182
11 Linearized General Relativity and Gravitational Waves
was about half the velocity of light. It is fair to say that this event was the first direct
evidence of truly strong gravitational effects, in which the geometry at the event
differed greatly from flat during the merger.
Later parts of the signal due to the merger and the following ringdown of the
remnant black hole require sophisticated numerical methods which we will not
discuss. Suffice it to say that the signal in its entirety can be reasonably well
calculated, and is in good agreement with the observation.
After GW150914 there have been many more black hole merger events detected
by LIGO. Up-to-date information and data links can be found at the LIGO website
(LIGO).
In 2017 another important type of event, GW170817, was seen by LIGO, the
inspiral and merger of two neutron stars into a final neutron star (Abbott 2017). Unlike
the black hole events the neutron star event produced electromagnetic radiation across
the entire spectrum, from radio waves to gamma rays, and left little doubt that LIGO
was truly detecting astronomical gravitational wave sources. It also verified that
gravitational waves move at the same speed as light to excellent accuracy.
It is fundamentally important to realize that the variety of black hole and neutron
star events as seen by LIGO constitutes an entirely new window on the universe and
not just a test of the predictions of relativity. The window is likely to greatly enhance
our understanding of astrophysics and the universe. For example the analysis of such
events can provide an independent measurement of the Hubble constant, as we will
discuss further in Part IV (LIGO 2017).
Our discussion has focused on the LIGO detector system based in the US. There
is also a collaborative system named Virgo based in Italy; several more earth-based
systems are expected to be operating in the near future. There are also plans for a
space system, the Laser Interferometric Space Antenna or LISA, which would be
millions of km in size and able to detect much lower frequencies than earth-based
systems. See reference (LIGO).
Gravitational waves could in principle be produced and detected in a laboratory
environment. However it is clear that this would be exceedingly difficult and thus the
astrophysical sources will likely be the only sources of information for the foreseeable
future; see Exercise 11.16.
Appendix 1: Solutions for Retarded Potentials
Equations involving the d’Alembertian operator and a source, such as (11.18), are
ubiquitous in physics. As such, anyone who has studied electromagnetism is familiar
with them (Jackson 1999). This Appendix is essentially a short reminder of the
solutions and their meaning. We consider an equation that relates a field ψ via the
d’Alembertian operator to some source f according to
11 Linearized General Relativity and Gravitational Waves
was about half the velocity of light. It is fair to say that this event was the first direct
evidence of truly strong gravitational effects, in which the geometry at the event
differed greatly from flat during the merger.
Later parts of the signal due to the merger and the following ringdown of the
remnant black hole require sophisticated numerical methods which we will not
discuss. Suffice it to say that the signal in its entirety can be reasonably well
calculated, and is in good agreement with the observation.
After GW150914 there have been many more black hole merger events detected
by LIGO. Up-to-date information and data links can be found at the LIGO website
(LIGO).
In 2017 another important type of event, GW170817, was seen by LIGO, the
inspiral and merger of two neutron stars into a final neutron star (Abbott 2017). Unlike
the black hole events the neutron star event produced electromagnetic radiation across
the entire spectrum, from radio waves to gamma rays, and left little doubt that LIGO
was truly detecting astronomical gravitational wave sources. It also verified that
gravitational waves move at the same speed as light to excellent accuracy.
It is fundamentally important to realize that the variety of black hole and neutron
star events as seen by LIGO constitutes an entirely new window on the universe and
not just a test of the predictions of relativity. The window is likely to greatly enhance
our understanding of astrophysics and the universe. For example the analysis of such
events can provide an independent measurement of the Hubble constant, as we will
discuss further in Part IV (LIGO 2017).
Our discussion has focused on the LIGO detector system based in the US. There
is also a collaborative system named Virgo based in Italy; several more earth-based
systems are expected to be operating in the near future. There are also plans for a
space system, the Laser Interferometric Space Antenna or LISA, which would be
millions of km in size and able to detect much lower frequencies than earth-based
systems. See reference (LIGO).
Gravitational waves could in principle be produced and detected in a laboratory
environment. However it is clear that this would be exceedingly difficult and thus the
astrophysical sources will likely be the only sources of information for the foreseeable
future; see Exercise 11.16.
Appendix 1: Solutions for Retarded Potentials
Equations involving the d’Alembertian operator and a source, such as (11.18), are
ubiquitous in physics. As such, anyone who has studied electromagnetism is familiar
with them (Jackson 1999). This Appendix is essentially a short reminder of the
solutions and their meaning. We consider an equation that relates a field ψ via the
d’Alembertian operator to some source f according to