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's theory of gravity revolutionized our understanding of the universe. It describes gravity not as a force, but as a consequence of curvature caused by massive objects. This groundbreaking concept explains phenomena like planetary orbits and light bending near massive bodies.

The theory introduces the , which states that gravity's effects are indistinguishable from acceleration. This idea leads to fascinating implications, such as the prediction of black holes and , which have been confirmed through observations and experiments.

Einstein's Theory of Gravity

Einstein's general theory of relativity

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Top images from around the web for Einstein's general theory of relativity

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  • Geometric theory of gravity describes gravity as consequence of spacetime curvature not a force
  • Massive objects curve spacetime and this curvature influences motion of other objects (planets orbiting the Sun)
  • Spacetime is four-dimensional continuum with three spatial dimensions and one time dimension
  • Presence of mass or energy curves spacetime
    • More massive objects induce greater
  • Objects in free fall follow (straight paths) in curved spacetime
    • Paths appear curved from outside perspective due to spacetime curvature (light bending near the Sun)

Principle of equivalence in gravity

  • Effects of gravity indistinguishable from effects of acceleration
    • Observer in closed elevator cannot distinguish between being stationary in gravitational field and being accelerated in absence of gravity (rocket accelerating in space)
  • and are equivalent
    • Inertial mass measures object's resistance to acceleration
    • Gravitational mass determines strength of object's gravitational field and response to external gravitational fields
  • All objects fall at the same rate in a gravitational field regardless of mass or composition
    • Confirmed experimentally to high degree of accuracy (feather and hammer drop on the Moon)

Calculation of Schwarzschild radius

  • Radius of for non-rotating
    • Boundary beyond which nothing including light can escape 's gravitational pull (point of no return)
  • (rsr_s) given by formula rs=2GMc2r_s = \frac{2GM}{c^2}
    • GG gravitational constant 6.67×10−11 m3 kg−1 s−26.67 \times 10^{-11} \text{ m}^3 \text{ kg}^{-1} \text{ s}^{-2}
    • MM mass of object
    • cc speed of light 3.00×108 m/s3.00 \times 10^8 \text{ m/s}
  • Sun (mass ≈1.99×1030 kg\approx 1.99 \times 10^{30} \text{ kg}) has radius about 2.95 km
  • Schwarzschild radius proportional to object's mass
    • More massive objects have larger Schwarzschild radii ( at Milky Way center)

Observational evidence for black holes

  • Black holes emit no light so cannot be directly observed
    • Existence inferred from gravitational effects on nearby matter and light (stars orbiting galactic centers)
  • Accretion disks around black holes
    • Matter falling into black hole forms hot bright accretion disk
    • X-ray emission from accretion disks indicates presence of compact massive objects ()
    • Black holes bend light due to strong gravitational fields causing distortions in images of background objects
    • Observations of gravitational lensing provide evidence for black holes (quasar lensing)
  • Gravitational waves
    • Merger of two black holes produces gravitational waves (ripples in spacetime) predicted by general relativity
    • Detection of gravitational waves from binary black hole mergers by and confirms existence of black holes
  • Supermassive black holes at galaxy centers
    • Observations of high-velocity stars orbiting Milky Way center suggest presence of supermassive black hole ()
    • Similar evidence found in other galaxies indicates supermassive black holes are common at galactic centers ()

Mathematical foundations of general relativity

  • forms the basis for general relativity, extending its principles to non-inertial reference frames
  • provides the mathematical framework for describing curved spacetime
  • is used to describe the curvature of spacetime in general relativity
  • The represents the distribution of mass and energy in spacetime, determining its curvature

Key Terms to Review (45)

Albert Einstein: Albert Einstein was a renowned German-born theoretical physicist who developed the theory of relativity, one of the two pillars of modern physics. His groundbreaking work, particularly in the field of gravity, has had a profound impact on our understanding of the universe.
Black hole: A black hole is a region in space where the gravitational pull is so strong that nothing, not even light, can escape from it. These objects are formed when massive stars collapse under their own gravity.
Black Hole: A black hole is an extremely dense and massive object in space from which nothing, not even light, can escape due to its immense gravitational pull. Black holes are formed when a massive star collapses in on itself at the end of its life cycle.
Curvature of Spacetime: The curvature of spacetime is a fundamental concept in Einstein's Theory of Gravity, also known as General Relativity. It describes how the presence of mass and energy distorts the fabric of the universe, creating a curvature in the four-dimensional spacetime continuum.
Cygnus X-1: Cygnus X-1 is a well-known binary star system located in the constellation Cygnus, consisting of a blue supergiant star and a black hole. This system is one of the strongest X-ray sources in the sky and has provided significant insights into the properties of black holes and the nature of gravity, particularly in the context of Einstein's Theory of Gravity, where it demonstrates how massive objects warp spacetime.
Dark matter: Dark matter is a form of matter that does not emit, absorb, or reflect light, making it invisible to current detection methods. Its presence is inferred from its gravitational effects on visible matter and the structure of the universe.
Einstein: Einstein's Theory of Gravity, also known as General Relativity, describes gravity as the curvature of spacetime caused by mass and energy. This theory revolutionized our understanding of gravitational forces and replaced Newton's law of universal gravitation.
Einstein Field Equations: The Einstein field equations are a set of ten coupled, nonlinear partial differential equations that describe the fundamental relationship between the curvature of spacetime and the distribution of matter and energy within it. They form the foundation of Einstein's theory of general relativity, which revolutionized our understanding of gravity and the universe.
Energy-Momentum Tensor: The energy-momentum tensor is a mathematical object in the theory of general relativity that describes the density and flux of energy and momentum in spacetime. It is a crucial component in Einstein's field equations, which govern the curvature of spacetime and the motion of objects within it.
Event horizon: The event horizon is the boundary surrounding a black hole beyond which nothing, not even light, can escape. It marks the limit where gravitational pull becomes so strong that escape velocity exceeds the speed of light.
Event Horizon: The event horizon is a boundary in spacetime beyond which events cannot affect an outside observer. It is a key concept in the theory of general relativity and is most commonly associated with black holes, where the event horizon marks the point of no return beyond which nothing, not even light, can escape the gravitational pull of the black hole.
Frame-Dragging: Frame-dragging, also known as the Lense-Thirring effect, is a prediction of Einstein's general theory of relativity that describes how the rotation of a massive object, such as a planet or a black hole, can 'drag' the space-time continuum around it. This effect is caused by the curvature of space-time and the conservation of angular momentum.
Friedmann-Lemaître-Robertson-Walker metric: The Friedmann-Lemaître-Robertson-Walker (FLRW) metric is a mathematical model that describes the large-scale structure and evolution of the universe. It is a solution to Einstein's field equations of general relativity, which govern the dynamics of the universe on cosmological scales.
General Covariance: General covariance is a fundamental principle in Einstein's theory of gravity, known as general relativity. It states that the laws of physics must take the same form in all coordinate systems, regardless of their state of motion or orientation. This principle is a cornerstone of general relativity, as it allows for the description of gravity as a consequence of the curvature of spacetime.
Geodesics: Geodesics are the shortest paths between two points on a curved surface or in a curved spacetime. They represent the natural motion of objects in the presence of gravity, as described by Einstein's theory of general relativity.
Gravitational Lensing: Gravitational lensing is a phenomenon predicted by Einstein's theory of general relativity, where the presence of massive objects in the universe can bend and distort the path of light traveling through spacetime. This effect acts as a natural 'lens' that can magnify, split, or even produce multiple images of distant celestial objects.
Gravitational Mass: Gravitational mass is a fundamental property of an object that determines the strength of the gravitational force it exerts on other objects and the gravitational force it experiences from other objects. It is a measure of an object's gravitational attraction and is a key concept in both Newton's Law of Universal Gravitation and Einstein's Theory of Gravity.
Gravitational Time Dilation: Gravitational time dilation is a phenomenon predicted by Einstein's theory of general relativity, where the passage of time is affected by the presence of gravitational fields. This effect occurs because gravity can warp the fabric of spacetime, causing time to slow down in regions with stronger gravitational fields.
Gravitational Waves: Gravitational waves are ripples in the fabric of spacetime caused by the accelerated motion of massive objects, such as colliding black holes or neutron stars. They are a prediction of Einstein's theory of general relativity and were first directly observed in 2015 by the Laser Interferometer Gravitational-Wave Observatory (LIGO).
Gravity Probe B: Gravity Probe B was a satellite-based experiment launched by NASA in 2004 to test two key predictions of Albert Einstein's general theory of relativity - the geodetic effect and frame-dragging. It was designed to measure the tiny changes in the orientation of the satellite's four ultra-precise gyroscopes relative to a distant guide star, in order to detect these relativistic effects.
Inertial Mass: Inertial mass is a fundamental property of an object that quantifies its resistance to changes in its state of motion. It is a measure of an object's inherent tendency to maintain its current state of rest or uniform motion, as described by Newton's first law of motion.
Karl Schwarzschild: Karl Schwarzschild was a German physicist who made important contributions to the understanding of gravity and the theory of general relativity. His work on the solutions to Einstein's field equations led to the discovery of the Schwarzschild solution, which describes the gravitational field of a spherically symmetric, non-rotating, uncharged mass, such as a black hole.
LIGO: LIGO (Laser Interferometer Gravitational-Wave Observatory) is a large-scale physics experiment and observatory designed to detect gravitational waves, the ripples in the fabric of spacetime predicted by Einstein's theory of general relativity. It is a crucial tool for studying the nature of gravity and the most energetic events in the universe.
M87*: M87* is the supermassive black hole at the center of the elliptical galaxy Messier 87 (M87), located about 55 million light-years from Earth. It is one of the most massive known black holes in the local universe and has been a subject of intense study in the context of Einstein's Theory of Gravity.
Neutron star: A neutron star is a highly dense remnant of a massive star that has undergone a supernova explosion and collapsed under gravity. Composed mostly of neutrons, it exhibits incredibly strong gravitational and magnetic fields.
Neutron Star: A neutron star is an extremely dense, collapsed stellar remnant that forms when a massive star runs out of fuel and undergoes gravitational collapse. These objects are characterized by their incredibly dense, neutron-degenerate matter and their strong gravitational and magnetic fields.
Non-Euclidean geometry: Non-Euclidean geometry is a type of geometry that diverges from the parallel postulate of Euclidean geometry. It includes both hyperbolic and elliptic geometries, which have applications in general relativity.
Perihelion Precession: Perihelion precession is a phenomenon observed in the motion of planets and other celestial bodies orbiting the Sun, where the point of closest approach to the Sun, known as the perihelion, slowly rotates or precesses around the Sun over time. This effect is a key prediction of Einstein's Theory of Gravity, known as General Relativity, and provides evidence for the accuracy of this theory. The perihelion precession is a consequence of the curvature of spacetime around massive objects, as described by Einstein's theory, and it has been observed in the orbits of several planets in the Solar System, most notably Mercury.
Pound-Rebka Experiment: The Pound-Rebka experiment was a landmark experiment conducted in 1959 that provided experimental evidence for the gravitational redshift predicted by Einstein's theory of general relativity. It demonstrated the effect of gravity on the frequency of light, confirming a key prediction of Einstein's theory of gravity.
Principle of equivalence: The principle of equivalence states that gravitational and inertial mass are equivalent, implying that the effects of gravity are indistinguishable from the effects of acceleration in a small region of space-time. This forms a cornerstone of Einstein's General Theory of Relativity.
Principle of Equivalence: The principle of equivalence is a fundamental concept in Einstein's theory of gravity, known as general relativity. It states that the effects of gravity are indistinguishable from the effects of acceleration, suggesting that gravity is not a force, but rather a consequence of the curvature of spacetime.
Ricci Tensor: The Ricci tensor is a contraction of the Riemann curvature tensor, which is a fundamental concept in Einstein's theory of general relativity. It describes the curvature of spacetime and plays a crucial role in the formulation of the Einstein field equations, which govern the relationship between the geometry of spacetime and the distribution of matter and energy within it.
Riemann Geometry: Riemann geometry is a non-Euclidean geometry developed by the German mathematician Bernhard Riemann. It describes the intrinsic curvature of space and forms the mathematical foundation for Einstein's theory of general relativity, which revolutionized our understanding of gravity and the structure of the universe.
Sagittarius A*: Sagittarius A* (Sgr A*) is the supermassive black hole at the center of the Milky Way galaxy. It is located approximately 26,000 light-years from Earth and is considered the gravitational center around which our entire galaxy rotates.
Schwarzschild: The Schwarzschild solution is an exact solution to Einstein's field equations in general relativity that describes the gravitational field outside a spherical mass. It is characterized by the Schwarzschild radius, beyond which nothing can escape the gravitational pull.
Schwarzschild Radius: The Schwarzschild radius is a critical distance around a massive object, such as a black hole, within which the object's gravitational pull is so strong that nothing, not even light, can escape. It represents the point of no return, where the object's gravitational field becomes so intense that it creates an event horizon, a boundary beyond which information cannot be transmitted to the outside world.
Schwarzschild Solution: The Schwarzschild solution is a particular solution to Einstein's field equations of general relativity, which describes the gravitational field outside a spherically symmetric, non-rotating, uncharged mass such as a black hole. It is named after the physicist Karl Schwarzschild, who found this solution in 1916, just a few months after Einstein published his theory of general relativity.
Space-time: Space-time is a four-dimensional continuum that fuses the three dimensions of space with the one dimension of time into a single interwoven construct. It is central to Einstein's theory of general relativity, where gravity is described as the curvature of this continuum.
Spacetime: Spacetime is a fundamental concept in physics that describes the unified four-dimensional continuum of space and time. It is the framework in which all physical phenomena, including the motion of objects, are described and understood.
Special Relativity: Special relativity is a fundamental theory in physics that describes the relationship between space and time, and the behavior of objects moving at high speeds relative to an observer. It was developed by Albert Einstein in 1905 and revolutionized our understanding of the physical universe.
Supermassive Black Hole: A supermassive black hole is an extremely dense and massive black hole at the center of most galaxies, including our own Milky Way. These black holes have a gravitational pull so strong that nothing, not even light, can escape their event horizon, making them some of the most mysterious and powerful objects in the universe.
Tensor Mathematics: Tensor mathematics is a branch of mathematics that deals with the study of tensors, which are multi-dimensional arrays that generalize the concepts of scalars, vectors, and matrices. Tensors are essential in the formulation and understanding of Einstein's Theory of Gravity, known as General Relativity, as they provide a powerful mathematical framework for describing the curvature of spacetime and the interactions between matter and energy.
Theory of general relativity: Einstein's theory of general relativity describes gravity as the curvature of spacetime caused by mass and energy. It extends the principles of special relativity to incorporate gravitational fields.
Virgo: Virgo is the sixth astrological sign in the zodiac and is associated with the concept of service, analysis, and attention to detail. In the context of Einstein's Theory of Gravity, Virgo's connection lies in its representation of the systematic and meticulous approach often required in understanding complex scientific theories and their applications.
Wheeler: Wheeler was a prominent physicist known for his work on general relativity and quantum mechanics. He contributed to the understanding of black holes and introduced the concept of 'geons,' gravitational-electromagnetic entities.
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