Why Light Bends by Gravity?

Introduction to General Relativity:

The Equivalence Principle

Einstein's theory of General Relativity builds on the Equivalence Principle, which states that the effects of gravity are indistinguishable from the effects of acceleration. This principle implies that a uniform gravitational field is locally equivalent to an accelerated frame of reference. 

Einstein's Field Equations

The heart of General Relativity is encapsulated in Einstein's field equations:

where:

• is the Ricci curvature tensor,
• is the Ricci scalar,
• is the metric tensor,
• is the cosmological constant,
• is the gravitational constant,
• is the speed of light,
• is the stress-energy tensor.

These equations describe how matter and energy influence the curvature of spacetime.

Spacetime Curvature and Geodesics:

Metric Tensor

The metric tensor gμν​ defines the geometry of spacetime. In the presence of a massive object, this tensor describes how distances and times are measured differently compared to flat spacetime.

Geodesics

In curved spacetime, the path that light follows is called a geodesic. Mathematically, a geodesic is the curve that minimizes the spacetime interval:

Light Bending.

Gravitational Lensing:

Bending of Light

When light passes near a massive object, its path bends due to the curvature of spacetime. This bending can be calculated using the lens equation:

where:

• is the observed position of the lensed image,
• is the true position of the source,
• is the deflection angle,
• is the distance between the lens and the source,
• is the distance to the source.

Deflection Angle

The deflection angle α can be derived from the Schwarzschild metric for a point mass M:

where, b is the impact parameter, the closest approach of the light ray to the massive object.

Historical Verification:

1919 Solar Eclipse

The first observational confirmation of light bending by gravity was made by Sir Arthur Eddington during the solar eclipse of 1919. Eddington measured the positions of stars near the Sun and found them to be shifted, confirming Einstein's prediction. 

Types of Gravitational Lensing:

Strong Lensing

Occurs when the alignment of source, lens, and observer is very close, resulting in multiple images, arcs, or Einstein rings.

Weak Lensing

Involves slight distortions in the images of background objects. This type is used to study the distribution of dark matter.

Microlensing

Causes temporary brightening of a background star when a smaller object like a star or planet passes in front of it. This technique is often used to detect exoplanets.

Mathematical Representation and Calculations:

Deflection Angle in a Weak Field

For weak gravitational fields, the deflection angle α is small, and the bending can be approximated using linearized gravity.

Exact Solutions

For strong fields near black holes or neutron stars, exact solutions to Einstein's field equations are required. The Schwarzschild and Kerr metrics are commonly used for these purposes. 

Applications and Implications:

Astrophysics

Gravitational lensing is used to study distant galaxies and quasars, revealing information about their mass and structure.

Cosmology

By observing the lensing of distant objects, scientists can map the distribution of dark matter and study the expansion of the universe. 

References and Further Reading:

1. Einstein, A. (1916). The Foundation of the General Theory of Relativity. Annalen der Physik, 354(7), 769-822.
2. Carroll, S. M. (2004). Spacetime and Geometry: An Introduction to General Relativity. Addison-Wesley.
3. Weinberg, S. (1972). Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity. Wiley.
4. Misner, C. W., Thorne, K. S., & Wheeler, J. A. (1973). Gravitation. W. H. Freeman.
5. Schneider, P., Ehlers, J., & Falco, E. E. (1992). Gravitational Lenses. Springer-Verlag.
6. Dyson, F. W., Eddington, A. S., & Davidson, C. (1920). A Determination of the Deflection of Light by the Sun's Gravitational Field, from Observations Made at the Total Eclipse of May 29, 1919. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 220(571-581), 291-333.  

The Brief History of The Sun.

The Sun:

The Sun is the star at the centre of our solar system. Its gravity holds the solar system together, keeping everything from the - biggest planets to the smallest bits of debris - in its orbit.

Heat and light are produced by nuclear events that occur deep beneath. In order to produce this energy, The Sun has been using four million tonnes of hydrogen fuel each second since its formation, or around 4.6 billion years ago.

Solar Flares:

A solar flare is a massive eruption that occurs on the Sun when energy that has been trapped in "twisted" magnetic fields- which are typically found above sunspots, Chromosphere -is suddenly released.

They may heat materials to millions of degrees in a matter of minutes, resulting in a burst of radiation that includes: radio waves, X-rays, and gamma rays.

Sun Spots:

Sunspots are areas where the magnetic field is about 2,500 times stronger than Earth's, much higher than anywhere else on the Sun. Because of the strong magnetic field, the magnetic pressure increases while the surrounding atmospheric pressure decreases.

This in turn lowers the temperature relative to its surroundings because the concentrated magnetic field inhibits the flow of hot, new gas from the Sun's interior to the surface.

Sunspots tends to occur in pairs that have magnetic fields pointing in opposite directions.

Why Sun Spots are Dark?

The sunspots are large concentrations of strong magnetic field. Some energy is partially prevented from passing through the surface by this magnetic field.

As a result, sunspots experience a lower surface temperature than other areas of the surface. It appears darker when the temperature is lower.

Coronal Mass Ejections (CMEs):

Coronal mass ejections (CMEs) are large expulsions of plasma and magnetic field from the sun's atmosphere the corona.

Compared to solar flares bursts of electromagnetic radiation that travel at the speed of light, reaching Earth in just over 8 minutes.

Formation of CMEs:

The more explosive CMES generally begin when highly twisted magnetic field structures (flux ropes) contained in the Sun's lower corona become too stressed and realign into a less tense configuration - a process called magnetic reconnection.

Near Earth CMEs Effects:

Auroras:

The CMEs causes stunning light displays known as auroras, visible in the polar regions of the earth.

Geomagnetic Storms:

CMEs can cause significant disturbances in Earth's magnetosphere, leading to geomagnetic storms which are; Satellite Operations, Power Grids, Communication Systems.

Radiation Hazards:

It Increases radiation levels at high altitudes, especially near the poles.

Preventing & Monitoring:

SPACE WEATHER FORECASTING:

To provide early alerts of possible CMEs, organisations such as NASA and NOAA's Space Weather Prediction Centre (SWPC) track solar activity.

AID:

Continuous monitoring and improved prediction models are essential to prevent the bad impacts of CMEs.

How to Find the Sun Spots Area:

To find the area of sunspots, I use the manual formula to calculate the area of the sunspots.

As = ((Af x n) / cos (B) x cos (L))

Where,

As - Area of the sunspot,

Af - Area factor constant for the solar chart image (i.e., 63.66),

n - Number of grid sares occupying the sunspot,

B- Heliographic latitude,

L - Angular distance of the sunspot from the solar disk centre.

The physical unit for the calculated area is a millionth of a hemisphere (MHS). 

Solar Cycle:

About every 11 years, the Sun's magnetic field gradually changes polarity, a process known as the solar cycle. This reversal causes changes in solar activity.

The solar cycle has been observed and recorded since the mid-18th century, with the current cycle being Solar Cycle 25. 

 "Sun, in fact, is the center of the universe" -Nicolaus Copernicus.