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General theory of relativity

Coordinate transformation   |   Field equation  |   Gravitational waves  |   Differential Equation

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GRAVITATIONAL WAVES

Gravitational waves are ripples in spacetime, that propagates at the speed of light. Such ripples are the properties of spacetime itself. It propagates at the speed of light.
metric tensor

The metric tensor can be decomposed into two component: one is the usual Minkoswki metric and other is small deviation (h) in the first order. We, can, in this way liniarize gravity which is a non-linear theory according to GR. The wave equation is expressed by De-Alembert () operator.


metric tensor

The perturbed metric h is itself a function of coordinates but the condition is that |h| << 1 so that higher order terms can be neglected. This is the method of perturbation which can be used to solve specific problem by approximating the solution by finding exact solution of related , simpler problem. In quantum field theory perturbation method is also useful in many cases when the specific problem is harder to solve.

metric tensor

This is the the gravitational wave equation in non-homogeneous form where a source term (T) is present on the right hand side. It has the effect on the medium which carry gravitational wave. The above equation can be derived from field equation. It is the wave equation in spactime , which encodes the properties of undulation of spacetime. The phenomena is the same as the propagation of electromagnetic field. In case of the latter the charged particle accelerates and in the former case heavier objects collides or accelerates. As an example when two neutron stars collides gravitational waves are created. But how can it be detected when spacetime is itself changing?

progation of gravitational wave

gravitational wave equation

Gravitational waves can penetrate regions of space that electromagnetic waves cannot. They are able to allow the observation of the merger of black holes and possibly other exotic objects in the distant Universe. Such systems cannot be observed with more traditional means such as optical telescopes or radio telescopes, and so gravitational wave astronomy gives new insights into the working of the Universe. In particular, gravitational waves could be of interest to cosmologists as they offer a possible way of observing the very early Universe. This is not possible with conventional astronomy, since before recombination the Universe was opaque to electromagnetic radiation. Precise measurements of gravitational waves will also allow scientists to test more thoroughly the general theory of relativity.

Jouney into the realm of physics

In 1900, the British physicist Lord Kelvin is said to have pronounced: "There is nothing new to be discovered in physics now. All that remains is more and more precise measurement." Within three decades, quantum mechanics and Einstein's theory of relativity had revolutionized the field. Today, no physicist would dare assert that our physical knowledge of the universe is near completion. To the contrary, each new discovery seems to unlock a Pandora's box of even bigger, even deeper physics questions. These are our picks for the most profound open questions of all. Inside you’ll learn about parallel universes, why time seems to move in one direction only, and why we don’t understand chaos.


What is dark energy?

No matter how astrophysicists crunch the numbers, the universe simply doesn't add up. Even though gravity is pulling inward on space-time — the "fabric" of the cosmos — it keeps expanding outward faster and faster. To account for this, astrophysicists have proposed an invisible agent that counteracts gravity by pushing space-time apart. They call it dark energy. In the most widely accepted model of dark energy, it is a "cosmological constant": an inherent property of space itself, which has "negative pressure" driving space apart. As space expands, more space is created, and with it, more dark energy. Based on the observed rate of expansion, scientists know that the sum of all the dark energy must make up more than 70 percent of the total contents of the universe. But no one knows how to look for it. The best researchers have been able to do in recent years is narrow in a bit on where dark energy might be hiding, which was the topic of a study released in August 2015.


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