Undergraduate
  1. Classical mechanics  1.1. dynamics  1.1.1. Motion in one dimension  1.1.2. Motion in two dimensions  1.1.3. projectile motion  1.1.4. Relative speed  1.1.5. Uniform circular motion  1.1.6. Non-uniform circular motion  1.1.7. Reference frames and transformations  1.2. Newton's Laws of Motion  1.2.1. First law of motion  1.2.2. Second law of motion  1.2.3. Third Law of Motion  1.2.4. Applications of Newton's Laws  1.2.5. Friction and its types  1.2.6. Free Body Diagram  1.2.7. Constraints and pseudo-forces  1.3. Work and Energy  1.3.1. work done by the force  1.3.2. Work–energy theorem  1.3.3. Kinetic energy  1.3.4. Potential energy in classical mechanics  1.3.5. Conservative and non-conservative forces  1.3.6. Energy Conservation  1.3.7. Power and efficiency  1.4. Speed and collisions  1.4.1. Linear momentum  1.4.2. Conservation of momentum  1.4.3. Impulse and impact force  1.4.4. Elastic and inelastic collision  1.4.5. Center of mass and speed  1.4.6. Rocket Propulsion  1.5. Rotational motion  1.5.1. Torque and Angular Momentum  1.5.2. Moment of inertia  1.5.3. Rotational Kinematics  1.5.4. Rotational Energy  1.5.5. Rolling Motion  1.5.6. Precession and gyroscopic motion  1.6. Gravitational force  1.6.1. Newton's law of universal gravitation  1.6.2. Gravitational potential energy  1.6.3. Orbital mechanics  1.6.4. Kepler's laws of planetary motion  1.6.5. Gravitational field and potential  1.7. Fluid mechanics  1.7.1. Pressure and Pascal's Principle  1.7.2. Buoyancy and Archimedes' principle  1.7.3. Fluid Dynamics and Bernoulli's Principle  1.7.4. Viscosity and Poiseuille's law  1.7.5. Surface tension and capillarity  1.8. Oscillations and waves  1.8.1. Simple Harmonic Motion  1.8.2. Damped and driven oscillations  1.8.3. Coupled oscillations and common modes  1.8.4. Wave properties and types  1.8.5. Sound Waves and the Doppler Effect  1.8.6. Wave interference and superposition
  2. Electromagnetism  2.1. Electrostatics  2.1.1. Electric charge and properties  2.1.2. Coulomb's law  2.1.3. Electric field and electric potential  2.1.4. Gauss's Law  2.1.5. Capacitance and Dielectric  2.1.6. Electric dipole and potential energy  2.2. Electric circuits  2.2.1. Current and Resistance  2.2.2. Ohm's law  2.2.3. Kirchhoff's Laws  2.2.4. RC Circuit  2.2.5. AC Circuits and Reactance  2.2.6. Electric power and energy  2.3. Magnetism  2.3.1. Magnetic Fields and Forces  2.3.2. Ampere's Law  2.3.3. Magnetic dipole moment  2.3.4. Biot-Savart law  2.3.5. Magnetic Materials and Hysteresis  2.4. Electromagnetic induction  2.4.1. Faraday's Law  2.4.2. Lenz's law  2.4.3. Self and mutual induction  2.4.4. Transformers and Inductive Circuits  2.5. Maxwell's equations  2.5.1. Gauss's law for electricity  2.5.2. Gauss's law for magnetism  2.5.3. Faraday's law of induction  2.5.4. Ampere-Maxwell law  2.5.5. Electromagnetic waves
  3. Thermodynamics  3.1. Laws of Thermodynamics  3.1.1. Zeroth law of thermodynamics  3.1.2. First law of thermodynamics  3.1.3. Second Law  3.1.4. Third Law  3.2. Heat and work  3.2.1. Heat transfer (conduction, convection, radiation)  3.2.2. Thermal expansion  3.2.3. Heat engines and refrigerators  3.2.4. Carnot cycle and efficiency  3.3. Statistical mechanics  3.3.1. Maxwell–Boltzmann distribution  3.3.2. Entropy and Probability  3.3.3. Partition function  3.3.4. Fermi–Dirac and Bose–Einstein statistics
  4. Optics  4.1. Geometrical Optics  4.1.1. Reflection and Refraction  4.1.2. Mirrors and lenses  4.1.3. Optical Instruments  4.1.4. Fermat's principle  4.2. Wave optics  4.2.1. Interference in wave optics  4.2.2. Diffraction  4.2.3. Polarization  4.2.4. Coherence and holography
  5. Quantum mechanics  5.1. Wave–particle duality  5.1.1. Blackbody radiation in wave–particle duality in quantum mechanics  5.1.2. Photoelectric effect  5.1.3. Compton scattering  5.1.4. De Broglie wavelength  5.2. Schrödinger Equation  5.2.1. Time-independent Schrödinger equation  5.2.2. Particle in a box  5.2.3. Quantum Tunneling  5.2.4. Potential wells and obstacles  5.3. Quantum States  5.3.1. Wave function  5.3.2. Quantum operators  5.3.3. Heisenberg uncertainty principle  5.3.4. Angular momentum and spin
  6. Relativity  6.1. Special relativity  6.1.1. Lorentz transformations  6.1.2. Time expansion and length contraction  6.1.3. Relativistic energy and momentum  6.2. General relativity  6.2.1. Principle of Equivalence  6.2.2. Schwarzschild metric  6.2.3. Gravitational waves  6.2.4. Black holes and event horizons
  7. Solid state physics  7.1. Crystal structure  7.1.1. Bravais lattices  7.1.2. X-ray diffraction  7.1.3. Band theory  7.1.4. Phonons and lattice vibrations  7.2. Electrical and Magnetic Properties  7.2.1. Conductors, Semiconductors and Insulators  7.2.2. Superconductivity  7.2.3. Hall effect
  8. Nuclear and particle physics  8.1. Atomic Structure  8.1.1. Atomic Model  8.1.2. Nuclear binding energy  8.2. Radioactivity  8.2.1. Alpha, beta, gamma decay  8.2.2. Half life  8.2.3. Nuclear Fission and Fusion  8.3. Particle physics  8.3.1. Standard Model  8.3.2. Quarks and Leptons  8.3.3. antimatter  8.3.4. Fundamental interactions
  9. Astrophysics and cosmology  9.1. Stellar evolution  9.1.1. Star formation  9.1.2. Black holes and neutron stars  9.1.3. White dwarfs and supernovae  9.2. Cosmology  9.2.1. The Big Bang Theory  9.2.2. Dark matter and dark energy  9.2.3. Cosmic microwave background

Undergraduate → Relativity → General relativity ↓


Gravitational waves


Gravitational waves are a remarkable prediction of Albert Einstein's general theory of relativity. They are ripples in the fabric of space-time, generated by some of the most violent and energetic processes in the universe. These waves travel at the speed of light, carrying information about their cataclysmic origin.

What are gravitational waves?

Gravitational waves are similar to the ripples that spread across a pond when a stone is thrown into the water. Whenever massive objects accelerate, such as when neutron stars or black holes orbit each other or merge, they can create ripples in spacetime. These waves carry energy away from the system, causing the objects to move closer to each other.

Giant object Gravitational wave

Einstein proposed these waves as part of his theory of general relativity, published in 1915. The theory describes gravity as a distortion of spacetime caused by mass: massive objects such as stars and planets distort the fabric of space and time around them. When these objects move or interact, they can create waves like this that travel outward.

Nature of gravitational waves

The strength and effect of gravitational waves depend on the mass of the objects and the nature of their motion. For two massive bodies orbiting each other, such as binary black holes, the effects can be so strong that they can be seen from distances of more than billions of light-years.

For understanding purposes, consider a binary system of two massive stars. As these stars orbit each other, they are pulled closer by gravity, speeding up and emitting gravitational waves. This change is like a dancer twirling herself at high speed.

Power emitted in gravitational waves (P) ∝ (G⁴m₁²m₂²a⁻⁵) / (c⁵)

Here G is the gravitational constant, m₁ and m₂ are the masses, a is the separation distance, and c is the speed of light.

Why are they difficult to detect?

Gravitational waves become extremely weak by the time they reach Earth. The most powerful gravitational waves are produced by catastrophic events, such as the merger of black holes. However, by the time they reach us, even these signals cause only tiny distortions in spacetime.

The mathematical treatment of gravitational waves shows that they produce changes that are only a fraction of the size of a proton. Therefore, their detection requires highly sensitive instruments. These instruments, such as the LIGO and Virgo observatories, are able to measure changes on the scale of a thousandth of the diameter of a proton.

Merging black holes

merging black holes

When two black holes merge, they create one of the strongest known sources of gravitational waves. As the black holes get closer, their violent merger sends out a shockwave of spacetime vibrations that are detected as gravitational waves.

Detection of gravitational waves

Gravitational waves remained theoretical for decades after Einstein predicted them. Many improvements in technology and science were needed before the first direct detection. This milestone came in September 2015 when the LIGO detector measured waves from merging black holes. This confirmation not only supported general relativity but also opened up a new way of viewing and understanding the universe.

How gravitational wave observatories work

These observatories are based on the principle of measuring minute changes in distance as gravitational waves pass through Earth. For example, LIGO uses lasers and mirrors arranged in an L-shape to monitor with extreme accuracy the relative motion of mirrors located kilometers apart.

laser beam

Mirrors are mounted at the ends of the two arms of the setup, and a laser beam is split to travel down each arm. Any passing gravitational wave slightly changes the length of the arms, causing variations in the pattern of light beams recombined at the detector. Measuring these changes helps scientists infer the characteristics of the detected gravitational waves, such as their origin.

Implications of gravitational waves

The discovery of gravitational waves has huge implications for physics and astronomy. They enable us to "hear" cosmic processes that were previously invisible to conventional telescopes. Gravitational waves provide data from regions of space that are otherwise obscured, such as the interiors of black holes or the farthest surface of the Sun.

In addition to proving Einstein's theory, these waves provide insight into the following phenomena:

  • The merger of neutron stars, which may provide clues to the creation of heavier elements.
  • Core collapse Supernovae, the death of stars by explosions.
  • The very early universe provides a glimpse of cosmological conditions just moments after the Big Bang.

Conclusion

Gravitational waves are a cornerstone of modern astrophysics, offering a new way to study and understand our universe. From the cataclysmic events that generate these waves to their careful detection, the science of gravitational waves is at the forefront of combining theory and technology. As observatories continue to refine their measurements, we are sure to learn much more about one of the universe's most mysterious and powerful phenomena.


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Gravitational waves

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