World Science Scholars
1.2 Gravity’s Messenger
summary
For most of history, light was the only way to observe the universe

• The earliest astronomers watched the sky with the naked eye. Today we have a slew of instruments that can detect light from the cosmos over a huge range of the electromagnetic spectrum.
• Modern astronomers combine data from multiple types of telescopes to create composite images of objects in space. These composite images can tell us more than any single telescope can.
• For example, the neutron star at the center of the supernova remnant Cassiopeia A is only visible by using x-ray telescopes. In the optical spectrum only hot ejected gas is visible. Together they tell the complete story of the star’s explosion.
• Black holes, however, are by definition impossible to observe directly using light telescopes since no light can ever escape their extreme gravity.
• The only way to study black holes using light telescopes is to observe any gas and dust falling into them. This can reveal some information about a black hole, like the frequency with which it spins around its axis, but closer study requires a new type of messenger.

Understanding Gravity

• In the 17th century Isaac Newton proposed a universal law of gravitation that conceived of gravity as a force between two masses ($m_1$ and $m_2$) separated by a distance $r$ according to the equation: $$F = \frac{G m_1 m_2}{r^2}$$
• Newton’s theory is very accurate for most situations and is still widely used today. However, Newton was worried about action at a distance – he wanted to understand how two masses know about and influence each other without apparently sending any signals.
• This problem was not solved until Einstein proposed general relativity in 1916. In his new conception gravity is not a force, but the geometry of spacetime. Massive objects cause spacetime to curve, and this curvature is what influences the motion of other objects in spacetime. Newton’s gravitational messenger turned out to be spacetime itself.
• Imagine putting a bowling ball on a cushion and then placing a marble at the edge of the cushion: the marble will roll toward the bowling ball due to the curvature. In the same way the curvature of spacetime determines how masses move.
• This was codified in an equation that relates the energy and mass contained in a system ($G_{uv}$) to the geometry of that system ($T_{uv}$): $$G_{\mu v} = \frac{8πG}{c^4}T_{\mu v}$$

Accelerating massive objects

• Einstein realized that massive (non-spherically symmetric) objects undergoing acceleration or oscillation would produce distortions that spread out across spacetime like ripples on a pond. These ripples are called gravitational waves.
• Light is actually created in a similar way: it is emitted when charged objects are accelerated.
• Like electromagnetic waves, gravitational waves carry energy and have amplitudes (called strain for gravitational waves) and frequencies associated with them. Gravitational waves are often represented as waveforms, which show their frequency and amplitude as they change over time.
• One major difference is that light waves can have very high frequencies (100MHz or faster), since charged particles are small and can be easily accelerated and oscillated. Quickly oscillating an object with the mass of the Sun is much more difficult, so gravitational waves are intrinsically low frequency waves (10kHz or slower) with wavelengths on the scale of kilometers.
• Gravitational wave frequencies are in the human auditory range, so they can be played as sounds in the same way that EM telescope data can be viewed as images.

Gravitational waves are extremely aloof

• Light is a “friendly creature” – it interacts with matter very easily, either through absorption or scattering. When astronomers detect light they need to figure out if it has been somehow changed along its journey.
• Gravitational waves are the opposite. They interact extremely weakly with matter, passing through everything essentially unchanged.
• This is very useful for gravitational wave astronomy because it means that any detected signal is largely unchanged from when it was generated at the source.

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