How do we test general relativity?
Testing the theory often means studying objects of tremendous masses only found in deep space
other bodies in the Solar System. Einstein used an approximation of the Schwarzschild metric – a solution to the field equations underpinning the theory – to show GR predicted this perfectly.
While this was an important first step on the road to validating GR, the theory would require something bigger if it was to receive the blessing of the scientific community. “GR also predicted that light would be deflected in passing by a massive body. For the Sun, the maximum deflection was only 1.7 arcseconds, so very tiny,” says Will, explaining Einstein’s second test. “The only way to detect it was during a total solar eclipse.”
English astronomer Arthur Eddington, one of GR’s early champions, took it upon himself to perform this second test, and he and colleague Frank Watson Dyson saw the solar eclipse of 1919 as the perfect opportunity to do this. During this eclipse the cluster of stars known as the Hyades would sit behind the Sun, with some of its stars visible near the eclipsed disc. This meant that their positions could be recorded and compared to previous records, revealing any apparent shifts caused by the Sun’s gravitational influence.
Eddington travelled to the island of Príncipe off the coast of west Africa to collect observations. Combined with data taken from Sobral, Brazil, by a second team, led by Andrew Crommelin from
“GR jettisoned the concept of gravity as an attractive force” Clifford Will
the Royal Greenwich Observatory, London, results conformed to Einstein’s theory. “The announcement of the verification of GR in November 1919 made Einstein an overnight science superstar,” says Will.
Despite these initial successes, the testing of GR slowed down after this, only experiencing a renaissance in the mid-20th century when the invention of equipment like radio telescopes shifted study beyond the Solar System. This renewed interest has included confirmation of Einstein’s third testing criteria – the discovery of gravitational redshift. “The first test of this effect would not happen until 1960, five years after Einstein’s death,” Will explains. “Today, of course, the redshift effect on the clocks in GPS satellites must be accounted for, otherwise these global navigation systems would not function properly.”
Moving beyond the limits of the Solar System has also made astronomical objects with far greater masses available for testing GR. “The tests of GR done within the Solar System with bodies like Mercury constitute what we call the ‘weak field’ regime – testing done with ‘weakly gravitating’ bodies,” says Venkatraman Krishnan. “We have entered a brand-new regime – the so-called ‘highly dynamical strong-field regime’ – testing gravity around strongly gravitating bodies that are also moving at a speed that is a significant fraction of the speed of light, as is the case for colliding neutron stars and black holes that emit gravitational waves.”
One of the most evocative consequences of GR’s treatment of space-time explored in this new age occurs around a massive rotating body. Near a massive object, GR suggests that the fabric of space-time will be dragged along in the direction of the body’s angular momentum. This ‘frame-dragging’ effect is tiny around a relatively small body like Earth. But the phenomenon – officially known as the Lense-Thirring effect – becomes much more extreme and measurable around truly massive cosmic objects like neutron stars and black holes.
“The common analogy that people use is the placement of a small ball in a bowl of honey – akin to a neutron star sitting in space-time. Add a drop of food colouring near the ball. Spin the ball quickly and notice that the honey turns with it. You will see that the ball drags the honey along, just like the rotating neutron star drags space-time,” says Venkatraman Krishnan, no stranger to the Lense-Thirring effect.
The astrophysicist was part of a team that studied the dragging of space-time around the white dwarf-pulsar binary PSR J1141–6545, located in the constellation of Musca, the Fly. As well as testing GR, the experiment also allowed the team to determine the radius of the system’s neutron star. As its mass is already known, this gives the researchers an idea of the density of the object.
This should ultimately help researchers gather information about its composition and possibly solve long-standing mysteries about neutron stars such as their mass limits and the composition of their interiors.
It’s no great surprise that the testing of GR – a theory of the astronomically massive – has often involved the most compact and massive space-time events possible: black holes. As they first emerged as pure theory from singularities that arose in the mathematical solutions of GR’s field equations, it’s only right black holes should play a vital role in the testing of the theory. The figurative shadow of the black hole may linger over GR, but it was the literal shadow of a black hole that informed a recent test of Einstein’s theory.
The first direct image of a supermassive black hole (SMBH) – the one at the centre of the galaxy Messier 87 released in April 2019 – has inspired this new test of GR. Astronomers at the Event Horizon Telescope (EHT) realised that if Einstein’s theory of gravity is correct, the shadow of a SMBH should have specific dimensions. The team used GR to calculate the size of the shadow of M87’s SMBH, finding that its image matched these parameters. Once again this verified Einstein’s theory – this time using an extragalactic object.
Closer to home – albeit still 26,000 light years away – the SMBH at the centre of the Milky Way, Sagittarius A* (Sgr A*), has played a role in modern GR tests. In 2020, a team of researchers led by Reinhard Genzel, director at the Max Planck