of gravitational microlensing by the primordial black holes [37]

## Implications

The evaporation of primordial black holes has been suggested as one possible explanation for gamma-ray bursts. This explanation is, however, considered unlikely.[clarification needed][citation needed] Other problems for which primordial black holes have been suggested as a solution include the dark matter problem, the cosmological domain wall problem[38] and the cosmological monopole problem.[39] Since a primordial black hole does not necessarily have to be small (they can have any size), primordial black holes may also have contributed to the later formation of galaxies.

Even if they do not solve these problems, the low number of primordial black holes (as of 2010, only two intermediate mass black holes were confirmed) aids cosmologists by putting constraints on the spectrum of density fluctuations in the early universe.

## String theory

General relativity predicts the smallest primordial black holes would have evaporated by now, but if there were a fourth spatial dimension – as predicted by string theory – it would affect how gravity acts on small scales and "slow down the evaporation quite substantially".[40] This could mean there are several thousand black holes in our galaxy. To test this theory, scientists will use the Fermi Gamma-ray Space Telescope which was put in orbit by NASA on June 11, 2008. If they observe specific small interference patterns within gamma-ray bursts, it could be the first indirect evidence for primordial black holes and string theory.[needs update]

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