General Relativity is Einstein's theory of gravitation that describes gravity as a result of the curvature of spacetime caused by the uneven distribution of mass/energy. It has been extensively tested and confirmed through observations of orbital precession, gravitational lensing, and gravitational redshift/time dilation. Black holes are a extreme prediction of GR where spacetime is so strongly curved that nothing, not even light, can escape once within the event horizon.
Digital Library of GLT Saraswati Bal Mandir. Gravitation is a natural phenomenon by which all physical bodies attract each other. It is most commonly experienced as the agent that gives weight to objects with mass and causes them to fall to the ground when dropped.
Digital Library of GLT Saraswati Bal Mandir. Gravitation is a natural phenomenon by which all physical bodies attract each other. It is most commonly experienced as the agent that gives weight to objects with mass and causes them to fall to the ground when dropped.
It is always amazing to see the interaction of planets, Sun, Stars, and other celestial objects in space which leads to astronomical events. In this chapter we will learn certain laws of physics which explains gravitation between celestial objects, free fall of body, mass and weight of the objects.
SUMMARY OF CHAPTER:-
Definition of Gravitation
Acceleration Due to Gravity
Variation Of “G” With Respect to Height And Depth
Escape Velocity
Orbital Velocity
Gravitational Potential
Time period of a Satellite
Height of Satellite
Binding Energy
Various Types of Satellite
Kepler’s Law of Planetary motion
In physics, gravity (from Latin gravitas 'weight'[1]) is a fundamental interaction which causes mutual attraction between all things that have mass. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the strong interaction, 1036 times weaker than the electromagnetic force and 1029 times weaker than the weak interaction. As a result, it has no significant influence at the level of subatomic particles.[2] However, gravity is the most significant interaction between objects at the macroscopic scale, and it determines the motion of planets, stars, galaxies, and even light.
On Earth, gravity gives weight to physical objects, and the Moon's gravity is responsible for sublunar tides in the oceans (the corresponding antipodal tide is caused by the inertia of the Earth and Moon orbiting one another). Gravity also has many important biological functions, helping to guide the growth of plants through the process of gravitropism and influencing the circulation of fluids in multicellular organisms.
The gravitational attraction between the original gaseous matter in the universe caused it to coalesce and form stars which eventually condensed into galaxies, so gravity is responsible for many of the large-scale structures in the universe. Gravity has an infinite range, although its effects become weaker as objects get farther away.
Gravity is most accurately described by the general theory of relativity (proposed by Albert Einstein in 1915), which describes gravity not as a force, but as the curvature of spacetime, caused by the uneven distribution of mass, and causing masses to move along geodesic lines. The most extreme example of this curvature of spacetime is a black hole, from which nothing—not even light—can escape once past the black hole's event horizon.[3] However, for most applications, gravity is well approximated by Newton's law of universal gravitation, which describes gravity as a force causing any two bodies to be attracted toward each other, with magnitude proportional to the product of their masses and inversely proportional to the square of the distance between them.
Current models of particle physics imply that the earliest instance of gravity in the universe, possibly in the form of quantum gravity, supergravity or a gravitational singularity, along with ordinary space and time, developed during the Planck epoch (up to 10−43 seconds after the birth of the universe), possibly from a primeval state, such as a false vacuum, quantum vacuum or virtual particle, in a currently unknown manner.[4] Scientists are currently working to develop a theory of gravity consistent with quantum mechanics, a quantum gravity theory,[5] which would allow gravity to be united in a common mathematical framework (a theory of everything) with the other three fundamental interactions of physics.
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
It is always amazing to see the interaction of planets, Sun, Stars, and other celestial objects in space which leads to astronomical events. In this chapter we will learn certain laws of physics which explains gravitation between celestial objects, free fall of body, mass and weight of the objects.
SUMMARY OF CHAPTER:-
Definition of Gravitation
Acceleration Due to Gravity
Variation Of “G” With Respect to Height And Depth
Escape Velocity
Orbital Velocity
Gravitational Potential
Time period of a Satellite
Height of Satellite
Binding Energy
Various Types of Satellite
Kepler’s Law of Planetary motion
In physics, gravity (from Latin gravitas 'weight'[1]) is a fundamental interaction which causes mutual attraction between all things that have mass. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the strong interaction, 1036 times weaker than the electromagnetic force and 1029 times weaker than the weak interaction. As a result, it has no significant influence at the level of subatomic particles.[2] However, gravity is the most significant interaction between objects at the macroscopic scale, and it determines the motion of planets, stars, galaxies, and even light.
On Earth, gravity gives weight to physical objects, and the Moon's gravity is responsible for sublunar tides in the oceans (the corresponding antipodal tide is caused by the inertia of the Earth and Moon orbiting one another). Gravity also has many important biological functions, helping to guide the growth of plants through the process of gravitropism and influencing the circulation of fluids in multicellular organisms.
The gravitational attraction between the original gaseous matter in the universe caused it to coalesce and form stars which eventually condensed into galaxies, so gravity is responsible for many of the large-scale structures in the universe. Gravity has an infinite range, although its effects become weaker as objects get farther away.
Gravity is most accurately described by the general theory of relativity (proposed by Albert Einstein in 1915), which describes gravity not as a force, but as the curvature of spacetime, caused by the uneven distribution of mass, and causing masses to move along geodesic lines. The most extreme example of this curvature of spacetime is a black hole, from which nothing—not even light—can escape once past the black hole's event horizon.[3] However, for most applications, gravity is well approximated by Newton's law of universal gravitation, which describes gravity as a force causing any two bodies to be attracted toward each other, with magnitude proportional to the product of their masses and inversely proportional to the square of the distance between them.
Current models of particle physics imply that the earliest instance of gravity in the universe, possibly in the form of quantum gravity, supergravity or a gravitational singularity, along with ordinary space and time, developed during the Planck epoch (up to 10−43 seconds after the birth of the universe), possibly from a primeval state, such as a false vacuum, quantum vacuum or virtual particle, in a currently unknown manner.[4] Scientists are currently working to develop a theory of gravity consistent with quantum mechanics, a quantum gravity theory,[5] which would allow gravity to be united in a common mathematical framework (a theory of everything) with the other three fundamental interactions of physics.
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
The Indian economy is classified into different sectors to simplify the analysis and understanding of economic activities. For Class 10, it's essential to grasp the sectors of the Indian economy, understand their characteristics, and recognize their importance. This guide will provide detailed notes on the Sectors of the Indian Economy Class 10, using specific long-tail keywords to enhance comprehension.
For more information, visit-www.vavaclasses.com
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
For more information, visit-www.vavaclasses.com
Model Attribute Check Company Auto PropertyCeline George
In Odoo, the multi-company feature allows you to manage multiple companies within a single Odoo database instance. Each company can have its own configurations while still sharing common resources such as products, customers, and suppliers.
Instructions for Submissions thorugh G- Classroom.pptxJheel Barad
This presentation provides a briefing on how to upload submissions and documents in Google Classroom. It was prepared as part of an orientation for new Sainik School in-service teacher trainees. As a training officer, my goal is to ensure that you are comfortable and proficient with this essential tool for managing assignments and fostering student engagement.
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
How to Split Bills in the Odoo 17 POS ModuleCeline George
Bills have a main role in point of sale procedure. It will help to track sales, handling payments and giving receipts to customers. Bill splitting also has an important role in POS. For example, If some friends come together for dinner and if they want to divide the bill then it is possible by POS bill splitting. This slide will show how to split bills in odoo 17 POS.
Students, digital devices and success - Andreas Schleicher - 27 May 2024..pptxEduSkills OECD
Andreas Schleicher presents at the OECD webinar ‘Digital devices in schools: detrimental distraction or secret to success?’ on 27 May 2024. The presentation was based on findings from PISA 2022 results and the webinar helped launch the PISA in Focus ‘Managing screen time: How to protect and equip students against distraction’ https://www.oecd-ilibrary.org/education/managing-screen-time_7c225af4-en and the OECD Education Policy Perspective ‘Students, digital devices and success’ can be found here - https://oe.cd/il/5yV
Ethnobotany and Ethnopharmacology:
Ethnobotany in herbal drug evaluation,
Impact of Ethnobotany in traditional medicine,
New development in herbals,
Bio-prospecting tools for drug discovery,
Role of Ethnopharmacology in drug evaluation,
Reverse Pharmacology.
2. Introduction
GR is Einstein’s theory of gravitation that
builds on the geometric concept of space-
time introduced in SR.
Is there a more fundamental explanation of
gravity than Newton’s law?
GR makes specific predictions of deviations
from Newtonian gravity.
3. Curved space-time
Gravitational fields alter the rules of
geometry in space-time producing “curved”
space
For example the geometry of a simple
triangle on the surface of sphere is different
than on a flat plane (Euclidean)
On small regions of a sphere, the geometry is
close to Euclidean
4. How does gravity curve space-time?
•With no gravity, a ball thrown upward continues upward
and the worldline is a straight line.
•With gravity, the ball’s worldline is curved.
•It follows this path because the spacetime surface on
which it must stay is curved.
•To fully represent the trajectory, need all 4 space-time
dimensions curving into a 5th dimension(!)
•Hard to visualize, but still possible to measure
t t
x x
No gravity gravity
5. Principle of Equivalence
A uniform gravitational field in some
direction is indistinguishable from a uniform
acceleration in the opposite direction
Keep in mind that an accelerating frame
introduces pseudo-forces in the direction
opposite to the true acceleration of the
frame (e.g. inside a car when brakes are
applied)
6. Elevator experiment
•First: elevator is supported and not
moving, but gravity is present. Equate
forces on the person to ma (=0 since a=0)
•Fs - mg = 0 so Fs = mg
•Fs gives the weight of the person.
Let upward
forces be
positive,
thus gravity
is -g
See also http://www.pbs.org/wgbh/nova/einstein/relativity/
•Second: no gravity, but an upward
acceleration a. The only force on
the person is Fs and so
•Fs = ma or Fs = mg if value of a
is the same as g
•Person in elevator cannot tell the
difference between gravitational
field and accelerating frame
•Third: there is gravity and the elevator
is also in free-fall
•Fs - mg = -mg or Fs = 0
•“Weightless”
7. Dichotomy in the concept of "mass"
“mass” a measure of an object’s resistance to changes in
movement (F=ma) inertial mass
“mass” a measure of an objects response to gravitational
attraction (F=GMm/r2) gravitational mass.
Dichotomy resolved by putting gravity and acceleration on an
equal footing.
The principle of equivalence is really
a statement that inertial and
gravitational masses are the same
for any object.
This equivalence means that all objects have the
same acceleration in a gravitational field (e.g. a
feather and bowling ball fall with the same
acceleration in the absence of air friction).
8. Where and vary from 0 to
3, thus this equation really
represents 16 equations
Ricci curvature tensor - R
Metric coefficients - g - relates
length interval to coordinate system (matrix)
Christoffel symbols – cross terms
The GR equations relate the curvature of spacetime with the
energy and momentum within the spacetime (Matter tells
spacetime how to curve, and curved space tells matter how to move).
Gμν = 8πTμν = Rμν – 1/2gμνR
how space is curved location and motion of matter
(energy-momentum tensor)
9. Tests of General Relativity
Orbiting bodies - GR predicts slightly
different paths than Newtonian gravitation
Most obvious in elliptical orbits where
distance to central body is changing and
orbiting object is passing through regions of
different space-time curvature
The effect - orbit does not close and each
perihelion has moved slightly from the
previous position
10. In our Solar System, the effect
is greatest for Mercury - closest
to Sun and high eccentricity
•Mercury’s perihelion position
advances by 5600 arc seconds
per century.
•All but 43 arc seconds can be
accounted for by Newtonian
effects and the perturbations of
other planets.
•Einstein was able to explain
those 43 arc seconds via GR.
a) Curved space-time for Mercury’s
orbit around the Sun. Since
Mercury’s orbit is elliptical, its
distance from the Sun changes. It
therefore passes through regions of
different curvature. b) This causes
the orbit to precess (amount of shift
exaggerated in this figure!)
11. Bending of Light
Einstein said that the warping of space-
time alters the path of light as it passes
near the source of a strong gravitational
field (i.e. photons follow geodesics).
When viewing light from a star, the
position of the star will appear different if
passing near a massive object (like the
Sun).
= 4GM/bc2
Where is the angle in radians and b is
the distance from light beam to object of
mass M
If b is radius of Sun (7x1010cm), is 8.5x10-6 rad or 1.74 arcseconds
12. Bent light path also causes a delay in the time for a signal to pass the
Sun. This effect has been measured by bouncing radio waves off
Mercury and Venus as they pass behind the Sun, and observing signals
from solar system space craft. GR effects have been confirmed to an
accuracy of 0.1% using these measurements.
Measurements must be made
during a solar eclipse, when light
from Sun is blocked and stars
near the Sun’s edge can be
seen.
Sir Arthur Eddington headed the
attempt to verify Einstein’s
prediction during an eclipse in
1919 as the Sun would move in
front of a cluster of distant stars.
13. Gravitational Lensing
A large galaxy or cluster can act as
a gravitational lens
light emitted from objects behind
the lens display distortion and
spherical aberration.
Measuring the degree of lensing
can be used to calculate the mass
of the intervening body.
One of the techniques to detect
the presence of dark matter.
Abell 2218
Light waves passing through areas of
different mass density in the
gravitational lens are refracted to
different degrees. Produces double
galaxy images and Einstein Rings (if
observer, lens, and source are aligned
in a specific way).
14. Gravitational Redshift
A photon’s wavelength is effected by a
gravitational field
Gravitational potential energy -GMm/r
To determine PE for a photon we assign an
effective mass based on E=mc2
m=E/c2 and since E=hc/ (energy of a photon)
m=h/(c)
Conservation of energy for a photon moving from r1 to r2
hc/1 - GMh/(r1c1) = hc/2 - GMh/(r2c2)
This gives
2/1 = [1-GM/(r2c2)]/[1-GM/(r1c2)]
Not a rigorous treatment, but a dimensional analysis approximation which
agrees with full GR calculation
15. 2/1 = ([1-2GM/(r2c2)]/[1-2GM/(r1c2)])1/2
Full GR calculation agrees with approximation in the limit 2GM/(rc2)<<1
If we let r2 go to infinity and use an approximation for small shifts
2/1 = 1 + GM/r1c2
The wavelength shift due to gravitational redshifting is then
/ = GM/rc2
How about a 1 solar mass compact stellar remnant (white dwarf)
with r = 7x108 cm?
Best cases of measured line shifts due to GR are the white dwarfs
Sirius B (3x10-4) and 40 Eridani (6x10-5)
What gravitational redshift would be measured for spectral lines
originating in the atmosphere of the Sun (in terms of /)?
M = 2 x 1033 g, r = 7 x 1010 cm and G = 6.67 x 10-8 dyn cm2/g2
16. Gravitational Time Dilation
t2/t1 = ([1-2GM/(r2c2)]/[1-2GM/(r1c2)])1/2
All clocks run slower in a strong gravitational field than they
do in a weaker field. The clock at r1 will run slower than that
at r2 (r2 is the position further from the source of gravity and
thus experiencing a weaker gravitational effect).
Gravitational time dilation has been measured using clocks
on airplanes, rockets. When the clocks return, they ran
slightly faster (ahead) compared to those on the ground.
Let r2 go to infinity to get T = To/(1-2GM/rc2)1/2
where T is time interval far from mass source
On Earth’s surface T = To/(1-2gR/c2)1/2
Time dilation is about 1 part in 109
18. Gravitational Radiation
Just as accelerated charged
particles give off EM radiation, GR
predicts that certain systems
should emit gravitational radiation.
LIGO – to detect the ripples in space-time
using laser interferometry to measure the
time it takes light to travel between
suspended mirrors. The space-time ripples
cause the distance measured by a light
beam to change as the gravitational wave
passes by.
LISA – NASA’s version in space!
Massive objects distort spacetime and a moving mass will produce
“ripples” in spacetime which should be observable (e.g. two orbiting or
colliding stellar remnants (e.g. neutron stars).
19. Black Holes
Stellar remnants of the highest mass
stars (see Chapter 18)
The most compact objects in the
Universe and therefore represent the
most extreme gravitational fields
Perfect place to investigate the effects
of GR
20. The escape speed for an
object with mass M and
size R is
2GM
Vesc =
For the Sun,
Radius = 700,000 km
Vesc = 620 km/s
What if we squeezed the Sun into 1/4 its current radius?
Vesc = 620 x 2 = 1240 km/s
What if we squeezed the Sun to ~10 km radius (Neutron star
size)?
Vesc = 163,000 km/s ( ~half the speed of light!)
R
21. Compressing the Sun further, we would eventually have the
escape speed equal to the speed of light.
No objects could then escape, including photons
Black Hole
The critical radius at which the escape speed equals the speed
of light is called the Schwarzschild Radius.
The sphere around a Black Hole at the Schwarzschild Radius is
called the “event horizon,” because no event inside that sphere
can ever be known outside of it.
22. Schwarzschild radii for objects with different masses:
1 earth mass: 1 cm
1 solar mass: 3 km Rs = 3km (M/Msun)
106
solar masses: 3 x 106
km – supermassive BH
109
solar masses: 3 x 109
km – supermassive BH
Schwarzschild worked out the curvature of space-time around a
point mass to arrive at the radius where a singularity occurs (some
quantity becomes infinite)
Rs = 2GM/c2
If an object is completely contained within its Rs, a singularity occurs!
Recall 2/1 = ([1-2GM/(r2c2)]/[1-2GM/(r1c2)])1/2
If we set r1 to the Schwarzschild radius, 2 becomes infinite for any
r2. No light can escape from within Rs.
23. The average density inside a 1 M blackhole is 1017 g/cm3
Greater than the density of an atomic nucleus!
But, density decreases for more massive BHs
= (1 x 1017 g/cm3)(M/M)-2
Density for 108 M is ~few g/cm3, not much denser than water.
Tidal effects are significant near the Rs gravitational force
falls off very quickly with small changes in distance.
Since g(r) = GM/r2
Differentiation yields dg(r)/dr = -2GM/r3
….so tidal forces are most significant at small r
What is the difference between the acceleration of gravity at the
feet and head of an astronaut just outside a 1 solar mass
blackhole?
24. Strange goings on near a Black Hole.
As you get close to a Black
Hole, the previous exercise
shows that you would get
stretched, then torn apart…
…because the gravitational
pull at your feet is 2x1012 cm/s2
greater than at your head
(about 2 billion times gravity on
Earth!)
Let’s imagine an indestructible
astronaut, and give her a clock
and a flashlight for her journey
to the Black Hole…
(We’ll remain behind at a safe
distance.)
25. As our astronaut friend approaches the Black Hole, we notice that her
flashlight appears redder and redder (to us).
When she hovers at a distance very close to the event horizon, the
radiation from her flashlight gets gravitationally redshifted even more….
to the infrared and finally radio….
Strange goings on near a Black Hole.
/ = GM/(rc2)
26. Another effect is seen in the
paths of the photons – photons
only follow “straight” paths when
directed straight up (away) from
the blackhole. All other light
beams will bend. Only light aimed
into the exit cone will escape.
At r = 1.5Rs, photons aimed
horizontally will orbit the
blackhole - photon sphere
For animations and descriptions of the event horizon and photon sphere see
http://apod.nasa.gov/htmltest/rjn_bht.html
27. Now note that light is like a clock…
…electromagnetic oscillations at a
given frequency.
We see our friend’s oscillations slowing down (due to
gravitational redshift).
Thus her clock slows down due to gravitational time dilation.
At the event horizon, her clock would appear (to us) to stop.
We would never see her cross the event horizon….!
Strange goings on near a Black Hole.
28. What does our astronaut friend see?
Her flashlight looks the same to her.
Her clock seems to run at the same speed.
Looking back at us, she sees…
Our flashlight gets bluer.
Our clock seems to speed up!
Strange goings on near a Black Hole.
If the astronaut was your twin sister, after her trip to the
Black Hole
…you would be older than her!
(Your clock really would be running faster than hers)
T = To/(1-2GM/Rc2)1/2
29. Strange goings on near a Black Hole.
What would our friend find inside the event horizon?
The astronaut would be pulled to the center and crushed down to a
point - the singularity
What actually happens is not known, because:
1) Current theories are not up to the task.
2) We can never do the experiment!
What if our friend continued on through the Event Horizon?
She would pass through and not perceive the event horizon in any way.
With a supermassive blackhole, even the tidal forces might be survived.
There is no physical boundary there but … she could never come back!
30. The observer outside the blackhole can
not tell anything about what is going on
inside the blackhole.
The only properties that can be deduced
are its mass, electric charge, and angular
momentum
“blackholes have no hair”
In a rotating blackhole, ang mtm is non-zero. The structure differs from
non-rotating BH (Kerr found the solutions to Einsteins equations for a rotating BH in 1963).
Non-rotating BH
Rotating BH
Stationary limit – objects within this limit
will be dragged around BH due to
rotation. Objects moving at light speed
here would appear “stationary” from
outside the limit since the reference
frame is moving at light speed. Touches
EH at poles and stretches to non-rotating
EH value.
Ergosphere - Energy can be extracted
from BH via particles in this region
moving on specific trajectories – Penrose
process (1969)
