Supernovae are one of the most promising gravitational wave sources. But, since the system of the supernovae is nearly spherically symmetric, the expected gravitational waves from them are relatively weak, compared to the case of the compact binary mergers. Thus, at least using the current gravitational wave detectors, only the gravitational waves from a supernova that occurred in our galaxy could be detected. To reliably extract information from gravitational waves originating from such a low event rate, thorough preparation is essential. However, because supernova gravitational waves strongly depend on model parameters, such as progenitor mass and the equation of state for dense matter, it may be difficult to extract physical properties even if the gravitational waves are detected. The universal relations between gravitational-wave signals and physical properties, independent of model parameters, are important for solving this difficulty. To discuss such a universal relation, in this article, we systematically examine the protoneutron-star oscillation frequencies with the linear analysis, the so-called asteroseismology, and compare them with the gravitational wave signals in the
We introduce the rapidly emerging field of multi-messenger gravitational lensing - the discovery and science of gravitationally lensed phenomena in the distant universe through the combination of multiple messengers. This is framed by gravitational lensing phenomenology that has grown since the first discoveries in the 20th century, messengers that span 30 orders of magnitude in energy from high energy neutrinos to gravitational waves, and powerful "survey facilities" that are capable of continually scanning the sky for transient and variable sources. Within this context, the main focus is on discoveries and science that are feasible in the next 5-10 years with current and imminent technology including the LIGO-Virgo-KAGRA network of gravitational wave detectors, the Vera C. Rubin Observatory, and contemporaneous gamma/X-ray satellites and radio surveys. The scientific impact of even one multi-messenger gravitational lensing discovery will be transformational and reach across fundamental physics, cosmology and astrophysics. We describe these scientific opportunities and the key challenges along the path to achieving them. This article is the introduction to the Theme Issue of the P
The modeling of gravitational wave ringdown has traditionally relied on linear perturbation theory, which mainly describes the late-time behavior of a perturbed black hole after a binary merger. However, the need for more accurate ringdown models has motivated the understanding of nonlinear gravitational effects. In this paper, we summarize the main properties and latest developments of quadratic effects in ringdown models, which are expected to be detectable with next-generation gravitational wave detectors, and will allow for new consistency tests of general relativity.
This chapter introduces gravitational wave cosmology, focusing on the use of gravitational waves as standard sirens to probe the expansion history of the Universe. It presents and explains the methodologies behind bright and dark siren analyses, including their respective data requirements and underlying assumptions. Particular attention is given to the theoretical foundations of these approaches, the statistical frameworks used to interpret gravitational-wave events, and the treatment of selection effects. Examples and applications are provided for each method, with the aim of offering a clear and accessible introduction to the tools and concepts enabling cosmological inference from gravitational-wave observations.
Gravitational lensing offers a powerful probe into the properties of dark matter and is crucial to infer cosmological parameters. The Legacy Survey of Space and Time (LSST) is predicted to find O(10^5) gravitational lenses over the next decade, demanding automated classifiers. In this work, we introduce GraViT, a PyTorch pipeline for gravitational lens detection that leverages extensive pretraining of state-of-the-art Vision Transformer (ViT) models and MLP-Mixer. We assess the impact of transfer learning on classification performance by examining data quality (source and sample size), model architecture (selection and fine-tuning), training strategies (augmentation, normalization, and optimization), and ensemble predictions. This study reproduces the experiments in a previous systematic comparison of neural networks and provides insights into the detectability of strong gravitational lenses on that common test sample. We fine-tune ten architectures using datasets from HOLISMOKES VI and SuGOHI X, and benchmark them against convolutional baselines, discussing complexity and inference-time analysis.
In this work we highlight an important perspective for the complete understanding of the stochastic gravitational background structure. The stochastic gravitational wave background is perhaps the most important current and future tool towards pinpointing the early Universe phenomenology related with the inflationary era and the subsequent reheating era. Many mysteries are inherent to the stochastic spectrum so in this work we highlight the fact that the complete understanding of early Universe physics and of astrophysical processes requires data from many distinct frequency band ranges. The combination of these data will provide a deeper and better understanding of the physics that forms the stochastic gravitational wave background, in both cases that it is of cosmological or astrophysical origin. We also discuss how the reheating temperature may be determined by combining multi-band frequency data from gravitational wave experiments and we also discuss how the shape of the gravitational wave energy spectrum can help us better understand the physical processes that formed it.
The opening of the gravitational wave window has significantly enhanced our capacity to explore the universe's most extreme and dynamic sector. In the mHz frequency range, a diverse range of compact objects, from the most massive black holes at the farthest reaches of the Universe to the lightest white dwarfs in our cosmic backyard, generate a complex and dynamic symphony of gravitational wave signals. Once recorded by gravitational wave detectors, these unique fingerprints have the potential to decipher the birth and growth of cosmic structures over a wide range of scales, from stellar binaries and stellar clusters to galaxies and large-scale structures. The TianQin space-borne gravitational wave mission is scheduled for launch in the 2030s, with an operational lifespan of five years. It will facilitate pivotal insights into the history of our universe. This document presents a concise overview of the detectable sources of TianQin, outlining their characteristics, the challenges they present, and the expected impact of the TianQin observatory on our understanding of them.
Gravitational radiation from known astrophysical sources is conventionally treated classically. This treatment corresponds, implicitly, to the hypothesis that a particular class of quantum-mechanical states -- the so-called coherent states -- adequately describe the gravitational radiation field. We propose practicable, quantitative tests of that hypothesis using resonant bar detectors monitored in coincidence with LIGO-style interferometers. Our tests readily distinguish fields that contain significant thermal components or squeezing. We identify concrete circumstances in which the classical (i.e., coherent state) hypothesis is likely to fail. Such failures are of fundamental interest, in that addressing them requires us to treat the gravitational field quantum-mechanically, and they open a new window into the dynamics of gravitational wave sources.
Einstein's General Theory of Relativity predicts that accelerating mass distributions produce gravitational radiation, analogous to electromagnetic radiation from accelerating charges. These gravitational waves have not been directly detected to date, but are expected to open a new window to the Universe in the near future. Suitable telescopes are kilometre-scale laser interferometers measuring the distance between quasi free-falling mirrors. Recent advances in quantum metrology may now provide the required sensitivity boost. So-called squeezed light is able to quantum entangle the high-power laser fields in the interferometer arms, and could play a key role in the realization of gravitational wave astronomy.
Of order one in 10^3 quasars and high-redshift galaxies appears in the sky as multiple images as a result of gravitational lensing by unrelated galaxies and clusters that happen to be in the foreground. While the basic phenomenon is a straightforward consequence of general relativity, there are many non-obvious consequences that make multiple-image lensing systems (aka strong gravitational lenses) remarkable astrophysical probes in several different ways. This article is an introduction to the essential concepts and terminology in this area, emphasizing physical insight. The key construct is the Fermat potential or arrival-time surface: from it the standard lens equation, and the notions of image parities, magnification, critical curves, caustics, and degeneracies all follow. The advantages and limitations of the usual simplifying assumptions (geometrical optics, small angles, weak fields, thin lenses) are noted, and to the extent possible briefly, it is explained how to go beyond these. Some less well-known ideas are discussed at length: arguments using wavefronts show that much of the theory carries over unchanged to the regime of strong gravitational fields; saddle-point contour
We investigate the gauge invariance of the second order gravitational waves induced by the first order scalar perturbations by following the Lie derivative method. It is shown explicitly that the second order gravitational waves are gauge invariant in the synchronous frame. In the gauge invariant framework, we derive the equation of motion of the second order gravitational waves and show that the second order gravitational waves are sourced from the first order scalar perturbations described well in the gauge invariant Newtonian frame. Since the observables of gravitational waves are measured in the synchronous frame, we define the energy density spectrum of the second order gravitational waves in terms of the gauge invariant synchronous variables. This way guarantees no fictitious tensor perturbations. It is shown that the gauge invariant energy density spectrum of the second order gravitational waves coincides with the one in the Newtonian gauge.
The lack of a well-established solution for the gravitational energy problem might be one of the reasons why a clear road to quantum gravity does not exist. In this paper, the gravitational energy is studied in detail with the help of the teleparallel approach that is equivalent to general relativity. This approach is applied to the solutions of the Einstein-Maxwell equations known as $pp$-wave spacetimes. The quantization of the electromagnetic energy is assumed and it is shown that the proper area measured by an observer must satisfy an equation for consistency. The meaning of this equation is discussed and it is argued that the spacetime geometry should become discrete once all matter fields are quantized, including the constituents of the frame; it is shown that for a harmonic oscillation with wavelength $λ_0$, the area and the volume take the form $A=4(N+1/2)l_p^2/n$ and $V=2(N+1/2)l_p^2λ_0$, where $N$ is the number of photons, $l_p$ the Planck length, and $n$ is a natural number associated with the length along the $z$-axis of a box with cross-sectional area $A$. The localization of the gravitational energy problem is also discussed. The stress-energy tensors for the gravitat
Gamma Ray Bursts (GRBs) are the most relativistic objects known so far, involving, on one hand an ultra-relativistic motion with a Lorentz factor $Γ> 100$ and on the other hand an accreting newborn black hole. The two main routes leading to this scenario: binary neutron star mergers and Collapsar - the collapse of a rotating star to a black hole, are classical sources for gravitational radiation. Additionally one expect a specific a gravitational radiation pulse associated with the acceleration of the relativistic ejecta. I consider here the implication of the observed rates of GRBs to the possibility of detection of a gravitational radiation signal associated with a GRB. Unfortunately I find that, with currently planned detectors it is impossible to detect the direct gravitational radiation associated with the GRB. It is also quite unlikely to detect gravitational radiation associated with Collapsars. However, the detection of gravitational radiation from a neutron star merger associated with a GRB is likely.
The existence of gravitational radiation is a natural prediction of any relativistic description of the gravitational interaction. In this chapter, we focus on gravitational waves, as predicted by Einstein's general theory of relativity. First, we introduce those mathematical concepts that are necessary to properly formulate the physical theory, such as the notions of manifold, vector, tensor, metric, connection and curvature. Second, we motivate, formulate and then discuss Einstein's equation, which relates the geometry of spacetime to its matter content. Gravitational waves are later introduced as solutions of the linearized Einstein equation around flat spacetime. These waves are shown to propagate at the speed of light and to possess two polarization states. Gravitational waves can interact with matter, allowing for their direct detection by means of laser interferometers. Finally, Einstein's quadrupole formulas are derived and used to show that nonspherical compact objects moving at relativistic speeds are powerful gravitational wave sources.
The geometric description of gravitational memory for strong gravitational waves is developed, with particular focus on shockwaves and their spinning analogues, gyratons. Memory, which may be of position or velocity-encoded type, characterises the residual separation of neighbouring `detector' geodesics following the passage of a gravitational wave burst, and retains information on the nature of the wave source. Here, it is shown how memory is encoded in the Penrose limit of the original gravitational wave spacetime and a new `timelike Penrose limit' is introduced to complement the original plane wave limit appropriate to null congruences. A detailed analysis of memory is presented for timelike and null geodesic congruences in impulsive and extended gravitational shockwaves of Aichelburg-Sexl type, and for gyratons. Potential applications to gravitational wave astronomy and to quantum gravity, especially infra-red structure and ultra-high energy scattering, are briefly mentioned.
We focus on understanding the beaming of gravitational radiation from gamma ray bursts (GRBs) by approximating GRBs as linearly accelerated point masses. For accelerated point masses, it is known that gravitational radiation is beamed isotropicly at high speeds, and beamed along the polar axis at low speeds. Aside from this knowledge, there has been very little work done on beaming of gravitational radiation from GRBs, and the impact beaming could have on gravitational wave (GW) detection. We determine the following: (1) the observation angle at which the most power is emitted as a function of speed, (2) the maximum ratio of power radiated away as a function of speed, and (3) the angular distribution of power ratios at relativistic and non-relativistic speeds. Additionally the dependence of the beaming of GW radiation on speed is essentially the opposite of the beaming of electromagnetic (EM) radiation from GRBs. So we investigate why this is the case by calculating the angular EM radiation distribution from a linear electric quadrupole, and compare this distribution to the angular gravitational radiation distribution from a GRB.
The most general classical electrodynamics which still respect the linear superposition principle but allow for otherwise arbitrary birefringence require, and imply, a refined spacetime geometry described by a fourth-rank tensor field. Canonical gravitational dynamics for this geometry, if required to co-evolve in causally consistent fashion with the electromagnetic field, were shown to be constructively determined by gravitational closure of the birefringent electromagnetic field equations. For weak gravitational fields of the resulting birefringent refinement of classical Einstein-Maxwell theory, we show in this article that the corresponding quantum electrodynamics is locally renormalizable at every loop order in gauge-invariant fashion and then employ this result to compute various fundamental processes. Combining quantum field theoretic results in locally essentially flat regions with the global spacetime structure predicted by the refined gravitational dynamics, we find that the anomalous magnetic moment of the electron, the cross sections of Bhabha scattering, and the hyperfine splitting of the hydrogen all pick up a dependence on position in the gravitational field. Particu
Neutron stars are excellent emitters of gravitational waves. Squeezing matter beyond nuclear densities invites exotic physical processes, many of which violently transfer large amounts of mass at relativistic velocities, disrupting spacetime and generating copious quantities of gravitational radiation. I review mechanisms for generating gravitational waves with neutron stars. This includes gravitational waves from radio and millisecond pulsars, magnetars, accreting systems and newly born neutron stars, with mechanisms including magnetic and thermoelastic deformations, various stellar oscillation modes and core superfluid turbulence. I also focus on what physics can be learnt from a gravitational wave detection, and where additional research is required to fully understand the dominant physical processes at play.
In this article, which will appear as a chapter in the Handbook of Gravitational Wave Astronomy, we will describe the detection of gravitational waves with space-based interferometric gravitational wave observatories. We will provide an overview of the key technologies underlying their operation, illustrated using the specific example of the Laser Interferometer Space Antenna (LISA). We will then give an overview of data analysis strategies for space-based detectors, including a description of time-delay interferometry, which is required to suppress laser frequency noise to the necessary level. We will describe the main sources of gravitational waves in the millihertz frequency range targeted by space-based detectors and then discuss some of the key science investigations that these observations will facilitate. Once again, quantitative statements given here will make reference to the capabilities of LISA, as that is the best studied mission concept. Finally, we will describe some of the proposals for even more sensitive space-based detectors that could be launched further in the future.
We predict a new mechanism for the spin light of neutrino ($SLν$) that can be emitted by a neutrino moving in gravitational fields. This effect is studied on the basis of the quasiclassical equation for the neutrino spin evolution in a gravitational field. It is shown that the gravitational field of a rotating object, in the weak-field limit, can be considered as an axial vector external field which induces the neutrino spin procession. The corresponding probability of the neutrino spin oscillations in the gravitational field has been derived for the first time. The considered in this paper $SLν$ can be produced in the neutrino spin-flip transitions in gravitational fields. It is shown that the total power of this radiation is proportional to the neutrino gamma factor to the fourth power, and the emitted photon energy, for the case of an ultra relativistic neutrino, could span up to gamma-rays. We investigate the $SLν$ caused by both gravitational and electromagnetic fields, also accounting for effects of arbitrary moving and polarized matter, in various astrophysical environments. In particular, we discuss the $SLν$ emitted by a neutrino moving in the vicinity of a rotating neutro