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 Toughest Predators Ever: Tyrannosaurus Rex.

    Tyrannosaurus Rex was one of the most ferocious creature to ever roam the Earth. With a gigantic body, keen teeth, and jaws powerful enough to smash a vehicle, this renowned carnivore controlled the forested river valleys of western North America during the late Cretaceous period, 68 million years ago.

    T. Rex is a well-known Tyrannosaur, yet our understanding of him is continually changing. Improved technologies, including as biomechanical modelling and x-ray imaging, have helped scientists obtain a better understand of how this apex predator lived.

    Tyrannosaurus rex, which means "King of the Tyrant Lizards," was designed to take control. This dinosaur's massive body covered up to 40 feet—roughly the length of a school bus—from its nose to the tip of its powerful tail. T. rex, weighing up to eight tonnes, raised headfirst across its territory with two powerful legs. These dinosaurs most likely hunted living animals and collected cadavers, and they occasionally ate one another.

    Tyrannosaurus rex had a good sense of smell, which helped it find its prey. While scientists have long known that this dinosaur's brain was dedicated to scent processing, current research has revealed that T. rex has nearly as many genes encoding its olfactory receptors as a house cat does today. This strong nostrils most likely helped T. rex find mates and identify other predators.

    The head of a Tyrannosaurus dinosaur was very terrifying. This ruthless carnivore was designed to crush through its prey, with a hard cranium that allowed it to concentrate all of its muscle power into a single bite, making a up to six tonnes of pressure. This dinosaur utilised its 60 hooked teeth, each about eight inches long, to puncture and hold flesh before throwing it into the air and eating it whole. To protect from overheating while crushing prey with its powerful jaws, the gigantic animal developed openings in its head to keep its brain cool, similar to those found in alligators.

Tyrannosaurus Rex.

    Tyrannosaurus rex, a ferocious dinosaur, had tiny arms that biologists debated. Some believe they were evolutionary leftovers or served non-predatory purposes, while others argue they were evolved for "cruel cutting" in close quarters. Considering their powerful thighs, these dinosaurs could only walk at 12 miles per hour, which scientists believe would have fractured their feet if they travelled faster.

    Tyrannosaurus rex, a dangerous predator with a life expectancy of 28 years, suffered a growth rise during its adolescent years. A 2020 analysis of Nano Tyrannus fossils found that the bones belonged to a young T. rex rather than another species. This shows that Tyrannosaurus rex's growth rate varied as it aged, and that it could slow down when food was limited. Despite its advantages, T. rex was unable to equal the 66 million-year-old catastrophe that killed three-quarters of all species on Earth. This catastrophe occurred when an asteroid or comet collided with Earth, destroying Tyrannosaurus rex and other non-avian dinosaurs and marking the end of the Cretaceous epoch. 

The mysteries behind the extinction of dinosaurs: A voyage through time.

Introduction: The Jurassic World: 

                        The extinction of the dinosaurs remains a deep mystery. This historical voyage looks into the interesting subject of the dinosaur extinction, uncovering fascinating information and a wealth of archaeological evidence related to the mysterious extinction of these amazing species. 

Dinosaurs in Jurassic Period.

The Rise and Fall of the Dinosaurs:

During the Mesozoic Era, dinosaurs first appeared and ruled the earth for millions of years. They changed over time, becoming anything from the massive Brachiosaurus to the speedy Velociraptor. They evolved in many habitats throughout thousands of years, affecting the path of evolution. 

But disaster came at the end of the Jurassic Period, some 66 million years ago. A fatal extinction caused by a terrible disaster eliminated many other species in addition to dinosaurs. The change that occurred between the Mesozoic and Cenozoic Eras was signalled by this event, which also cleared the way for the creation of mammals.

Theories of Extinction:

Among the many ideas that explain why dinosaurs became extinct, two have received a lot of attention.

Asteroid Impact: 

                            The most well-known idea suggests that Earth was struck by a huge asteroid or comet that caused widespread destruction. Massive amounts of energy would have been released by this impact, resulting in the destabilisation of the food chain, wildfires, tsunamis, and a nuclear winter-like state as dust and debris blanketed the sky and blocked sunlight.

Volcanic Activity: 

                            Another convincing argument argues that the extinction of dinosaurs was mostly caused by volcanic eruptions, especially those of the Deccan Traps in modern-day India. Large amounts of greenhouse gases would have been emitted during these eruptions, causing environmental disturbance and climate change.

                           Scientists are still deeply divided about the exact order of events and how they contributed to the extinction disasters.

Tyrannosaurus rex (T. rex) went extinct around 65 million years ago.

Curious Archaeological Finds:

Secrets into the past are provided by archaeological finds, such as fossilised bones and geological data that provide light on the mystery surrounding the demise of the dinosaurs.

 Chicxulub Crater: 

                              Buried beneath Mexico's Yucatán Peninsula, the Chicxulub crater is one of the most significant pieces of evidence in support of the asteroid impact idea. This massive crater, which is over 180 km in diameter and was discovered in the 1970s, is dated to around 66 million years ago, which matches with the period of the extinction disasters.

Fossil Record:

                            The record of fossils documents the wide range of dinosaur species that once roamed the earth, providing an understanding of life before to the extinction disasters. By analysing these fossils, one may learn more about the anatomy, behaviour, and ecological functions of these prehistoric beings and get insight into their environment.

Asteroid impact, Volcanic activity are the causes that how Dinosaurs are extinction.

Geochemical study: 

                                Exceptions related to asteroid impacts and volcanic activity in the late Cretaceous have been found by geochemical study of sediment layers. The trace elements and geochemical traces provide important hints regarding the environmental conditions and probably catastrophic events that led to the extinction disasters. 

Conclusion: Solving the Mystery:

Scientists are still fascinated by the mysterious surrounding the eventual extinction of dinosaurs, which motivates investigation and study. Although hypotheses such as volcanic activity and asteroid impact theories exist, the actual origin is still unknown. Each archaeological find that reveals more about Earth's past helps us to solve this puzzle and highlights the strength and danger of life on our planet... 

 

“All the explanations proposed seem to be only partly satisfactory. They range from massive climatic change to mammalian predation to the extinction of a plant with apparent laxative properties, in which case the dinosaurs died of constipation.” 

---CARL SAGAN.