Research led by Alina Yousaf

Writers: Arhama Javed, Hamna Azeem, Alina Yousaf

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I. INTRODUCTION

 A black hole is a region of space-time where gravity is so strong that nothing (no particles or even electromagnetic radiation such as light) can escape from it. Marcia Bartusiak traces the term "black hole" to physicist Robert H. Dicke who in the early 1960s reportedly compared the phenomenon to the Black Hole of Calcutta, notorious as a prison where people entered but never left alive.

 The idea of a body so massive that even light could not escape was briefly proposed by astronomical pioneer and English clergyman John Michell in letter published in November 1784. John Michellused the term "dark star" for "black hole". Michell's simplistic calculations assumed such a body might have the same density as the Sun, and concluded that such a body would form when a star's diameter exceeds the Sun's by a factor of 500 and the surface escape velocity exceeds the usual speed of light. Michell correctly noted that such supermassive but non-radiating bodies might be detectable through their gravitational effects on nearby visible bodies. Scholars of the time were initially excited by the proposal that giant but invisible stars might be hiding in plain view, but enthusiasm dampened when electron-degenerate matter above a certain limiting mass (now called the Chandrasekhar limit at 1.4 M☉) has no stable solutions. His arguments were opposed by many of his contemporaries like Eddington and Lev Landau, who argued that some yet unknown mechanism would stop the collapse. They were partly correct as a white dwarf slightly more massive than the Chandrasekhar limit will collapse into a neutron star which is stable. But in 1939, Robert Oppenheimer and others predicted that neutron stars above another limit (the Tolman–Oppenheimer–Volkoff limit) would collapse further for the reasons presented by Chandrasekhar, and concluded that no law of physics was likely to intervene and stop at least some stars from collapsing to black holes.

 The wavelike nature of light became apparent in the early nineteenth century. In 1915, Albert Einstein developed his theory of general relativity, having earlier shown that gravity does influence light's motion. Only a few months later, Karl Schwarzschild found a solution to the Einstein field equations, which describes the gravitational field of a point mass and a spherical mass. A few months after Schwarzschild, Johannes Droste independently gave the same solution for the point mass and wrote more extensively about its properties. This solution had a peculiar behaviour at what is now called the Schwarzschild radius. The nature of this surface was not quite understood at the time.

 In 1924, Arthur Eddington showed that the singularity disappeared after a change of coordinates. It took until 1933 for Georges Lemaître to realize that this meant the singularity at the Schwarzschild radius was a non-physical coordinate singularity. Arthur Eddington did however comment on the possibility of a star with mass compressed to the Schwarzschild radius in a 1926 book, noting that Einstein's theory allows us to rule out overly large densities for visible stars like Betelgeuse. In 1931, Subrahmanyan Chandrasekhar calculated, using special relativity, that a non-rotating body of rapidly rotating neutron stars. Until that time, neutron stars, like black holes, were regarded as just theoretical curiosities; but the discovery of pulsars showed their physical relevance and spurred a further interest in all types of compact objects that might be formed by gravitational collapse. In this period more general black hole solutions were found.

 Their original calculations, based on the Pauli Exclusion Principle, gave it as 0.7 M☉; subsequent consideration of strong force-mediated neutron-neutron repulsion raised the estimate to approximately 1.5 M☉ to 3.0 M☉. Observations of the neutron star merger GW170817, which is thought to have generated a black hole shortly afterward, have refined the TOV limit estimate to ~2.17 M☉. Oppenheimer and his co-authors interpreted the singularity at the boundary of the Schwarzschild radius as indicating that this was the boundary of a bubble in which time stopped. This is a valid point of view for external observers, but not for infilling observers. Because of this property, the collapsed stars were called "frozen stars", because an outside observer would see the surface of the star frozen in time at the instant where its collapse takes it to the Schwarzschild radius.

 In 1958, David Finkelstein identified the Schwarzschild surface as an event horizon, "a perfect unidirectional membrane: causal influences can cross it in only one direction". This did not strictly contradict Oppenheimer's results, but extended them to include the point of view of infalling observers. Finkelstein's solution extended the Schwarzschild solution for the future of observers falling into a black hole. A complete extension had already been found by Martin Kruskal, who was urged to publish it. These results came at the beginning of the golden age of general relativity, which was marked by general relativity and black holes becoming mainstream subjects of research. This process was helped by the discovery of pulsars by Jocelyn Bell Burnell in 1967, which, by 1969, were shown to be work rapidly rotating neutron stars. Until that time, neutron stars, like black holes, were regarded as just theoretical curiosities; but the discovery of pulsars showed their physical relevance and spurred a further interest in all types of compact objects that might be formed by gravitational collapse. In this period more general black hole solutions were found.

 In 1963, Roy Kerr found the exact solution for a rotating black hole. Two years later, Ezra Newman found the axisymmetric solution for a black hole that is both rotating and electrically charged. Through the work of Werner Israel, Brandon Carter, and David Robinson the no-hair theorem emerged, stating that a stationary black hole solution is completely described by the three parameters of the Kerr–Newman metric: mass, angular momentum, and electric charge. Work by James Bardeen, Jacob Bekenstein, Carter, and Hawking in the early 1970s led to the formulation of black hole thermodynamics. These laws describe the behaviour of a black hole in close analogy to the laws of thermodynamics by relating mass to energy, area to entropy, and surface gravity to temperature. The analogy was completed when Hawking, in 1974, showed that quantum field theory implies that black holes should radiate like a black body with a temperature proportional to the surface gravity of the black hole, predicting the effect now known as Hawking radiation.

 On 11 February 2016, the LIGO Scientific Collaboration and the Virgo collaboration announced the first direct detection of gravitational waves, which also represented the first observation of a black hole merger. On 10 April 2019, the first direct image of a black hole and its vicinity was published, following observations made by the Event Horizon Telescope in 2017 of the supermassive black hole in Messier 87's galactic centre.

 At first, it was suspected that the strange features of the black hole solutions were pathological artifacts from the symmetry conditions imposed, and that the singularities would not appear in generic situations. This view was held in particular by Vladimir Belinsky, Isaak Khalatnikov, and Evgeny Lifshitz, who tried to prove that no singularities appear in generic solutions. However, in the late 1960s Roger Penrose and Stephen Hawking used global techniques to prove that singularities appear generically. For this work, Penrose received half of the 2020 Noble prizes in Physics.

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II. FORMATION OF BLACK HOLE

 Given the bizarre character of black holes, it was long questioned whether such objects could actually exist in nature or whether they were merely pathological solutions to Einstein's equations. Einstein himself wrongly thought black holes would not form, because he held that the angular momentum of collapsing particles would stabilize their motion at some radius. This led the general relativity community to dismiss all results to the contrary for many years. However, a minority of relativists continued to contend that black holes were physical objects, and by the end of the 1960s, they had persuaded the majority of researchers in the field that there is no obstacle to the formation of an event horizon.

 Penrose demonstrated that once an event horizon forms, general relativity without quantum mechanics requires that a singularity will form within. Shortly afterwards, Hawking showed that many cosmological solutions that describe the Big Bang have singularities without scalar fields or other exotic matter. The Kerr solution, the no-hair theorem, and the laws of black hole thermodynamics showed that the physical properties of black holes were simple and comprehensible, making them respectable subjects for research. Conventional black holes are formed by gravitational collapse of heavy objects such as stars, but they can also in theory be formed by other processes.

 1. Gravitational collapse

  Gravitational collapse occurs when an object's internal pressure is insufficient to resist the object's own gravity. For stars this usually occurs either because a star has too little fuel left to maintain its temperature through stellar nucleosynthesis or because a star that would have been stable receives extra matter in a way that does not raise its core temperature. In either case the star's temperature is no longer high enough to prevent it from collapsing under its own weight. The collapse may be stopped by the degeneracy pressure of the star's constituents, allowing the condensation of matter into an exotic denser state. The result is one of the various types of compact star. Which type forms depends on the mass of the remnant of the original star left if the outer layers have been blown away (for example, in a Type II supernova). The mass of the remnant, the collapsed object that survives the explosion, can be substantially less than that of the original star. Remnants exceeding 5 M☉ are produced by stars that were over 20 M☉ before the collapse.

 If the mass of the remnant exceeds about 3–4 M☉ (the Tolman–Oppenheimer–Volkoff limit) either because the original star was very heavy or because the remnant collected additional mass through accretion of matter, even the degeneracy pressure of neutrons is insufficient to stop the collapse. No known mechanism (except possibly quark degeneracy pressure, see quark star) is powerful enough to stop the implosion and the object will inevitably collapse to form a black hole.

 The gravitational collapse of heavy stars is assumed to be responsible for the formation of stellar mass black holes. Star formation in the early universe may have resulted in very massive stars, which upon their collapse would have produced black holes of up to 103 M☉. These black holes could be the seeds of the supermassive black holes found in the centers of most galaxies. It has further been suggested that massive black holes with typical masses of ~105 M☉ could have formed from the direct collapse of gas clouds in the young universe. These massive objects have been proposed as the seeds that eventually formed the earliest quasars observed already at redshift. While most of the energy released during gravitational collapse is emitted very quickly, an outside observer does not actually see the end of this process. Even though the collapse takes a finite amount of time from the reference frame of infalling matter, a distant observer would see the infalling material slow and halt just above the event horizon, due to gravitational time dilation. Light from the collapsing material takes longer and longer to reach the observer, with the light emitted just before the event horizon forms delayed an infinite amount of time. Thus the external observer never sees the formation of the event horizon; instead, the collapsing material seems to become dimmer and increasingly red-shifted, eventually fading away.

 Gravitational collapse requires great density. In the current epoch of the universe these high densities are found only in stars, but in the early universe shortly after the Big Bang densities were much greater, possibly allowing for the creation of black holes. High density alone is not enough to allow black hole formation since a uniform mass distribution will not allow the mass to bunch up. In order for primordial black holes to have formed in such a dense medium, there must have been initial density perturbations that could then grow under their own gravity. Different models for the early universe vary widely in their predictions of the scale of these fluctuations. Various models predict the creation of primordial black holes ranging in size from Planck mass to hundreds of thousands of solar masses.

 Despite the early universe being extremely dense— far denser than is usually required to form a black hole—it did not re-collapse into a black hole during the Big Bang. Models for gravitational collapse of objects of relatively constant size, such as stars, do not necessarily apply in the same way to rapidly expanding space such as the Big Bang.

 2. High-energy collisions

 Gravitational collapse is not the only process that could create black holes. In principle, black holes could be formed in high-energy collisions that achieve sufficient density. As of 2002, no such events have been detected, either directly or indirectly as a deficiency of the mass balance in particle accelerator experiments. This suggests that there must be a lower limit for the mass of black holes. Theoretically, this boundary is expected to lie around the Planck mass (mP=√ħ c/G ≈ 1.2×1019 GeV/c2 ≈ 2.2×10−8 kg), where quantum effects are expected to invalidate the predictions of general relativity. This would put the creation of black holes firmly out of reach of any high-energy process occurring on or near the Earth. However, certain developments in quantum gravity suggest that the minimum black hole mass could be much lower as low as 1 TeV/c2.

 This would make it conceivable for micro black holes to be created in the high-energy collisions that occur when cosmic rays hit the Earth's atmosphere or possibly in the Large Hadron Collider at CERN. These theories are very speculative and the creation of black holes in these processes is deemed unlikely by many specialists. Even if micro black holes could be formed, it is expected that they would evaporate in about 10−25 seconds, posing no threat to the Earth.

III. GROWTH OF BLACK HOLE

 Once a black hole has formed, it can continue to grow by absorbing additional matter. Any black hole will continually absorb gas and interstellar dust from its surroundings. This is the primary process through which supermassive black holes seem to have grown. A similar process has been suggested for the formation of intermediate-mass black holes found in globular clusters. Black holes can also merge with other objects such as stars or even other black holes. This is thought to have been important, especially in the early growth of supermassive black holes, which could have formed from the aggregation of many smaller objects. The process has also been proposed as the origin of some intermediate-mass black holes.

IV.  PROPERTIES OF BLACK HOLES

 1.Mass and Size:

Mass is the defining property of a black hole, determining its size, gravitational influence, and classification. Unlike most celestial objects, a black hole’s mass is concentrated into an infinitely dense region called the singularity, making it unique in how it interacts with its environment. There are three primary categories based on mass:

●       Stellar-mass black holes: These black holes typically have masses between 5 to 100 times that of the sun and are formed from the remnants of massive stars.

●       Intermediate- mass black holes: Ranging from a few hundred to several thousand solar masses, these black holes likely form through the merging of smaller black holes or large star clusters.

●       Supermassive black holes: Found at the centers of galaxies these have masses ranging from millions to billions of solar masses. Their formation remains an era of active research, though they are believed to grow by accreting mass and merging with other black holes.

The size of black hole, defined by its Schwarzschild radius, is proportional to its mass. This radius marks the boundary where not even light can escape the gravitational pull, also known as the event horizon.

 2.Event Horizon:

 The event horizon is the “point of no return” around a black hole. Once any matter or light crosses this boundary, it cannot escape the intense gravitational pull. While the event horizon itself is not a physical surface, it represents the limit of observability for objects near a black hole. The event horizon radius depends solely on the black hole’s mass, which means a more massive black hole has a proportionally larger event horizon.

 3.Singularity:

 At the core of black hole lies the singularity, where gravity is thought to be infinite and space-time curvature becomes infinite. According to general relativity, this is a single point where all of the black hole’s mass is concentrated. However, the concept of a singularity is theoretical, as current physics breaks down in describing this region. Quantum mechanics suggests that the singularity may not exist in the way general relativity predicts, and ongoing research aims to reconcile these differing models.

 4.Spin (Angular Momentum):

 Black holes can rotate, and this rotation is measured by their angular momentum, rotating black holes, known as Kerr black holes, possess unique characteristics compared to non-rotating, or Schwarzschild black holes. The rotational speed of a black hole affects the space-time around it, causing it to wrap and twist a phenomenon known as frame dragging, which can have significant implications for objects orbiting close to the black hole.

 5.Accretion Disk:

 Black holes often pull in surrounding gas, dust, and even stars, forming an accretion disk around them. As matter spirals inward, friction and gravitational forces cause it to heat up, emitting intense radiation, often in the form of X-rays. This emission can be so powerful that it makes the region around the black hole one of the brightest sources in the universe, visible from vast distances. Accretion disks play a crucial role in studying black holes, as they allow astronomers to detect and analyze black holes indirectly.

 6.Hawking Radiation:

 The renowned physicist Stephen Hawking theorized that black holes are not completely black. Due to quantum effects near the event horizon, black holes emit radiation known as Hawking radiation. This radiation leads to a gradual loss of mass over time, causing black holes to “evaporate”. For massive black holes, the rate of evaporation is extremely slow, but for tiny black holes, this process could be significant. Hawking radiation remains one of the most intriguing aspects of black holes, as it bridges general relativity and quantum mechanics.

 7.Gravitational Waves:

 When black holes merge, they create ripples in space-time known as gravitational waves. These waves carry information about the black hole’s properties, such as mass and spin, and have allowed scientists to detect black hole mergers billions of light-years away. The observation of gravitational waves in 2015 confirmed Einstein’s prediction and opened a new way to study black holes and other cosmic phenomena.

 8.Impact on Surrounding Space-Time:

 Black holes exert an intense gravitational influence on the fabric of space-time. Their extreme gravitational field leads to phenomena such as time dilation, where time moves more slowly in their vicinity compared to regions farther away. This effect has been confirmed by observing stars orbiting close to the supermassive black hole at the center of the milky way. Black holes can alter the paths of nearby stars and gas, leading to complex, sometimes chaotic orbits.

V. HAWKING RADIATION

 In 1975, Stephen Hawking made a surprising discovery: black holes aren't completely black. If we consider quantum theory, black holes actually emit a faint glow called Hawking radiation, which includes light particles (photons), neutrinos, and some heavier particles. This glow is too weak to be seen because the black holes we know about are surrounded by hot gas that overshadows this faint radiation.

Hawking calculated that the temperature of this radiation depends on the size of the black hole. For a black hole with the same mass as our Sun, the temperature would be incredibly tiny—about 6×10^−8/M kelvins, where M is the mass of the black hole in solar masses. This means only very small black holes would give off enough radiation to notice.

Astonishingly a black hole can eventually shrink and disappear. If left alone with no new matter falling in, it would slowly lose mass through this radiation. Over time, it would shrink faster and faster until it explodes in a huge burst of energy.

 How Does Hawking Radiation Work?

 Around a black hole, pairs of "virtual particles" are always being created. Normally, these particles quickly cancel each other out. But near a black hole’s edge (called the event horizon), one particle might fall in while the other escapes, becoming part of Hawking radiation. However, these particles have to get energy from empty space to appear in the first place. Normally this energy is repaid when they recombine, but as that can’t happen in the case of Hawking radiation particles effectively default on the borrowed energy. The energy has to come from somewhere: the black hole. So over time a black hole slowly loses mass due to the constant need to cover these energy debts to empty space. It means that a black hole slowly evaporates over time. The number of years it would take a black hole with the same mass as the Sun to evaporate is 1*10^64 years – many times the current age of the Universe.

 Bogoliubov transformations:

 Nonetheless it’s not exactly how the Hawking radiation works. Precisely it involves something called Bogoliubov transformations, which describe how particles and energy behave in curved spacetime.

Precisely in quantum theory, "particles" and "antiparticles" are defined based on how we split waves of energy into positive and negative frequencies. But this split depends on your point of view, like the coordinate system you’re using to measure time. For flat, simple spacetime, everyone agrees on what counts as a particle or a vacuum (empty space). But in the curved spacetime around a black hole, different observers might see things differently.

When a black hole forms, what someone far away in the future considers "particles" might not match what someone in the distant past would have considered "particles." This mismatch creates the effect we call Hawking radiation. It also explains why, from far away, the black hole appears to have a temperature and entropy (a measure of disorder).

 Why Is This Important?

 Hawking radiation isn’t just about black holes glowing faintly—it’s a clue about how quantum mechanics and gravity work together, two of the biggest wonders of physics. And it has huge implications for our understanding of the universe.

Possible implications of Hawking radiation in near future

Studying Hawking radiation could help develop a unified theory of quantum gravity, which could revolutionize our understanding of the universe.

Another implication might be research into Hawking radiation that could improve our ability to simulate and understand high-energy processes in extreme astrophysical conditions, leading to advancements in fields like plasma physics and fusion energy.

 If miniature black holes (artificial) can be created and manipulated safely, their Hawking radiation could provide us with immense energy.  This implication, though speculative, this could revolutionize energy production in space exploration or advanced civilizations.

The study of how information is retained or lost in black holes with the help of Hawking radiation, could have implications on quantum computing, cryptography, and data security.

 Hindrances to implications of Hawking radiation:

 Detecting Hawking radiation from black holes is extremely difficult because it is faint compared to other emissions near a black hole.

Creating conditions to exploit Hawking radiation is far beyond current capabilities.

Handling miniature black holes would pose many risks and challenges.

VI. Conclusion:

 The theory of general relativity predicts that a sufficiently compact mass can deform spacetime to form a black hole. The boundary of the region from which no escape is possible is called the event horizon. Although the event horizon has an enormous effect on the fate and circumstances of an object crossing it, according to general relativity it has no locally detectable features. In many ways, a black hole acts like an ideal black body, as it reflects no light. Moreover, quantum field theory in curved space-time predicts that event horizons emit Hawking radiation, with the same spectrum as a black body of a temperature inversely proportional to its mass. This temperature is on the order of billionths of a kelvin for black holes of stellar mass, making it essentially impossible to observe.

 Black holes of stellar mass are expected to form when very massive stars collapse at the end of their life cycle. After a black hole has formed, it can continue to grow by absorbing mass from its surroundings. By absorbing other stars and merging with other black holes, supermassive black holes of millions of solar masses (M☉) may form. There is consensus that supermassive black holes exist in the centers of most galaxies.

 The presence of a black hole can be inferred through its interaction with other matter and with electromagnetic radiation such as visible light. Matter that falls onto a black hole can form an external accretion disk heated by friction, forming quasars, some of the brightest objects in the universe. Stars passing too close to a supermassive black hole can be shredded into streamers that shine very brightly before being "swallowed." If there are other stars orbiting a black hole, their orbits can be used to determine the black hole's mass and location. Such observations can be used to exclude possible alternatives such as neutron stars. In this way, astronomers have identified numerous stellar black hole candidates in binary systems and established that the radio source known as Sagittarius A*, at the core of the Milky Way galaxy, contains a supermassive black hole of about 4.3 million solar masses.

 VII.References:

 1. Wald, R. M. (1997). "Gravitational Collapse and Cosmic Censorship". Black Holes, Gravitational Radiation and the Universe. Springer. pp. 69–86.

2. Schutz, Bernard F. (2003). Gravity from the ground up. Cambridge University Press. p. 110.

3. Davies, P. C. W. (1978). "Thermodynamics of Black Holes" (PDF). Reports on Progress in Physics. 41 (8): 1313–1355.

4. Montgomery, Colin; Orchiston, Wayne; Whittingham, Ian (2009). "Michell, Laplace and the origin of the black hole concept". Journal of Astronomical History and Heritage. 12 (2): 90–96.

5. Clery D (2020). "Black holes caught in the act of swallowing stars". Science. 367(6477): 495.

6. Joshi, P. S. (2007). Gravitational Collapse and Spacetime Singularities. Cambridge University Press

7.Heckman, T. M., & Best, P. N. (2014). The Coevolution of Galaxies and Supermassive Black Holes: Insights from Surveys of the Contemporary Universe. Annual Review of Astronomy and Astrophysics, 52, 589–660

8.Thorne, K. S., Price, R. H., & Macdonald, D. A. (1986). Black Holes: The Membrane Paradigm. Yale University Press

9.Parikh, M. K., & Wilczek, F. (2000). Hawking Radiation as Tunneling. Physical Review Letters, 85(24), 5042–5045.

10. The Editors of Encyclopaedia Britannica. (2024, November 4). Hawking radiation | Black Holes, Quantum Mechanics, Particle Physics. Encyclopedia Britannica. https://www.britannica.com/science/Hawking-radiation

11. Robert M. Wald, General Relativity, Sections 14.2–14.4, University of Chicago Press, Chicago, 1984.  (A good precise introduction to the subject.)

12. Stephen W. Hawking, Particle creation by black holes, Commun. Math. Phys. 43 (1975), 199–220.  (The original paper.) W. Hawking, Particle creation by black holes, Commun. Math. Phys. 43 (1975), 199–220.  (The original paper.)

13. Hawking Radiation. (n.d.-b). https://jila.colorado.edu/~ajsh/bh/hawk.html

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