# Does gravito electromagnetism explain cosmic expansion

## Introduction to general relativity - Introduction to general relativity

** The general theory of relativity ** is a theory of gravitation, developed by Albert Einstein between 1907 and 1915. The general theory of relativity says that the gravitational effect between masses results from their warping of the observed space-time.

At the beginning of the 20th century, Newton's law of universal gravitation had been accepted as a valid description of the force of gravity between masses for more than two hundred years. In Newton's model, gravity is the result of an attraction between massive objects. Although even Newton was troubled by the unknown nature of this force, the framework was extremely successful in describing motion.

Experiments and observations show that Einstein's description of gravity explains several effects that Newton's law does not explain, such as: B. Tiny anomalies in the orbits of Mercury and other planets. General relativity also predicts novel effects of gravity, such as gravitational waves, gravitational lenses, and an effect of gravity on time known as gravitational time dilation. Many of these predictions have been confirmed by experiment or observation, most recently by gravitational waves.

General relativity has become an essential tool in modern astrophysics. It forms the basis for the current understanding of black holes, regions of space where the gravitational effect is strong enough that even light cannot escape. Its strong gravity is believed to be responsible for the intense radiation emitted by certain types of astronomical objects (such as active galactic nuclei or microquasars). General relativity is also part of the framework of the standard big bang model of cosmology.

Although general relativity is not the only relativistic theory of gravity, it is the simplest such theory that is consistent with the experimental data. Still, a number of unanswered questions remain, the most basic of which is how general relativity can be reconciled with the laws of quantum physics to produce a complete and self-consistent theory of quantum gravity.

### From the special to the general theory of relativity

In September 1905 Albert Einstein published his special theory of relativity, which reconciles Newton's laws of motion with electrodynamics (the interaction between objects with an electric charge). Special relativity introduced a new framework for all of physics by proposing new concepts of space and time. Some of the physical theories accepted at the time were inconsistent with this framework; A key example was Newton's theory of gravity, which describes the mutual attraction that bodies experience because of their mass.

Several physicists, including Einstein, were looking for a theory that would reconcile Newton's law of gravitation and special relativity. Only Einstein's theory was found to be consistent with experimentation and observation. To understand the basic ideas of the theory, it is instructive to follow Einstein's thinking between 1907 and 1915, from his simple thought experiment with an observer in free fall to his completely geometric theory of gravity.

### Equivalence principle

A person in a free falling elevator experiences weightlessness; Objects either hover immobile or drift at a constant speed. Since everything collapses in the elevator, no gravitational effect can be observed. In this way, the experiences of an observer in free fall are indistinguishable from those of an observer in space, far from a significant source of gravity. Such observers are the privileged ("inertial") observers that Einstein described in his theory of special relativity: observers for whom light moves at constant speed along straight lines.

Einstein hypothesized that the similar experiences of weightless observers and inertial observers in special relativity represent a fundamental property of gravity, and made this the cornerstone of his general theory of relativity, which was formalized in his principle of equivalence. Roughly speaking, the principle is that a person in a free falling elevator cannot tell that they are in free fall. Any experiment in such a free-falling environment has the same results as for an observer who is at rest or moving evenly in space, far from any sources of gravity.

### Gravity and acceleration

Most of the effects of gravity disappear in free fall, but effects similar to those of gravity can be accelerated through an accelerated frame of reference * generated * become . An observer in an enclosed space cannot say which of the following statements is true:

- Objects fall to the ground because space rests on the surface of the earth and the objects are pulled down by gravity.
- Objects fall to the ground because the space is on board a rocket in space that is traveling at 9.81 m / s
^{ 2 }accelerated and far from any source of gravity. The objects are drawn to the ground by the same "inertial force" that pushes the driver of an accelerating car onto the back of their seat.

Conversely, every effect observed in an accelerated frame of reference should also be observed in a gravitational field with a corresponding strength. This principle enabled Einstein to predict several novel effects of gravity in 1907, as explained in the next section.

An observer in an accelerated frame of reference must introduce what physicists call fictional forces to account for the acceleration experienced by the observer and the objects around him. In the example where the driver is pushed into his seat, the force felt by the driver is an example; Another is the force you can feel when you pull your arms up and out when you try to spin like a top. Einstein's masterful realization was that the constant, familiar gravitational pull of the earth's gravitational field is basically the same as these fictional forces. The apparent size of the fictitious forces always seems to be proportional to the mass of an object on which they act. For example, the driver's seat exerts just enough force to accelerate the driver at the same speed as the car. By analogy, Einstein suggested that an object in a gravitational field should feel a gravitational force proportional to its mass, as contained in Newton's law of gravitation.

### Physical consequences

In 1907 Einstein was eight years away from completing the general theory of relativity. Even so, he was able to make a number of novel, verifiable predictions based on his starting point for developing his new theory: the principle of equivalence.

The first new effect is the gravitational frequency shift of light. Watch two observers aboard an accelerating missile ship. On board such a ship there is a natural concept of "up" and "down": the direction the ship is accelerating is "up", and unattached objects accelerate in the opposite direction and "fall". Suppose one of the observers is "higher" than the other. When the lower observer sends a light signal to the higher observer, the acceleration causes the light to be shifted red, as can be calculated from the special theory of relativity; The second observer measures a lower frequency for the light than the first. Conversely, the light sent from the higher observer to the lower one is blue-shifted, ie shifted to higher frequencies. Einstein argued that such frequency shifts must also be observed in a gravitational field. This is illustrated in the figure on the left, which shows a wave of light gradually shifting red as it moves up against gravitational acceleration. This effect has been confirmed experimentally as described below.

This gravitational frequency shift corresponds to a gravitational time dilation: Since the "higher" observer measures the same light wave in order to have a lower frequency than the "lower" observer, the time for the higher observer must pass faster. Hence, time runs slower for observers who are lower in a gravitational field.

It is important to emphasize that for any observer there are no observable changes in the flow of time for events or processes that rest in their frame of reference. Five-minute eggs, as measured by any observer's clock, have the same consistency. When a year goes by on each clock, each observer ages by that amount. In short, every watch is perfectly in tune with all of the processes that take place in its immediate vicinity. Only when the clocks between different observers are compared can one determine that time is running more slowly for the lower observer than for the higher one. This effect is minute, but has also been experimentally confirmed in several experiments, as described below.

In a similar way, Einstein predicted the gravitational deflection of light: In a gravitational field, light is deflected downwards. Quantitatively, his results were wrong by a factor of two; The correct derivation requires a more complete formulation of general relativity, not just the equivalence principle.

### Tidal effects

The equivalence between gravitational and inertial effects is not a complete theory of gravity. When it comes to explaining gravity near our own location on the surface of the earth, finding that our frame of reference is not in free fall, so fictional forces are to be expected, provides an appropriate explanation. However, a free falling frame of reference on one side of the earth cannot explain why people on the opposite side of the earth experience an attraction in the opposite direction.

A more basic manifestation of the same effect involves two bodies falling to earth side by side. In a frame of reference that is in free fall next to these bodies, they appear to float weightlessly - but not exactly like that. These bodies do not fall in exactly the same direction, but on a single point in space: the earth's center of gravity. Hence there is a component of movement from each body to the other (see figure). In a small environment, such as free-falling lift, this relative acceleration is tiny, while with skydivers on opposite sides of the earth the effect is large. Such differences in force are also responsible for the tides in the Earth's oceans, which is why the term "tidal effect" is used for this phenomenon.

The equivalence between inertia and gravity cannot explain tidal effects - it cannot explain variations in the gravitational field. This requires a theory that describes how matter (like the great mass of the earth) affects the inertial environment around it.

### From acceleration to geometry

While studying the equivalence of gravity and acceleration and the role of tidal forces, Einstein discovered several analogies to the geometry of surfaces. An example is the transition from an inertial reference frame (in which free particles roll out at constant speeds on straight paths) to a rotating reference frame (in which additional terms must be introduced that correspond to fictitious forces in order to explain the particle movement): this is analogous to the Transition from a Cartesian coordinate system (in which the coordinate lines are straight lines) to a curved coordinate system (in which the coordinate lines do not have to be straight).

A deeper analogy relates tidal forces to a property of surfaces known as * Is called curvature * . For gravitational fields, the absence or presence of tidal forces determines whether or not the influence of gravity can be eliminated by selecting a free falling frame of reference. Similarly, the absence or presence of curvature determines whether or not a surface conforms to a plane. In the summer of 1912 Einstein, inspired by these analogies, looked for a geometric formulation of gravity.

The elementary objects of geometry - points, lines, triangles - are traditionally defined in three-dimensional space or on two-dimensional surfaces. In 1907, Hermann Minkowski, Einstein's former mathematics professor at the Eidgenössisches Polytechnikum, introduced the Minkowski space, a geometric formulation of Einstein's special theory of relativity, in which geometry encompassed not only space but also time. The basic unit of this new geometry is the four-dimensional space-time. The trajectories of moving bodies are curves in space-time; The orbits of bodies moving at constant speed without changing direction are straight lines.

The geometry of generally curved surfaces was developed by Carl Friedrich Gauss in the early 19th century. This geometry was in turn generalized to higher-dimensional spaces in the Riemannian geometry, which Bernhard Riemann had introduced in the 1850s. Using Riemannian geometry, Einstein formulated a geometric description of gravity, in which Minkowski's spacetime is replaced by distorted, curved spacetime, just as curved surfaces are a generalization of ordinary flat surfaces. ** Embedding diagrams ** are used to illustrate curved spacetime in educational contexts.

After recognizing the validity of this geometric analogy, it took Einstein another three years to find the missing cornerstone of his theory: the equations that describe how matter affects the curvature of space-time. After he had formulated the so-called Einstein equations (more precisely his field gravity equations), he presented his new theory of gravity at several meetings of the Prussian Academy of Sciences at the end of 1915 and culminated in his final presentation on November 25, 1915.

### Geometry and gravity

Paraphrased as John Wheeler, Einstein's geometric theory of gravity can be summarized as follows: The * Space-time tells matter how to move; Matter tells spacetime how to bend * . What this means is covered in the following three sections, which examine the motion of so-called test particles, examine which properties of matter are the source of gravity, and finally introduce Einstein's equations that relate these properties of matter to curvature of spacetime.

### Investigation of the gravitational field

In order to map the gravitational influence of a body, it is useful to think about what physicists call probe or test particles: particles that are influenced by gravity but are so small and light that we can neglect their own gravitational effect. In the absence of gravity and other external forces, a test particle moves at constant speed along a straight line. In the language of spacetime, this corresponds to the statement that such test particles move along straight world lines in spacetime. In the presence of gravity, spacetime is non-Euclidean or curved, and straight world lines may not exist in curved spacetime. Instead, test particles move along lines called geodesics that are "as straight as possible," meaning they follow the shortest path between the start and end points, taking curvature into account.

A simple analogy is as follows: In geodesy, the science of measuring the size and shape of the earth, a geodesy (from the Greek "geo" to divide earth and "daiein") is the shortest path between two points on the earth's surface. Such a route is roughly a segment of a great circle, such as a line of longitude or the equator. These paths are certainly not straight, simply because they have to follow the curvature of the earth's surface. However, under this condition, they are as straight as possible.

The properties of geodesics differ from those of straight lines. For example, parallel lines never meet in a plane, but this does not apply to the geodesics on the earth's surface: for example, longitudes at the equator are parallel, but intersect at the poles. Similarly, the world lines of the test particles in free fall are spacetime geodesics, the straightest lines in spacetime. Yet there are crucial differences between them and the really straight lines that can be traced in the gravity-free space-time of special relativity. In the special theory of relativity, parallel geodesy remains parallel. In a gravitational field with tidal effects, this is generally not the case. For example, if two bodies are initially at rest relative to each other, but then fall into the earth's gravitational field, they will move towards each other when they fall towards the center of the earth.

Compared to planets and other astronomical bodies, everyday objects (people, cars, houses, even mountains) have little mass. With such objects, the laws governing the behavior of test particles are sufficient to describe what happens. In particular, an external force must be applied in order to deflect a test particle from its geodetic path. A chair on which someone is sitting exerts an external upward force that prevents the person from falling freely towards the center of the earth and thus following a geodesy, which they would otherwise do without matter between them and the center of the earth. This is how general relativity explains the daily experience of gravity on the earth's surface * Not * as a downward pull of a gravitational force, but as an upward pressure of external forces. These forces divert all bodies resting on the earth's surface from the geodesics that they would otherwise follow. For matter objects, whose own gravitational influence cannot be neglected, the laws of motion are somewhat more complicated than for test particles, although it remains true that spacetime tells matter how it should move.

### Gravity sources

In Newton's description of gravity, the force of gravity is caused by matter. More precisely, it is caused by a certain property of material objects: their mass. In Einstein's theory and related theories of gravity, the curvature at any point in space-time is also caused by the matter present. Here, too, mass is a key property in determining the gravitational influence of matter. In a relativistic theory of gravity, however, mass cannot be the only source of gravity. The theory of relativity connects mass with energy and energy with momentum.

The equivalence between mass and energy expressed by the formula * E. * = * mc *^{ 2 } , is the best-known consequence of the special theory of relativity. In the theory of relativity, mass and energy are two different ways of describing a physical quantity. If a physical system has energy, it also has the corresponding mass and vice versa. In particular, all properties of a body that are associated with energy, such as B. its temperature or the binding energy of systems such as nuclei or molecules, contribute to the mass of this body and therefore act as sources of gravity.

In the special theory of relativity, energy is closely related to momentum. Just as space and time are, in this theory, different aspects of a larger unit called space - time, energy and momentum are just different aspects of a unitary four-dimensional set that physicists call four momentum. Hence, if energy is a source of gravity, momentum must also be a source. The same applies to the quantities that are directly related to energy and impulses, namely internal pressure and tension. Taken together, in the general theory of relativity, it is mass, energy, momentum, pressure and tension that serve as sources of gravity: This is how matter tells space-time how it bends. In the mathematical formulation of the theory, all of these quantities are only aspects of a more general physical quantity called the energy-momentum tensor.

### Einstein's equations

Einstein's equations are at the heart of general relativity. They provide an accurate formulation of the relationship between spacetime geometry and the properties of matter using the language of mathematics. More specifically, they are formulated using the concepts of Riemannian geometry, in which the geometric properties of a space (or spacetime) are described by a quantity called a metric. The metric encodes the information required to compute the basic geometric concepts of distance and angle in a curved space (or spacetime).

A spherical surface like that of the earth provides a simple example. The position of any point on the surface can be described by two coordinates: the geographical latitude and longitude. In contrast to the Cartesian coordinates of the plane, the coordinate differences do not correspond to the distances on the surface, as shown in the diagram on the right: For someone at the equator, a movement of 30 degrees of longitude to the west (magenta line) corresponds to a distance of approximately 3,300 kilometers (2,100 miles) ), while for someone 55 degrees latitude, moving 30 degrees westward (blue line) will travel a mere 1,900 kilometers (1,200 miles). Coordinates therefore do not provide enough information to describe the geometry of a spherical surface or the geometry of a more complicated space or a more complicated spacetime. This information is exactly what is encoded in the metric. This function is defined at every point on the surface (or space or spacetime) and relates coordinate differences to differences in distance. All other quantities that are of interest to the geometry, such as B. the length of a particular curve or the angle at which two curves meet can be calculated from this metric function.

The metric function and its rate of change from point to point can be used to define a geometric quantity called the Riemann curvature tensor, which precisely describes how the Riemann manifold, spacetime in relativity, is curved at each point. As already mentioned, the matter content of space-time defines another quantity, the energy-momentum tensor ** T ** , and the principle "space-time tells matter how it moves and matter tells space-time how it curves" means that these quantities must be related to one another. Einstein formulated this relationship using the Riemann curvature tensor and the metric to get a different geometric quantity ** G ** which is now called the Einstein tensor, which describes some aspects of the way space-time is curved. * Einstein's equation * then states that

ie up to a constant multiple the size becomes ** G ** (which measures the curvature) with size ** T ** (which measures the matter content) equated. Here is * G * the gravitational constant of Newton's gravity and * c * the speed of light from the special theory of relativity.

This equation is often referred to in the plural as * Einstein's equations * as the sizes ** G ** and ** T ** can be determined by several functions of the coordinates of space-time and the equations equate each of these component functions. A solution to these equations describes a certain geometry of space-time; For example, the Schwarzschild solution describes the geometry around a spherical, non-rotating mass such as a star or a black hole, while the Kerr solution describes a rotating black hole. Still other solutions can describe a gravitational wave or, in the case of the Friedmann-Lemaître-Robertson-Walker solution, an expanding universe. The simplest solution is the uncurved Minkowski space-time, the space-time described by special relativity theory.

### Experiments

No scientific theory is of course true; Every model has to be verified experimentally. Newton's law of gravitation was accepted because it accounted for the motion of planets and moons in the solar system with considerable accuracy. As the accuracy of the experimental measurements gradually improved, some deviations from Newton's predictions, which were taken into account in general relativity, were observed. Similarly, the predictions of general relativity also need to be verified experimentally, and Einstein himself developed three tests now known as the classical tests of theory:

- Newton's gravity predicts that the orbit a single planet follows around a perfectly spherical star should be an ellipse. Einstein's theory predicts a more complicated curve: the planet behaves as if it were moving around an ellipse, but at the same time the ellipse as a whole slowly rotates around the star. In the figure on the right, the ellipse predicted by Newton's gravity is shown in red and part of the orbit predicted by Einstein is shown in blue. For a planet orbiting the Sun, this deviation from Newton's orbits is known as the anomalous perihelion shift. The first measurement of this effect for the planet Mercury was made in 1859. The most accurate results for Mercury and other planets are based on measurements made between 1966 and 1990 with radio telescopes. General relativity predicts the correct anomalous perihelion shift for all planets on which this can be accurately measured (Mercury, Venus, and Earth).
- According to general relativity, light does not travel along straight lines when it is propagated in a gravitational field. Instead, it is distracted in the presence of massive bodies. In particular, the starlight is deflected as it approaches the sun, resulting in apparent displacements of up to 1.75 arc seconds in the positions of the stars in the sky (one arc second corresponds to 1/3600 degrees). In the context of Newton's gravity, a heuristic argument can be put forward that leads to a light deflection of half this amount. The various predictions can be tested by observing stars that are close to the Sun during a solar eclipse. In this way, a British expedition to West Africa in 1919 under the direction of Arthur Eddington, by observing the solar eclipse in May 1919, confirmed that Einstein's prediction was correct and Newton's predictions were incorrect. Eddington's results were not very accurate; Later observations of the deflection of light from distant quasars by the Sun, using high-precision radio astronomy techniques, have confirmed Eddington's results with significantly better accuracy (the first such measurements are from 1967, the most recent comprehensive analysis from 2004).
- Gravitational redshift was first measured by Pound and Rebka in a laboratory in 1959. It is also observed in astrophysical measurements, especially in light escaping from the white dwarf Sirius B. The related effect of gravitational time dilation was measured by transporting atomic clocks at altitudes between tens of thousands of kilometers (first by Hafele and Keating in 1971; most accurately by the gravity probe A introduced in 1976).

Of these tests, only Mercury's perihelion advancement was known before Einstein's final publication of General Relativity in 1916. The subsequent experimental confirmation of his other predictions, particularly the first measurements of the deflection of light by the sun in 1919, catapulted Einstein to international fame. These three experiments justified the adoption of general relativity over Newton's theory and, moreover, over a number of alternatives to the proposed general relativity theory.

Other tests of general relativity include precision measurements of the Shapiro effect, or gravitational time delay for light, measured by the Cassini spacecraft in 2002. A series of tests focus on effects predicted by general relativity on the behavior of gyroscopes moving through space. One of these effects, geodetic precession, was tested with the Lunar Laser Ranging Experiment (high-precision measurements of the moon's orbit). Another one that relates to rotating masses is called frame dragging. The geodetic and frame drag effects were both tested by the Gravity Probe B satellite experiment launched in 2004. The results confirmed the theory of relativity to 0.5% and 15% respectively in December 2008.

By cosmic standards, gravity is weak throughout the solar system. Since the differences between the predictions of Einstein's and Newton's theories are most pronounced under strong gravity, physicists have long been interested in testing various relativistic effects in an environment with comparatively strong gravitational fields. This has become possible thanks to precise observations of binary pulsars. In such a star system, two highly compact neutron stars orbit each other. At least one of them is a pulsar - an astronomical object that emits a narrow beam of radio waves. These rays hit the earth at very regular intervals, much like the rotating beam of a lighthouse means that an observer will see the lighthouse blink and can be observed as a very regular series of pulses. The general theory of relativity predicts specific deviations from the regularity of these radio pulses. For example, at times when the radio waves are passing close to the other neutron star, they should be deflected by the star's gravitational field. The observed pulse patterns are impressively close to those predicted by general relativity.

A specific set of observations relates to extremely useful practical applications, namely satellite navigation systems such as the Global Positioning System, which are used for both precise positioning and timekeeping. Such systems are based on two sets of atomic clocks: clocks on board satellites orbiting the earth and reference clocks stationed on the earth's surface. General relativity predicts that these two clocks should tick slightly differently due to their different movements (an effect already predicted by special relativity) and their different positions in the earth's gravitational field. To ensure the accuracy of the system, either the satellite clocks are slowed down by a relativistic factor or this factor becomes part of the evaluation algorithm. Tests of system accuracy (especially the very thorough measurements that are part of the definition of universal coordinated time) are, in turn, evidence of the validity of relativistic predictions.

A number of other tests have checked the validity of different versions of the principle of equivalence. Strictly speaking, all gravitational time dilation measurements are tests of the weak version of this principle, not general relativity itself. So far, general relativity has passed all observation tests.

### Astrophysical Applications

Models based on general relativity play an important role in astrophysics. The success of these models is further evidence of the theory's validity.

### Gravitational lenses

Because light is deflected in a gravitational field, light from a distant object can reach an observer in two or more ways. For example, light from a very distant object such as a quasar can pass along one side of a massive galaxy and be easily deflected to reach an observer on Earth, while light falling along the opposite side of the same galaxy is also deflected and reach the same observer from a slightly different direction. As a result, that particular observer sees an astronomical object in two different locations in the night sky. This type of focusing is known for optical lenses, and therefore the corresponding gravitational effect is called gravitational lenses.

Observational astronomy uses lens effects as an important tool to infer properties of the lens object. Even in cases in which this object is not directly visible, the shape of a lens image provides information about the mass distribution that is responsible for the deflection of light. In particular, the gravitational lens offers a way of measuring the distribution of dark matter that does not emit light and can only be observed through its gravitational effects. A particularly interesting application is large-scale observations, in which the lens masses are distributed over a significant part of the observable universe and can be used to obtain information about the large-scale properties and the evolution of our cosmos.

### Gravitational waves

Gravitational waves, a direct consequence of Einstein's theory, are distortions of geometry that propagate at the speed of light and can be viewed as waves in spacetime. They should not be confused with the gravitational waves of fluid dynamics, which are a different concept.

In February 2016, the Advanced LIGO team announced that it had directly observed gravitational waves from a fusion with black holes.

The effect of gravitational waves was indirectly determined when observing specific binary stars. Such pairs of stars orbit each other and gradually lose energy by emitting gravitational waves. For ordinary stars like the Sun, this energy loss would be too small to be detectable, but this energy loss was observed in 1974 in a binary pulsar called PSR1913 + 16. In such a system, one of the orbiting stars is a pulsar. This has two consequences: A pulsar is an extremely dense object known as a neutron star, where the gravitational wave emission is much stronger than that of ordinary stars. A pulsar also emits a narrow beam of electromagnetic radiation from its magnetic poles. As the pulsar rotates, its beam sweeps across the earth, where it is seen as a regular series of radio pulses, just as a ship at sea observes regular flashes of rotating light in a lighthouse. This regular pattern of radio impulses acts as a highly precise "clock". It can be used to measure the binary star's orbital time, and it is sensitive to space-time distortions in its immediate vicinity.

The discoverers of PSR1913 + 16, Russell Hulse and Joseph Taylor, were awarded the 1993 Nobel Prize in Physics. Several other binary pulsars have since been found. Most useful are those where both stars are pulsars as they provide accurate tests of general relativity.

A number of land-based gravitational wave detectors are currently in operation, and a mission to launch a space-based detector, LISA, with a precursor mission (LISA Pathfinder) launched in 2015 is currently under development. Gravitational wave observations can be used to get information about compact objects like neutron stars and black holes, and to study the state of the early universe fractions one second after the Big Bang.

### Black holes

When mass is concentrated in a sufficiently compact area of space, general relativity predicts the formation of a black hole - an area of space with a gravitational effect so strong that even light cannot escape. It is believed that certain types of black holes are the final state in the evolution of massive stars. On the other hand, supermassive black holes with the mass of millions or billions of suns will reside in the cores of most supposed galaxies, and they play key roles in current models of how galaxies have formed over the past billion years.

Matter falling on a compact object is one of the most efficient mechanisms for releasing energy in the form of radiation, and matter falling on black holes is blamed for some of the brightest astronomical phenomena imaginable. Notable examples of great interest to astronomers are quasars and other types of active galactic nuclei

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