Analysis the Principle and State-of-Art Observations for

Gravitational Waves

Haozhe Wang

Nanjing No.1 High School AP Department, Nanjing, China

Keywords: Gravitational Wave, LIGO, Virgo.

Abstract: Gravitational wave searching is one of the key issues for astrophysics. This study provides a comprehensive

exploration of the fundamental principles of gravitational waves, detection techniques, and their applications

in astrophysics, with an in-depth outlook on future research directions and technological advancements. The

article first analyzes the theoretical foundation of gravitational waves, tracing their origin in general relativity

and detailing the diverse gravitational waves, including compact binary coalescence, unpredictable,

continuous, and burst gravitational waves. It then delves into the working principles and technological

challenges of detection systems for gravitational waves, like LIGO and Virgo, focusing on the various noise

sources that affect detector sensitivity within the 10 Hz to 10 kHz frequency range. The article also

summarizes significant gravitational wave detection events, such as GW150914, and discusses their profound

significance for astrophysical research. The introduction of deep learning technologies, such as convolutional

neural networks, is anticipated to further optimize the identification and classification of gravitational wave

signals, providing more powerful tools for astrophysical research.

1 INTRODUCTION

In 1916, the renowned physicist Einstein published a

groundbreaking paper on general relativity. He

concluded that only the third type of wave carries

energy, because the condition precisely eliminates the

existence of waves that cannot carry energy. Through

exchanges and cooperation with De Sitter,

Nordström, and Schrödinger, Einstein discovered a

mathematical error in his derivation and abandoned

the coordinate condition. This led to the identification

of two types of waves: longitudinal and transverse

waves. Although longitudinal waves do not carry

energy, they can still be considered as apparent

entities without using single-mode coordinates,

because in a field-free system (flat Minkowski

metric), longitudinal waves can be eliminated through

coordinate transformations. Ultimately, Einstein

discovered plane transverse gravitational waves

(Weinstein, 2016). In 2015, the Laser Interferometer

Gravitational-Wave Observatory (LIGO) used two

advanced detectors, i.e., H1 in Hanford, Washington,

and L1 in Livingston, Louisiana, to observe

gravitational wave signals. This observation is

considered the beginning of the era of gravitational

wave astronomy. The most convincing discovery was

the event GW150914 (the fusion of two black holes).

It was the result of LIGO's use of Optical resonators

that are coupled together to enhance the sensitivity of

interferometer transducers (Abbott, et al., 2016).

Gravitational waves have become a new tool for

exploring the universe. In the study of dark matter

(DM) and primordial black holes (PBHs), impact of

gravitational lensing on gravitational waves signals

can cause deflection, amplification, or time delay.

This allows for the distinction between dressed

primordial black holes and ordinary primordial black

holes by studying the distribution of dark matter

around primordial black holes (Lin, et al., 2025).

Gravitational waves are often produced by binary

mergers and are observed through a network of

cutting-edge gravitational wave detection systems.

The first type of gravitational wave is called ground-

based gravitational wave. LIGO and Virgo have

collaborated on the observation of ground-based

gravitational waves. For example, during the first

observation run (O1) from September 12, 2015, to

January 19, 2016, Advanced LIGO detected

gravitational waves resulting from three binary black

hole combinations. From November 30, 2016, to

August 25, 2017, Advanced LIGO conducted O2. On

August 1, 2017, Advanced Virgo also began

Wang, H.

Analysis the Principle and State-of-Art Observations for Gravitational Waves.

DOI: 10.5220/0013827100004708

Paper published under CC license (CC BY-NC-ND 4.0)

In Proceedings of the 2nd International Conference on Innovations in Applied Mathematics, Physics, and Astronomy (IAMPA 2025), pages 429-433

ISBN: 978-989-758-774-0

429

observing gravitational waves. Improvements were

made to the gravitational wave detectors at different

stages of observation to enhance sensitivity and

reduce scattered light noise (Abbott, et al., 2019). The

second type of gravitational wave is called space-

based gravitational wave. On December 3, 2015, the

European Space Agency launched the LISA

Pathfinder (LPF) to demonstrate the end-to-end free

fall of test masses (TMs), laying the experimental

foundation for future space-based gravitational wave

(GW) observatories like LISA (Armano, et al., 2016).

This paper aims to analyse the fundamental

principles of gravitational waves and the description

and understanding of gravitational wave observations.

Subsequent sections will cover the definition and

principles of gravitational wave generation,

gravitational wave detection devices and their

principles, recent observational results and

phenomena, current limitations in gravitational wave

research, and future prospects.

2 DESCRIPTIONS OF

GRAVITATIONAL WAVE

First, one can understand the basic properties of

gravitational waves by introducing the fundamentals

of gravitational waves in linearized gravity. To make

the situation more realistic, one needs to first study

the globally vacuum spacetime, where the two

polarization components of gravitational waves are

reflected by the transverse-traceless gauge. These two

components can be regarded as two independent

waveforms (seen from Fig. 1) (Flanagan & Hughes,

2005).

Subsequently, one considers the definition of

gravitational waves in a finite region of spacetime.

Although gravitational waves cannot be distinguished

from the time-varying near-zone fields produced by

external sources in a finite region, they can be

approximately defined when the wavelength of the

gravitational wave is much smaller than the

characteristic length of the background metric.

Next, one will further understand the types of

gravitational waves from the perspective of their

origins. The first type is compact binary coalescence

gravitational waves, which are produced due to the

merger of binary stars. Specifically, after rotating for

a certain period, the two stars will merge, during

which gravitational waves are generated. The second

type is stochastic gravitational waves, which produce

a relatively weak gravitational wave signal. This

signal has no specific waveform and is difficult to

detect. The name originates from the randomness of

its waveform. The third type is continuous

gravitational waves, which are generated by the

rotation of a compact massive object, such as a

neutron star. Due to the asymmetry of the massive

object, the rotation of the massive object produces

gravitational waves carrying weak energy. The fourth

type is burst gravitational waves. The gravitational

wave signal is difficult to detect due to modelling

difficulties, which are due to the origin of burst

gravitational waves: the non-spherical collapse of a

star (Ray, et al., 2024).

To better understand gravitational waves and their

characteristics, one compares them with

electromagnetic waves (though there are essential

differences between the two). First, both have wave-

like properties: electromagnetic waves are vibrations

of the electromagnetic field in spacetime while

gravitational waves are tiny propagating ripples in the

curvature of spacetime itself. The main difference lies

in the ease of detection; gravitational waves are

difficult to detect, while electromagnetic waves are

relatively easy. Second, gravitational radiation is

primarily produced by the collective motion and

mutual interference of macroscopic masses, i.e.,

celestial bodies in the universe, microscopic charge

motion is responsible for generating electromagnetic

waves, forming incoherent superpositions of waves

with a dipole structure in the wave zone.

Similarly, the interaction of electromagnetic

waves with matter is significant, whereas

gravitational waves propagate freely in the universe.

The ratio of wavelength to source size is exactly the

opposite for the two, which also leads to the fact that

electromagnetic waves can be used for imaging,

while gravitational waves cannot. Therefore, based

on these differences, it can be found that the two also

complement information about astrophysical sources,

which can provide effective methods for subsequent

astronomical research (Le Tiec & Novak, 2017).

Figure 1: Lines of force for a purely + GW (left), and for a

purely x GW (right)Figure kindly provided by Kip Thorne

(Flanagan & Hughes, 2005).

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430

3 PRINCIPLES AND FACILITIES

Wave Observatory (LIGO) has achieved a significant

breakthrough in the field of gravitational wave

detection, especially with the first direct detection of

the gravitational wave event GW150914. This

detection was made possible by the two advanced

detectors, LIGO and Virgo, which began

observations from September 2015 to August 2017.

Let's delve into the LIGO detectors. LIGO detectors

utilize Michelson interferometers, which rely on

changes in the phase of light to indirectly measure the

strain amplitude of gravitational waves. The test

masses (mirrors) within the detectors are designed to

be in a state of "free fall," allowing them to respond

freely to the minute displacements caused by

gravitational waves without being affected by other

environmental interferences.

Overall, LIGO detectors exhibit high sensitivity,

particularly in the frequency range of 100 to 300 Hz.

This good broadband response is beneficial for

measuring astrophysical sources of different masses.

The simultaneous observation by two detectors

compensates for the directional sensitivity deficiency

of the interferometers and enhances the ability to

locate signals. The LIGO detectors ingeniously

isolate the test masses from ground vibrations. The

increased circulating laser power makes quantum

noise controllable. The use of optical resonators in the

detectors enhances signal strength and the measurable

range of signals. Thus, it is not difficult to understand

the principle of gravitational wave detectors, which

convert spacetime perturbations into measurable

signals. The introduction and process of LIGO and

Virgo detectors are as follows: The LIGO data

sampling rate is 16, 384 Hz, while the Virgo data

sampling rate is 20 kHz. Calibration is required to

convert the interferometer photodiode output into

strain data. The detectors record hundreds of

thousands of auxiliary channels. Fourier domain

analysis is used for LIGO-Virgo data. Fast Fourier

Transform (FFT) is employed to convert time-domain

data into frequency-domain data. Subsequently,

Tukey window functions are applied to reduce

spectral leakage. The data is then whitened and finally

bandpass filtered to enhance signals in specific

frequency bands. Non-stationarity can occur in the

data, and one needs to assess the non-stationarity of

the data using wavelet transforms and discrete

wavelet packet transforms as given in Fig. 2 (Abbott,

et al., 2020). The physical parameters of gravitational

waves can be estimated using Bayesian theorem,

Markov Chain Monte Carlo (MCMC), and nested

sampling algorithms, while the waveform can be

determined using numerical relativity waveform

models (Abbott, et al., 2020).

Figure 2: A sketch of the searching process (Abbott, et al., 2020).

4 STATE-OF-ART

OBSERVATIONS

Since the LIGO-Virgo Collaboration (LVC) reported

the gravitational wave detection results from the O1

and O2 phases, including the highly significant event

GW150914, numerous research institutions and

scholars have conducted multiple gravitational wave

detections in recent years. One will now introduce

each of the gravitational wave detection events and

their attributes one by one.The first event is

GW170121. As the most confident newly discovered

Analysis the Principle and State-of-Art Observations for Gravitational Waves

431

binary black hole merger event, it has a probability of

astrophysical origin exceeding 0.99, which almost

certainly indicates that it is a genuine astrophysical

event. The event's inverse false alarm rate (IFAR) is

approximately 2.8×10

, signifying that the expected

frequency of similar signals generated solely by noise

under similar observational conditions is extremely

low.

The second and third events are GW170304 and

GW170727. Both are newly discovered events with

high confidence levels, each with an astrophysical

origin probability close to 0.98. This suggests a high

likelihood that they are of astrophysical origin. The

IFAR values of these two events are similar, both

around 370 O2, indicating their high significance

against the noise background. The fourth event is

GW170425. With a probability of around 0.77 for

astrophysical origin and an IFAR of approximately 29

O2, GW170425 is a newly discovered event with a

moderate confidence level. Although its confidence

level is slightly lower than the aforementioned events,

it still has a relatively high probability of being an

astrophysical event. The fifth event is GW170202.

This event has a probability of astrophysical origin of

about 0.7 and an IFAR of around 6 O2 (Schmidt,

2020). It is a candidate event with a certain level of

confidence. Among all the newly discovered events,

it is at a medium confidence level, yet it still has a

high probability of being an astrophysical event. The

sixth event is GW170403. As a candidate event close

to the detection threshold, GW170403 has a

probability of about 0.55 for being of astrophysical

origin, with an IFAR of roughly 5 in O2. Although its

confidence level is relatively low, it still has a certain

probability of being an astrophysical event and is

worth further investigation (Venumadhav, et al.,

2020).

5 LIMITATIONS AND

PROSPECTS

Noise sources in the frequency range of 10 Hz to 10

kHz can interfere with the sensitivity of long-baseline

interferometric detectors. These noise sources

comprise fundamental noise sources (seismic noise,

thermal noise from test masses, suspension systems,

and coatings), as well as quantum noise. Let’s first

take a specific look at seismic noise. Seismic noise

(<10 Hz) is associated with periods of extreme

weather (such as storms), which limits the low-

frequency performance of detectors because the

gravitational field of disturbances cannot be shielded.

Next is suspension thermal noise, which mainly

comes from two aspects: one is the mechanical

dissipation inside the suspension system material,

manifested as random vibrations caused by Brownian

motion; the other is due to the thermodynamic

properties of the suspension material, such as the

thermal expansion coefficient, which causes tiny

temperature fluctuations in the environment to be

transferred to the system, thereby generating

thermoelastic noise. The third type is mirror and

coating thermal noise. Mirror thermal noise mainly

comes from three mechanical loss mechanisms in the

fused silica substrate: surface loss, thermoelastic loss,

and bulk loss. Coating thermal noise mainly comes

from the multilayer dielectric coating structure on the

test mass used to achieve high reflectivity. The last

one is quantum noise, which is the fundamental noise

source that limits most frequencies in the LIGO

detection band (Hammond, et al., 2014).

For the future, the outlook is as follows. Since the

successful monitoring gravitational waves has

opened up new avenues in astrophysics, one needs

more advanced technology to continue detecting, and

it is hoped to conduct more pulsar timing array

experiments. One will also further apply CNNs to

determine whether the gravitational wave signals

appearing in the data stream are originating from

binary black holes or binary neutron stars. Because

the rate of events is much higher than astrophysical

expected, one needs realistic mock data challenges

(MDCs) to collect data. One needs to ensure that the

results remain interpretable and that one fully

understands why a given confidence level is

calculated, thereby implementing two feasible

machine learning methods, i.e., Logistic Regression

(LR, a simple machine learning model that works by

converting the input feature vector into a probability)

as well as Multilayer Perceptron (MLP, multiple

layers of neurons transform the input feature vector

into the output probability for each prediction class)

(Ashton, et al., 2025).

6 CONCLUSIONS

This article systematically analyzes the fundamental

principles of gravitational waves, detection

techniques, and their applications in astrophysics, and

provides an in-depth outlook on future research

directions and technological improvements.

Specifically, the article first reviews the theoretical

foundation of gravitational waves, covering their

origin in general relativity and the different types of

gravitational waves, including compact binary

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432

coalescence gravitational waves, stochastic

gravitational waves, continuous gravitational waves,

and burst gravitational waves. Next, the article

provides a detailed introduction to the working

principles and detection techniques of detectors such

as LIGO and Virgo, focusing on the impact of noise

sources in the frequency range of 10 Hz to 10 kHz

(such as seismic noise, suspension thermal noise,

mirror and coating thermal noise, and quantum noise)

on detector sensitivity. The article also summarizes

the main achievements in gravitational wave

detection in recent years, such as the discovery of

important events like GW150914, and discusses the

significant importance of these discoveries for

astrophysical research. In addition, the article

explores the potential applications of gravitational

waves in the study of dark matter and primordial

black holes, as well as the gravitational lensing effect

of gravitational wave signals. Looking to the future,

with the advancement of technology and the conduct

of more pulsar timing array experiments,

gravitational wave detection will become more

accurate and efficient. Meanwhile, the application of

deep learning technologies (such as CNN) will further

enhance the ability to identify and classify

gravitational wave signals. Finally, the significance

of the research lies in systematically summarizing the

current status and challenges of gravitational wave

detection, providing direction for future technological

improvements and scientific research. By conducting

an in-depth analysis of the properties of gravitational

waves and detection techniques, this article paves

new ways for astrophysical research, especially in

understanding extreme astrophysical events and dark

matter in the universe.

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