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Since the discovery of the first fast radio burst (FRB) in 2007, and their confirmation as an abundant extragalactic population in 2013, the study of these sources has expanded at an incredible rate. In our 2019 review on the subject, we presented a growing, but still mysterious, population of FRBs—60 unique sources, 2 repeating FRBs, and only 1 identified host galaxy. However, in only a few short years, new observations and discoveries have given us a wealth of information about these sources. The total FRB population now stands at over 600 published sources, 24 repeaters, and 19 host galaxies. Higher time resolution data, sustained monitoring, and precision localisations have given us insight into repeaters, host galaxies, burst morphology, source activity, progenitor models, and the use of FRBs as cosmological probes. The recent detection of a bright FRB-like burst from the Galactic magnetar SGR 1935 + 2154 provides an important link between FRBs and magnetars. There also continue to be surprising discoveries, like periodic modulation of activity from repeaters and the localisation of one FRB source to a relatively nearby globular cluster associated with the M81 galaxy. In this review, we summarise the exciting observational results from the past few years. We also highlight their impact on our understanding of the FRB population and proposed progenitor models. We build on the introduction to FRBs in our earlier review, update our readers on recent results, and discuss interesting avenues for exploration as the field enters a new regime where hundreds to thousands of new FRBs will be discovered and reported each year.

Pulsar surveys offer a rare opportunity to monitor the radio sky for impulsive burst-like events with millisecond durations. We analyzed archival survey data and found a 30-jansky dispersed burst, less than 5 milliseconds in duration, located 3° from the Small Magellanic Cloud. The burst properties argue against a physical association with our Galaxy or the Small Magellanic Cloud. Current models for the free electron content in the universe imply that the burst is less than 1 gigaparsec distant. No further bursts were seen in 90 hours of additional observations, which implies that it was a singular event such as a supernova or coalescence of relativistic objects. Hundreds of similar events could occur every day and, if detected, could serve as cosmological probes.

Continued timing observations of the double pulsar PSR J0737–3039A/B, which consists of two active radio pulsars (A and B) that orbit each other with a period of 2.45 h in a mildly eccentric ( e=0.088 ) binary system, have led to large improvements in the measurement of relativistic effects in this system. With a 16-yr data span, the results enable precision tests of theories of gravity for strongly self-gravitating bodies and also reveal new relativistic effects that have been expected but are now observed for the first time. These include effects of light propagation in strong gravitational fields which are currently not testable by any other method. In particular, we observe the effects of retardation and aberrational light bending that allow determination of the spin direction of the pulsar. In total, we detect seven post-Keplerian parameters in this system, more than for any other known binary pulsar. For some of these effects, the measurement precision is now so high that for the first time we have to take higher-order contributions into account. These include the contribution of the A pulsar’s effective mass loss (due to spin-down) to the observed orbital period decay, a relativistic deformation of the orbit, and the effects of the equation of state of superdense matter on the observed post-Keplerian parameters via relativistic spin-orbit coupling. We discuss the implications of our findings, including those for the moment of inertia of neutron stars, and present the currently most precise test of general relativity’s quadrupolar description of gravitational waves, validating the prediction of general relativity at a level of 1.3×10-4 with 95% confidence. We demonstrate the utility of the double pulsar for tests of alternative theories of gravity by focusing on two specific examples and also discuss some implications of the observations for studies of the interstellar medium and models for the formation of the double pulsar system. Finally, we provide context to other types of related experiments and prospects for the future.

Despite its importance to our understanding of physics at supranuclear densities, the equation of state (EoS) of matter deep within neutron stars remains poorly understood. Millisecond pulsars (MSPs) are among the most useful astrophysical objects in the Universe for testing fundamental physics, and place some of the most stringent constraints on this high-density EoS. Pulsar timing—the process of accounting for every rotation of a pulsar over long time periods—can precisely measure a wide variety of physical phenomena, including those that allow the measurement of the masses of the components of a pulsar binary system1. One of these, called relativistic Shapiro delay2, can yield precise masses for both an MSP and its companion; however, it is only easily observed in a small subset of high-precision, highly inclined (nearly edge-on) binary pulsar systems. By combining data from the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) 12.5-yr data set with recent orbital-phase-specific observations using the Green Bank Telescope, we have measured the mass of the MSP J0740+6620 to be 2.14-0.09+0.10 M⊙ (68.3% credibility interval; the 95.4% credibility interval is 2.14-0.18+0.20 M⊙). It is highly likely to be the most massive neutron star yet observed, and serves as a strong constraint on the neutron star interior EoS.Cromartie et al. have probably found the most massive neutron star discovered so far by combining NANOGrav 12.5-yr data with radio data from the Green Bank Telescope. Millisecond pulsar J0740+6620 has a mass of 2.14 M⊙, ~0.1 M⊙ more massive than the previous record holder, and very close to the upper limit on neutron star masses from Laser Interferometer Gravitational-Wave Observatory measurements.

The double pulsar system PSR J0737-3039A/B is unique in that both neutron stars are detectable as radio pulsars. They are also known to have much higher mean orbital velocities and accelerations than those of other binary pulsars. The system is therefore a good candidate for testing Einstein's theory of general relativity and alternative theories of gravity in the strong-field regime. We report on precision timing observations taken over the 2.5 years since its discovery and present four independent strong-field tests of general relativity. These tests use the theory-independent mass ratio of the two stars. By measuring relativistic corrections to the Keplerian description of the orbital motion, we find that the \"post-Keplerian\" parameter s agrees with the value predicted by general relativity within an uncertainty of 0.05%, the most precise test yet obtained. We also show that the transverse velocity of the system's center of mass is extremely small. Combined with the system's location near the Sun, this result suggests that future tests of gravitational theories with the double pulsar will supersede the best current solar system tests. It also implies that the second-born pulsar may not have formed through the core collapse of a helium star, as is usually assumed.

PSR B1931+24 (J1933+2421) behaves as an ordinary isolated radio pulsar during active phases that are 5 to 10 days long. However, when the radio emission ceases, it switches off in less than 10 seconds and remains undetectable for the next 25 to 35 days, then switches on again. This pattern repeats quasi-periodically. The origin of this behavior is unclear. Even more remarkably, the pulsar rotation slows down 50% faster when it is on than when it is off. This indicates a massive increase in magnetospheric currents when the pulsar switches on, proving that pulsar wind plays a substantial role in pulsar spin-down. This allows us, for the first time, to estimate the magnetospheric currents in a pulsar magnetosphere during the occurrence of radio emission.

The clocklike properties of pulsars moving in the gravitational fields of their unseen neutron-star companions have allowed unique tests of general relativity and provided evidence for gravitational radiation. We report here the detection of the 2.8-second pulsar J0737-3039B as the companion to the 23-millisecond pulsar J0737-3039A in a highly relativistic double neutron star system, allowing unprecedented tests of fundamental gravitational physics. We observed a short eclipse of J0737-3039A by J0737-3039B and orbital modulation of the flux density and the pulse shape of J0737-3039B, probably because of the influence of J0737-3039A's energy flux on its magnetosphere. These effects will allow us to probe magneto-ionic properties of a pulsar magnetosphere.

The merger 1 of close binary systems containing two neutron stars should produce a burst of gravitational waves, as predicted by the theory of general relativity 2 . A reliable estimate of the double-neutron-star merger rate in the Galaxy is crucial in order to predict whether current gravity wave detectors will be successful in detecting such bursts. Present estimates of this rate are rather low 3 , 4 , 5 , 6 , 7 , because we know of only a few double-neutron-star binaries with merger times less than the age of the Universe. Here we report the discovery of a 22-ms pulsar, PSR J0737–3039, which is a member of a highly relativistic double-neutron-star binary with an orbital period of 2.4 hours. This system will merge in about 85 Myr, a time much shorter than for any other known neutron-star binary. Together with the relatively low radio luminosity of PSR J0737–3039, this timescale implies an order-of-magnitude increase in the predicted merger rate for double-neutron-star systems in our Galaxy (and in the rest of the Universe).

Pulsars: transient population A previously unknown population of superdense neutron stars has been identified. Termed RRATs, for rotating radio transients, their radio emissions vary on very short timescales, with bursts of 2 to 30 milliseconds occurring at intervals of 4 minutes to 3 hours. Eleven such objects have been found so far but their ephemeral nature suggests that there are many more in our Galaxy that remain unseen. This discovery implies a several-fold increase in the estimated radio-pulsar population, currently about 100,000. The radio sky is relatively unexplored for transient signals 1 , although the potential of radio-transient searches is high. This was demonstrated recently by the discovery of a previously unknown type of source 2 , 3 , varying on timescales of minutes to hours. Here we report a search for radio sources that vary on much shorter timescales. We found eleven objects characterized by single, dispersed bursts having durations between 2 and 30 ms. The average time intervals between bursts range from 4 min to 3 h with radio emission typically detectable for <1 s per day. From an analysis of the burst arrival times, we have identified periodicities in the range 0.4–7 s for ten of the eleven sources, suggesting origins in rotating neutron stars. Despite the small number of sources detected at present, their ephemeral nature implies a total Galactic population significantly exceeding that of the regularly pulsing radio pulsars. Five of the ten sources have periods >4 s, and the rate of change of the pulse period has been measured for three of them; for one source, we have inferred a high magnetic field strength of 5 × 10 13  G. This suggests that the new population is related to other classes of isolated neutron stars observed at X-ray and γ-ray wavelengths 4 .

The discovery of radio pulsars over a half century ago was a seminal moment in astronomy. It demonstrated the existence of neutron stars, gave a powerful observational tool to study them, and has allowed us to probe strong gravity, dense matter, and the interstellar medium. More recently, pulsar surveys have led to the serendipitous discovery of fast radio bursts (FRBs). While FRBs appear similar to the individual pulses from pulsars, their large dispersive delays suggest that they originate from far outside the Milky Way and hence are many orders-of-magnitude more luminous. While most FRBs appear to be one-off, perhaps cataclysmic events, two sources are now known to repeat and thus clearly have a longer lived central engine. Beyond understanding how they are created, there is also the prospect of using FRBs—as with pulsars—to probe the extremes of the Universe as well as the otherwise invisible intervening medium. Such studies will be aided by the high-implied all-sky event rate: there is a detectable FRB roughly once every minute occurring somewhere on the sky. The fact that less than a hundred FRB sources have been discovered in the last decade is largely due to the small fields-of-view of current radio telescopes. A new generation of wide-field instruments is now coming online, however, and these will be capable of detecting multiple FRBs per day. We are thus on the brink of further breakthroughs in the short-duration radio transient phase space, which will be critical for differentiating between the many proposed theories for the origin of FRBs. In this review, we give an observational and theoretical introduction at a level that is accessible to astronomers entering the field.