Scalar-Tensor Theories are cool…


A geometrical illustrations of compact binary systems

Today, I gave a talk about two of my recent research projects at University of Wisconsin-Milwaukee. I got several excellent questions and a few nonsense questions as well. Here I’m gonna try to put myself in a testimony to see how well I can describe the first project to the public who might not have any knowledge of General Theory of Relativity. Here we go! Challenge accepted!

The first and the main project is about studying one of the most promising sources of gravitational waves i.e. inspiralling compact binary systems. Before you ask me: what are compact binary systems?,  I’m going to tell you about gravitational waves. Gravitational waves have the similar idea in behind as electromagnetic waves have, those waves your TV and radio receive from the radio/TV stations. If you accelrate “charged” particles (electromagnetically charged) like protons and electrons they will emit electromagnetic waves. That’s exactly how radio stations send off radio signals to the air. What about accelerating gravitationally-charged particles? Do they emit gravitational waves? The answer is yes. But since the strength of gravitational interaction is extremely small compared to electromagnetic interactions, we will need to accelerate extremely huge massive objects to produce detectable waves. Can we produce gravitational waves at home? No way! Not even in any human made laboratory on the planet Earth. However, the nature is violent and there are many super massive accelerating objects out there like super-massive black holes and neutron stars that can make strong enough gravitational wave signals that we may detect with our detectors on the Earth or in the space. A binary system of such super-massive objects orbiting around each other are among the most promising sources of gravitational waves. This is what astrophysicists call compact binary systems.

Einstein’s general theory of relativity predict these gravitational waves and describes how they should look like. Using the perturbation methods, it gives an exact mathematical formula for the equations of motion of the binary components in this theory. Einstein’s theory also gives the accurate form of the gravitational waves. The accurate knowledge of the waveform is required to extract the signal from the noisy data. People have done almost all of  the work in the framework of Einstein’s theory. Today, we know the equations of motion for compact binary systems very accurately. We also know the waveform with a good approximation in this theory.

But, is Einstein’s theory of gravity the ultimate theory of gravity? In other words, was Einstein right? The answer is probably not! Although, this theory has passed all the performed tests successfully but there are many questionable issues in the modern physics that can not be addressed properly with the Einstein’s theory in small scales and high energies. Therefore, people has started to think about alternative theories of gravity, more seriously. One of the simplest and interesting alternative class of theories that doesn’t disagree with the current tests of gravity as well as Einstein’s theory but has its own advantages is called Scalar-Tensor Theories of Gravity.

What was my talk about after all, today? It was about studying compact binary systems as the most promising source of gravitational waves not in Einstein’s theory but in Scalar-Tensor theories of gravity. More specifically, we have obtained the equations of motion for the components of the compact binary systems very accurately. Do you want to see the equations? The answer is no, you don’t! Are you crazy?! They are so damn lengthy and complicated.  But the good news is that they completely under control and useful. It is a step forward to understand and test the alternative theories of gravity.

Ok… Ok… OKAY… If you really, really, really want to see the equations you can see them here.

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