Introduction to Gravitational Wave Science

18 Oct 2025, 09:00 → 24 Jan 2026, 12:00 Asia/Shanghai

1502 (SEU-YC)

Gabriel Luz Almeida (Shing-Tung Yau center, Southeast University), Hongbin Wang (Southeast university), Yuchen Du (Shing-Tung Yau Center, Southeast University), Zhengwen Liu (Southeast University)

The groundbreaking detection of Gravitational Waves has inaugurated a transformative and exciting epoch in fundamental physics. These ripples in spacetime provide a unique and powerful probe for exploring the universe, enabling us to test Einstein's theory of General Relativity in its most extreme regimes and profoundly deepen our understanding of gravitational dynamics.

This lecture series is designed to give young explorers (undergraduates, graduate students, postdocs and early-career researchers) a systematic introduction to the foundations of Gravitational Wave Science. Our goal is to equip you with the basic knowledge and skills necessary to thrive and unravel the enigmas of the cosmos in this rapidly advancing field. Topics covered include the nature and generation of gravitational waves, key astrophysical and cosmological sources (such as binary black holes and neutron stars), theoretical modeling approaches, as well as an overview of detection methods and data analysis techniques. More precisely, we will use Gravitational Waves (vol 1) by Michele Maggiore as the main textbook. The lectures will primarily cover “Part I: Gravitational-Wave Theory,” along with several selected sections from “Part II: Gravitational-Wave Experiments.”

Prerequisites: A deep passion for science is paramount, paired with excellent scientific curiosity and a high aspiration for academic excellence. At minimum, you should have a solid foundation in electrodynamics and special relativity. Prior familiarity with general relativity is not strictly required but will be highly beneficial for your learning experience.

Instructors: Zhengwen Liu, Gabriel Almeida, Hongbin Wang, Yuchen Du

Website: indico.global/e/gw-lect2025 (all schedules and materials will posted and updated here)

Time: Saturday 9:00 - 12:00 (Start Date: 18 Oct 2025)

Location: 东南大学四牌楼校区 (具体教室将在日程处更新)

Additional Information

• Formal registration is not required, but for planning and logistical purposes, we kindly ask interested individuals to send your basic information to seuqft@yeah.net.
• This series of lectures is voluntarily organized by the QFT Group at SEU. It carries no academic credit (non-credit bearing), but participants are strongly encouraged to complete problem sets and assignments to maximize their learning.
• The format will be discussion-based, with active participation strongly encouraged.
• Lectures will be presented in English.

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References

[1] M. Maggiore, Gravitational Waves. Vol. 1: Theory and Experiments, Oxford, 2007 (main textbook)

[2] M. Maggiore, Gravitational Waves. Vol. 2: Astrophysics and Cosmology, Oxford, 2018

[3] E.Poisson and C. M. Will, Gravity: Newtonian, Post-Newtonian, Relativity, Cambridge, 2014

[4] M. C.  Miller and N. Yunes, Gravitational Waves in Physics and Astrophysics: An Artisan's Guide, IOP, 2021

[5] E.Flanagan and S. Hughes, The Basics of Gravitational Wave Theory, NJP 7 (2005) 204 [gr-qc/0501041]

[6] A. Le Tiec and J. Novak, Theory of Gravitational Waves, arXiv: 1607.04202

[7] S. Speziale and D. A. Steer, An Introduction to Gravitational Wave Theory, arXiv: 2508.21817

[8] A. Buonanno, Gravitational waves, Lectures in Les Houches Summer School 2007, arXiv:0709.4682

[9] A.Buonanno, Gravitational Waves from Inspiraling Binary Black Holes, CQG 19 (2002) 1267 [gr-qc/0203030]

Saturday 18 October

09:00 → 10:15 Lecture 1: Introduction to gravitational-wave science

We begin our journey with a broad overview of the science of Gravitational Waves (GWs). In this lecture, we will address fundamental questions such as, "What are gravitational waves?" and "What astrophysical events in the Universe can produce them?" We will also review the key discoveries of the past decade, following the first direct detection of GWs. This first lecture begins with a brief overview of the limitations of Newtonian gravity and its successor, Einstein's General Theory of Relativity. We then introduce the astrophysical sources of gravitational waves and trace the key historical developments leading to their discovery.

Speaker: Gabriel Luz Almeida (Shing-Tung Yau center, Southeast University)

Lectures 1 and 2.pdf

10:30 → 12:00 Lecture 2: Introduction to gravitational-wave science (II)

In this second lecture, we introduce the basic principles of gravitational wave detection, the characteristic waveforms produced by compact binary systems, and their important physical properties. We conclude the lecture with a discussion on the future prospects of Gravitational-Wave Astronomy and its potential to revolutionize our understanding of the cosmos.

Speaker: Gabriel Luz Almeida (Shing-Tung Yau center, Southeast University)

Saturday 25 October

09:00 → 10:15 Lecture 3: Basic review on special and general relativity

In the first lecture this Saturday, we will review the elementary tools of Special and General Relativity that are essential for introducing Linearized Gravity. We will begin by covering the foundational principles of both theories, then reviewing basic definitions of their geometric descriptions, before moving on to the basics of these theories' symmetry groups.

Speaker: Gabriel Luz Almeida (Shing-Tung Yau center of the Southeast University)

Lecture 3.pdf

10:30 → 12:00 Lecture 4: Introduction to the linearized theory of gravity

In this second lecture, we will study the Linearized Theory of Gravity, starting from the expansion of the Einstein field equations. As we will see, the symmetry group of General Relativity plays a crucial role. In particular, by exploring its properties, we will arrive at a wave equation that gives rise to the notion of Gravitational Waves. This lecture covers the textbook's §1.1.

Speaker: Gabriel Luz Almeida (Shing-Tung Yau center, Southeast University)

Problem_set_1-Lectures_3_and_4.pdf

Saturday 1 November

09:00 → 10:15 Lecture 5: The transverse-traceless gauge

In this lecture, we will study the wave equation in a vacuum. We will show how a suitable gauge choice allows us to write the wave solutions explicitly in terms of only two physical modes. As we will see, this is accomplished by adopting the so-called TT (transverse-traceless) gauge. This lecture covers the textbook's §1.2.

Speaker: Gabriel Luz Almeida (Shing-Tung Yau center of the Southeast University)

10:30 → 12:00 Lecture 6: Geodesic equation and geodesic deviation

This lecture will prepare us for next week's topic—the interaction of gravitational waves with test masses. To that end, we will study the geodesic equation and the equation of geodesic deviation in detail, in particular, going through the derivation of the latter starting from the former. These two equations are important to understand how one can detect the passage of a GW. This lecture covers the textbook's §1.3.1.

Speaker: Gabriel Luz Almeida (Shing-Tung Yau center, Southeast University)

Problem_set_2-Lectures_5_and_6.pdf

Saturday 8 November

09:00 → 10:15 Lecture 7: Interaction of GWs with test masses - The TT frame

In this lecture, we will cover how GWs interact with test masses, focusing on the specific frame of the TT gauge. In this part, we will learn how to understand physically the coordinate system related to the TT gauge. Today's lectures cover the textbook's §1.3.

Speaker: Gabriel Luz Almeida (Shing-Tung Yau center of the Southeast University)

Lecture 7 and 8.pdf

10:30 → 12:00 Lecture 8: Interaction of GWs with test masses - The detector frame

In this lecture, we will cover how GWs interact with test masses, focusing on another relevant frame, called the detector frame. Similarly to the previous lecture, we will understand in physical terms what does this reference frame corresponds to. With this, we finish the textbook's §1.3.

Speaker: Gabriel Luz Almeida (Shing-Tung Yau center, Southeast University)

Problem_set_3-Lectures_7_and_8.pdf

Saturday 15 November

09:00 → 10:15 Lecture 9: Separation of scales on generic curved background

Today's pair of lectures will be devoted to the study and derivation of the energy-momentum tensor of GWs based on the geometrical approach. In particular, in this first part, corresponding to the ninth lecture, we will introduce the concept of separation of scales, which will be important to understand how, in general, GWs can be meaninfully defined on curved backgrounds.

Speaker: Gabriel Luz Almeida (Shing-Tung Yau center, Southeast University)

Lecture 9 and 10.pdf

10:30 → 12:00 Lecture 10: The energy-momentum tensor of GWs

For the second part, lecture number ten, we will separate the Einstein's equation into its low- and a high-frequency parts. As we will see, this separation is grounded on the separation of scales introduced in the previous lecture, each having a deep physical meaning. In particular, we will be able to explicitly derive the energy-momentum tensor of GWs from the low-frequency part.

Speaker: Gabriel Luz Almeida (Shing-Tung Yau center, Southeast University)

Problem_set_4-Lectures_9_and_10.pdf

Saturday 22 November

09:00 → 10:15 Lecture 11: The energy flux of GWs

Having derived the energy-momentum tensor carried by the GWs in the previous lecture, today we will obtain important relations out of it. In particular, we will derive the energy flux, showing that it can be written in terms of the two physical modes of the GW, i.e., the plus and cross polarizations. Also in this lecture, we will discuss to what extent an expansion around flat spacetime makes sense.

Speaker: Gabriel Luz Almeida (Shing-Tung Yau center, Southeast University)

10:30 → 12:00 Lecture 12: A brief introduction to the Mathematica package xAct

During today's second lecture, we will introduce xAct, a Mathematica package for efficient tensor calculation. Our focus on this brief introduction will be the derivation of important formulae used along the first chapter of our textbook. In particular, used in the derivation of the energy-momentum tensor of GWs, we will derive the expression for the Ricci tensor up to second order in the perturbation.

Speaker: Gabriel Luz Almeida (Shing-Tung Yau center, Southeast University)

Problem_set_5-Lectures_11_and_12.pdf

xAct.nb

Saturday 29 November

09:00 → 10:15 Lecture 13: A brief review of the classical field theory

In the first lecture, I would like to give a brief review of the classical field theory, including the derivation of Euler-Lagrange equation of fields, symmetry transformation and Noether's theorem in a general form. After that we will discuss a particular symmetry transformation, the translation under which we will get the expression of the energy-momentum tensor as the conservative current.

Speaker: Hongbin Wang (Southeast university)

10:30 → 12:00 Lecture 14: The energy-momentum tensor

In this lecture, I will derive the expression of energy-momentum tensor of the classical electromagnetic field and the gravitational field, from the field-theoretical point of view. We will talk about the electromagnetic field as a good example to understand the basic concepts and techniques in field theory, and then derive the expression of energy-momentum tensor which should be consistent with the one derived in chapter 1. Finally we will discuss some difference between the electromagnetic field and the gravitational field.

Speaker: Hongbin Wang (Southeast university)

lecture1.pdf

Saturday 6 December

09:00 → 19:15 Lecture: 15

In this lecture, we derived the angular momentum expression for gravitational waves from the Noether's theorem, by the symmetry of the action under rotations in three dimensions.

Speaker: Hongbin Wang (Southeast university)

10:30 → 22:30 Lecture: 16

In this lecture, we talked about why the gravitational field is the spin-2 fields. We examine different cases, from spin-0, spin-1 and spin more than 3. We found all of these cases except spin-2 are ruled out by some physical prediction contradictory to the facts.

Speaker: Hongbin Wang (Southeast university)

lecture2.pdf