A star more massive than about 20 solar masses is highly likely to leave a remnant core with a mass that exceeds 3 solar masses. In this case, theoretically, gravity would achieve its final victory as neutron degeneracy would fail and nothing would oppose gravitational collapse. The core would therefore collapse into an object known as a singularity . A singularity is an object with a radius of zero and therefore, since it has a finite mass, its density is infinite. Well, that’s just not right, is it?
First, let’s consider the hypothetical case were the sun suddenly turned into a
Black Hole (like in the bad Walt Disney Movie). At out position on the
Earth, well yeah, we would be exterminated because of the lack of sunlight, but the Earth itself would still be orbiting and object that has a mass of 1 solar mass. This is an important point – to an external observer a black hole is merely a point with mass. As long as you are a long way from that point, you will not notice anything strange – it’s only when you get near the black hole, that strange things start to happen – some of which are detailed below.
The concept of the black hole was first espoused in 1798 by the French mathematician Laplace, who coined the term corps obscures
Laplace reasoned that if light is made up of particles (as Newton thought) then if a star was sufficiently massive the escape velocity of particles from that star might be larger than the speed of light. In this case, no light emitted by the object could ever escape the object and therefore it would be black. As we will see, this is a relatively naïve characterization of a black hole. The escape velocity from any object can be expressed as a function of its density and therefore Laplace, knowing the speed of light at that time, was able to calculate the mass and radius a star must have in order for it to be black.
The resulting calculations were so absurd that Laplace thought that no such configuration of matter could exist in the Universe.
Curved Space-time :
The early 20th century brought many new and profound developments to our cosmology and for the first time showed that Newtonian theory was not a complete specification of gravity. In the late 19th century, precision observations of the position of Mercury showed that it did not agree with the predictions from Newtonian theory. This is similar to the case of Mars, where Kepler used positional discrepancies to show that planetary orbits had to be elliptical in shape. The resolution for Mercury isn't quite so simple. It turns out that Newton never explicitly considered the "shape" of spacetime but implicitly

assumed that space is completely flat. The resolution of the positional discrepancy of
Mercury requires that space be "curved" in the vicinity of Mercury so that Mercury orbits inside this curvature. Such an orbit will differ slightly from an orbit in purely flat space.
This is Shown in Figure 2.1.
Visualization of the orbital precession of Mercury as it is orbiting in curved space near the Sun. The curved space causes the orbit to precess over time thus tracing out a different orbital path with each new orbit
But, why would space be curved in the vicinity of Mercury? The answer lies in Mercury's proximity to the Sun. Einstein postulated that gravity is really the manifestation of curved space and that very massive objects cause a greater degree of curvature and hence have a greater gravitational influence. Mercury is sufficiently close to the Sun that it orbits in curved space. The rest of the planets are far enough away from the Sun that the degree of curvature caused by the mass of the Sun is negligible. While a full description of the

General Theory of Relativity is well beyond our scope, we can summarize it qualitatively as follows:
Space communicates with matter and instructs it how to move and, in turn, matter communicates with space and instructs it how to curve .
In this way, the distribution of mass determines the overall curvature of the Universe as well as the particular pathways that objects, including light, must follow. We can then use General relatively and the curvature of space time to better characterize a black hole.
Shown below in some relative scale are the local curvatures of space time that exist near certain kinds of objects. The most severe curvature is clearly for the case of the black hole.
In terms of space-time curvature, a black hole can be though of as a region of space time which has locally infinite curvature . Thus once an object enters into a black hole (i.e. crosses the event horizon – see below) – that object effectively disappears from the Universe because now it is disconnected from space-time and in a very real sense is stranded inside its own, little, mini-Universe. Of course, the accretion of this object by the black hole has allowed its mass to grow and so now the external universe interacts with a larger mass black hole.
The Event Horizon :

Black holes can be described as objects with a mass and a “radius” as long as we use a physically sensible mechanism for defining a radius. Such a definition was first provided by Karl Schwarzschild in 1916 who simple asked the question – at what radius in an object of mass M does the escape velocity equal the speed of light. The answer to that is the Schwarzschild radius:
is the universal gravitational constant of Newton. The meaning of R s
is that light can not escape if it is emitted from a region with R < R s
. For an object of 1 solar mass, R s
is 3 km. Compare this with a typical 0.6 M sun
White Dwarf, which would have a radius of about 1 R earth
(6370km), and a
1.4 M sun
neutron star, which would have a radius of about 10km.
Events which occur in the Universe are transmitted via photons at the speed of light. Therefore, if say an event occurs at a distance of 1 km inside a 1 solar mass black hole, that event can never be transmitted to the rest of the
Universe since there is no way the information (e.g. the photons) can escape from that region of the black hole.
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Journey to a Black Hole :
So what do we know so far about black holes? a) they are totally collapsed objects b) gravity is so strong that not even light can escape within some distance from the point of total collapse (e.g. the singularity) c) they represent local regions of the Universe where the curvature is infinite d) from a large distance away they act merely as point masses
Now let’s imagine what might happen if we have a cloud of gas falling towards a black hole. When the gas cloud is far from the black hole it feels a uniform gravitational acceleration. However, when the gas cloud gets within a few Schwarzschild radii (3-5 R s) it stars to experience differential gravitational forces. The part of the cloud that is closest to the event horizon is accelerated more rapidly than the part farther away. This differential gravitational force is known as a tidal force and it’s the same as the earthmoon system. The side of the earth that is closest to the moon feels a slightly stronger force than the side opposite the moon and this causes a small deformation in the shape of the Earth. That deformation manifests itself via rising and falling ocean levels (e.g. the tides).
But the tidal forces near the event horizon are enormous and they have the effect of tidally compressing and heating the gas. In fact the gas becomes so hot that it starts to emit X-rays and this is the way in which black holes have been discovered. The image below shows an artists conception of this process. Far from the black hole, the gas is cold but as it nears the event horizon an accretion disk develops (blue disk in the image below). That accretion disk becomes rather dense and it blocks the flow of radiation through it, so the radiation can more readily escape at perpendicular to the disk and so jets of X-ray emission occur. The inner radius of the accretion disk is the event horizon (R s
) and the outer radius is 3—5 R s
. So black holes in our galaxy have been discovered by closely observing binary

systems that emit X-ray. The fact that the system is a binary star also allows for masses to be measured. The first such system discovered is called
Cygnus X-1 where x-ray emission is emanating from an unseen companion star to a much bigger star yet the mass of that unseen companion is about 6--
9 solar masses. It therefore has to be a black hole, with X-ray emission coming from his accretion disk. Hence, black holes really can not escape detection. When matter falls into them, it heats up and emits X-rays. https://publicaffairs.llnl.gov/news/news_releases/2005/images/NASA_bla ck_hole.jpg
A concept that we have not yet introduced in this course but what that is now needed is the gravitational redshift . This effect theoretically existed and has been observed for some white dwarfs. As we have seen, there is equivalence between energy and mass and this is the physical basis for thermonuclear fusion and energy generation in stars. This means that photons have an energy related mass and therefore are affected by gravity
(this is another prediction of Einstein’s theory of General Theory of
Relativity). Hence, photons that are emitted from an object with a very strong surface gravity (like a white dwarf) lose part of their energy in

escaping from the surface. That energy loss means that the wavelength of the photon increases (towards the red – hence the term redshift) to longer wavelengths. Remember, the energy of a photon is inversely proportional to its wavelength; long wavelength photons have less energy than short wavelength photons. For white dwarfs stars, the gravitational redshift is equivalent in velocity to about 100 km/sec. In term of wavelength this represents approximately a 3 parts in 10,000 shift in wavelength – very small but still measurable. Hence, if a 10,000 angstrom photon were emitted by some process from the surface of a white dwarf, that photon would arrive to an external observer at a wavelength of 10,003 angstroms because a small amount of energy was lost in escaping the surface gravity of the white dwarf. We will see below that another way to understand the event horizon is that it represents the surface of infinite gravitational redshift .
Imagine two friends, Batman and Robin, whom decide to take a journey to a black hole. Batman, being the macho hero, decides that he will travel towards the event horizon and signal Robin with information about his condition as he approaches the event horizon. Robin will stay at a safe distance to monitor the progress of Batman. Batman has developed a special bat-laser beacon that emits a blue laser pulse once a second. Robin is monitoring this signal and they have agreed in advance, that if Batman is in trouble, he will send two pulses a second and Robin will use the BatShip to come and rescue him. Unfortunately, this isn’t going to work, as we will see below. Here is the sequence of events that will occur.
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Batman initially is gravitationally pulled towards the Black hole but still is relatively far away from the event horizon
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Robin is orbiting the black hole in a stationary circular orbit, in the
BatShip, at a safe distance and is recording Batman’s laser pulses and receiving one every second.
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Batman observes the BatShip getting increasing far away but there is no cause for concern.
Sometime later the situation changes:
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Batman is still sending laser pulses, according to this Bat watch, at one per second.
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Robin, however, notices that the laser flashes are taking longer to arrive than they did before and that furthermore, the laser pulses were

transitioning from blue to green. Robin dismissed this as yet another one of Batman’s practical jokes.
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A few more minutes has passed and Robin now beings to concern.
Laser pulses are now coming once every 3 seconds and they are deep red in color. Robin knows that Batman doesn’t have a red laser device (because those are no longer cool) and suddenly becomes very confused as to what is going on.
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In the meantime, Batman is approaching the event horizon and accelerating. He has trouble seeing the BatShip and the outside world is beginning to look wildly distorted as the positions of the stars appear to have changed from when he first started. He is also beginning to feel a slight tidal tug on his Bat Cape, but his Bat Suit was built to withstand severe tidal forces.
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By now Robin is getting a laser flash once very hour and those are arriving at radio wavelengths (fortunately, Robin brought the Bat
Radio). Robin is wondering what the Batman is doing? Why is he no longer sending pulses at the rate of one per second – why did he rather suddenly switch to radio pulses every hour?
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Another hour passes and no pulse is observed. And then another hour pasts and then another hour pasts and then a few months past and finally an extremely long wavelength pulse is observed.
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Meanwhile Batman has finally arrived at the Event Horizon and realizes that he is in a lot of trouble. He starts to frantically signal
Robin, at the rate of 10 pulses per second, but alas, all of those photons had to expend all of their energy just to leave from the event horizon and therefore Robin received no message.
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Sadly, Batman slips across the event horizon to be heard from no more while Robin is just left waiting for another pulse to signify that the Batman is still alive. Alas, Robin now waits forever.
In summary, the powerful gravity of a black hole warps space and time around it:
 Time appears to stand still at the event horizon as seen by a distant observer. This is the meaning of infinite gravitational redshift.
 Time flows as it always does as seen by an in falling astronaut.
 Light emerging from near the black hole is Gravitationally Redshifted to longer (red) wavelengths