Introduction to Gravitational Wave Science
from
Saturday, 18 October 2025 (09:00)
to
Saturday, 20 June 2026 (17:00)
Monday, 13 October 2025
Tuesday, 14 October 2025
Wednesday, 15 October 2025
Thursday, 16 October 2025
Friday, 17 October 2025
Saturday, 18 October 2025
09:00
Lecture 1: Introduction to gravitational-wave science
-
Gabriel Luz Almeida
(
Shing-Tung Yau center, Southeast University
)
Lecture 1: Introduction to gravitational-wave science
Gabriel Luz Almeida
(
Shing-Tung Yau center, Southeast University
)
09:00 - 10:15
Room: 逸夫建筑馆1502
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.
10:30
Lecture 2: Introduction to gravitational-wave science (II)
-
Gabriel Luz Almeida
(
Shing-Tung Yau center, Southeast University
)
Lecture 2: Introduction to gravitational-wave science (II)
Gabriel Luz Almeida
(
Shing-Tung Yau center, Southeast University
)
10:30 - 12:00
Room: 逸夫建筑馆1502
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.
Sunday, 19 October 2025
Monday, 20 October 2025
Tuesday, 21 October 2025
Wednesday, 22 October 2025
Thursday, 23 October 2025
Friday, 24 October 2025
Saturday, 25 October 2025
09:00
Lecture 3: Basic review on special and general relativity
-
Gabriel Luz Almeida
(
Shing-Tung Yau center of the Southeast University
)
Lecture 3: Basic review on special and general relativity
Gabriel Luz Almeida
(
Shing-Tung Yau center of the Southeast University
)
09:00 - 10:15
Room: 逸夫建筑馆1502
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.
10:30
Lecture 4: Introduction to the linearized theory of gravity
-
Gabriel Luz Almeida
(
Shing-Tung Yau center, Southeast University
)
Lecture 4: Introduction to the linearized theory of gravity
Gabriel Luz Almeida
(
Shing-Tung Yau center, Southeast University
)
10:30 - 12:00
Room: 逸夫建筑馆1502
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.
Sunday, 26 October 2025
Monday, 27 October 2025
Tuesday, 28 October 2025
Wednesday, 29 October 2025
Thursday, 30 October 2025
Friday, 31 October 2025
Saturday, 1 November 2025
09:00
Lecture 5: The transverse-traceless gauge
-
Gabriel Luz Almeida
(
Shing-Tung Yau center of the Southeast University
)
Lecture 5: The transverse-traceless gauge
Gabriel Luz Almeida
(
Shing-Tung Yau center of the Southeast University
)
09:00 - 10:15
Room: 逸夫建筑馆1502
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.
10:30
Lecture 6: Geodesic equation and geodesic deviation
-
Gabriel Luz Almeida
(
Shing-Tung Yau center, Southeast University
)
Lecture 6: Geodesic equation and geodesic deviation
Gabriel Luz Almeida
(
Shing-Tung Yau center, Southeast University
)
10:30 - 12:00
Room: 逸夫建筑馆1502
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.
Sunday, 2 November 2025
Monday, 3 November 2025
Tuesday, 4 November 2025
Wednesday, 5 November 2025
Thursday, 6 November 2025
Friday, 7 November 2025
Saturday, 8 November 2025
09:00
Lecture 7: Interaction of GWs with test masses - The TT frame
-
Gabriel Luz Almeida
(
Shing-Tung Yau center of the Southeast University
)
Lecture 7: Interaction of GWs with test masses - The TT frame
Gabriel Luz Almeida
(
Shing-Tung Yau center of the Southeast University
)
09:00 - 10:15
Room: 逸夫建筑馆1502
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.
10:30
Lecture 8: Interaction of GWs with test masses - The detector frame
-
Gabriel Luz Almeida
(
Shing-Tung Yau center, Southeast University
)
Lecture 8: Interaction of GWs with test masses - The detector frame
Gabriel Luz Almeida
(
Shing-Tung Yau center, Southeast University
)
10:30 - 12:00
Room: 逸夫建筑馆1502
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.
Sunday, 9 November 2025
Monday, 10 November 2025
Tuesday, 11 November 2025
Wednesday, 12 November 2025
Thursday, 13 November 2025
Friday, 14 November 2025
Saturday, 15 November 2025
09:00
Lecture 9: Separation of scales on generic curved background
-
Gabriel Luz Almeida
(
Shing-Tung Yau center, Southeast University
)
Lecture 9: Separation of scales on generic curved background
Gabriel Luz Almeida
(
Shing-Tung Yau center, Southeast University
)
09:00 - 10:15
Room: 逸夫建筑馆1502
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.
10:30
Lecture 10: The energy-momentum tensor of GWs
-
Gabriel Luz Almeida
(
Shing-Tung Yau center, Southeast University
)
Lecture 10: The energy-momentum tensor of GWs
Gabriel Luz Almeida
(
Shing-Tung Yau center, Southeast University
)
10:30 - 12:00
Room: 逸夫建筑馆1502
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.
Sunday, 16 November 2025
Monday, 17 November 2025
Tuesday, 18 November 2025
Wednesday, 19 November 2025
Thursday, 20 November 2025
Friday, 21 November 2025
Saturday, 22 November 2025
09:00
Lecture 11: The energy flux of GWs
-
Gabriel Luz Almeida
(
Shing-Tung Yau center, Southeast University
)
Lecture 11: The energy flux of GWs
Gabriel Luz Almeida
(
Shing-Tung Yau center, Southeast University
)
09:00 - 10:15
Room: 逸夫建筑馆1502
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.
10:30
Lecture 12: A brief introduction to the Mathematica package xAct
-
Gabriel Luz Almeida
(
Shing-Tung Yau center, Southeast University
)
Lecture 12: A brief introduction to the Mathematica package xAct
Gabriel Luz Almeida
(
Shing-Tung Yau center, Southeast University
)
10:30 - 12:00
Room: 逸夫建筑馆1502
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.
Sunday, 23 November 2025
Monday, 24 November 2025
Tuesday, 25 November 2025
Wednesday, 26 November 2025
Thursday, 27 November 2025
Friday, 28 November 2025
Saturday, 29 November 2025
09:00
Lecture 13: A brief review of the classical field theory
-
Hongbin Wang
(
Southeast university
)
Lecture 13: A brief review of the classical field theory
Hongbin Wang
(
Southeast university
)
09:00 - 10:15
Room: 逸夫建筑馆1502
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.
10:30
Lecture 14: The energy-momentum tensor
-
Hongbin Wang
(
Southeast university
)
Lecture 14: The energy-momentum tensor
Hongbin Wang
(
Southeast university
)
10:30 - 12:00
Room: 逸夫建筑馆1502
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.
Sunday, 30 November 2025
Monday, 1 December 2025
Tuesday, 2 December 2025
Wednesday, 3 December 2025
Thursday, 4 December 2025
Friday, 5 December 2025
Saturday, 6 December 2025
09:00
Lecture 15: Angular momentum for gravitational waves
-
Hongbin Wang
(
Southeast university
)
Lecture 15: Angular momentum for gravitational waves
Hongbin Wang
(
Southeast university
)
09:00 - 10:15
Room: 1502
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.
10:30
Lecture 16: Why spin-2
-
Hongbin Wang
(
Southeast university
)
Lecture 16: Why spin-2
Hongbin Wang
(
Southeast university
)
10:30 - 22:30
Room: 1502
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.
Sunday, 7 December 2025
Monday, 8 December 2025
Tuesday, 9 December 2025
Wednesday, 10 December 2025
Thursday, 11 December 2025
Friday, 12 December 2025
Saturday, 13 December 2025
09:00
Lecture 17: The Pauli-Fierz action
-
Hongbin Wang
(
Southeast university
)
Lecture 17: The Pauli-Fierz action
Hongbin Wang
(
Southeast university
)
09:00 - 10:00
Room: 1502
In this lecture, we derived the Pauli-Fierz action, which is gauge-invariant and leads to the correct equation for linear order of gravitional field.
10:00
Lecture 18: The propagator
-
Hongbin Wang
(
Southeast university
)
Lecture 18: The propagator
Hongbin Wang
(
Southeast university
)
10:00 - 11:00
Room: 1502
From the action leading to the linear equation of motion, we derived the propagator of gravitons in De Donder gauge. From the propagator we derived the expression of the gravitional interaction between two static point particles, which showed the consistency with Newton's gravity.
Sunday, 14 December 2025
Monday, 15 December 2025
Tuesday, 16 December 2025
Wednesday, 17 December 2025
Thursday, 18 December 2025
Friday, 19 December 2025
Saturday, 20 December 2025
09:00
Lecture 19: Higher-order terms
-
Hongbin Wang
(
Southeast university
)
Lecture 19: Higher-order terms
Hongbin Wang
(
Southeast university
)
09:00 - 10:00
Room: 1502
In this lecture, we explained the nonlinearity of gravity, and how construct higher-order terms in the action. From the dimensions, we saw how to determine the higher-order interacting terms in the action.
10:00
Lecture 20: GR as the effective theory
-
Hongbin Wang
(
Southeast university
)
Lecture 20: GR as the effective theory
Hongbin Wang
(
Southeast university
)
10:00 - 11:00
Room: 1502
In the low-energy case, we saw we need only consider the leading terms in the expansion, from which point of view we explained the general relativity as a totally adequate low-energy field theory.
Sunday, 21 December 2025
Monday, 22 December 2025
Tuesday, 23 December 2025
Wednesday, 24 December 2025
Thursday, 25 December 2025
Friday, 26 December 2025
Saturday, 27 December 2025
09:00
Lecture 21: The theory of massive gravitons
-
Hongbin Wang
(
Southeast university
)
Lecture 21: The theory of massive gravitons
Hongbin Wang
(
Southeast university
)
09:00 - 10:00
Room: 1502
In this lecture, we considered the theory of massive gravitons. From some basic observations, we could determine the range of mass of gravitons.
10:00
Lecture 22: The problems in theory of massive gravitons
-
Hongbin Wang
(
Southeast university
)
Lecture 22: The problems in theory of massive gravitons
Hongbin Wang
(
Southeast university
)
10:00 - 11:00
Room: 1502
By analogy with the massive electromagnetic field, we considered the massive gravitational field, deriving the propagators of massive gravitons. From some contradiction, we haven't established a "correct" theory of massive gravitons.
Sunday, 28 December 2025
Monday, 29 December 2025
Tuesday, 30 December 2025
Wednesday, 31 December 2025
Thursday, 1 January 2026
Friday, 2 January 2026
Saturday, 3 January 2026
Sunday, 4 January 2026
Monday, 5 January 2026
Tuesday, 6 January 2026
Wednesday, 7 January 2026
Thursday, 8 January 2026
Friday, 9 January 2026
Saturday, 10 January 2026
Sunday, 11 January 2026
Monday, 12 January 2026
Tuesday, 13 January 2026
Wednesday, 14 January 2026
Thursday, 15 January 2026
Friday, 16 January 2026
Saturday, 17 January 2026
Sunday, 18 January 2026
Monday, 19 January 2026
Tuesday, 20 January 2026
Wednesday, 21 January 2026
Thursday, 22 January 2026
Friday, 23 January 2026
Saturday, 24 January 2026
Sunday, 25 January 2026
Monday, 26 January 2026
Tuesday, 27 January 2026
Wednesday, 28 January 2026
Thursday, 29 January 2026
Friday, 30 January 2026
Saturday, 31 January 2026
Sunday, 1 February 2026
Monday, 2 February 2026
Tuesday, 3 February 2026
Wednesday, 4 February 2026
Thursday, 5 February 2026
Friday, 6 February 2026
Saturday, 7 February 2026
Sunday, 8 February 2026
Monday, 9 February 2026
Tuesday, 10 February 2026
Wednesday, 11 February 2026
Thursday, 12 February 2026
Friday, 13 February 2026
Saturday, 14 February 2026
Sunday, 15 February 2026
Monday, 16 February 2026
Tuesday, 17 February 2026
Wednesday, 18 February 2026
Thursday, 19 February 2026
Friday, 20 February 2026
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Sunday, 22 February 2026
Monday, 23 February 2026
Tuesday, 24 February 2026
Wednesday, 25 February 2026
Thursday, 26 February 2026
Friday, 27 February 2026
Saturday, 28 February 2026
Sunday, 1 March 2026
Monday, 2 March 2026
Tuesday, 3 March 2026
Wednesday, 4 March 2026
Thursday, 5 March 2026
Friday, 6 March 2026
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Sunday, 8 March 2026
Monday, 9 March 2026
Tuesday, 10 March 2026
Wednesday, 11 March 2026
Thursday, 12 March 2026
Friday, 13 March 2026
Saturday, 14 March 2026
13:00
Lecture 23: Warm up and review
-
Yuchen Du
(
Shing-Tung Yau Center, Southeast University
)
Lecture 23: Warm up and review
Yuchen Du
(
Shing-Tung Yau Center, Southeast University
)
13:00 - 14:15
Room: 1502
In this lecture, we will first warm up by reviewing some key ingredients about general relativity and some contents in previous chapters.
14:30
Lecture 24: Gravitational waves from weak field source
-
Yuchen Du
(
Shing-Tung Yau Center, Southeast University
)
Lecture 24: Gravitational waves from weak field source
Yuchen Du
(
Shing-Tung Yau Center, Southeast University
)
14:30 - 16:00
Room: 1502
Then we will derive gravitational waves from weak-field sources, furthermore focus on the non-relativistic sources. We will also discuss a commonly used technique/formula, the quadruple formula. Through a careful study of two examples, we will clarify the relation between two different ways, the direct integration and the quadruple formula, of calculating the leading order of gravitational waves. More importantly, we will get a clear physical picture of generation of the gravitational waves.
Sunday, 15 March 2026
Monday, 16 March 2026
Tuesday, 17 March 2026
Wednesday, 18 March 2026
Thursday, 19 March 2026
Friday, 20 March 2026
Saturday, 21 March 2026
13:00
Lecture 25: Binary system bound by scalar field
-
Yuchen Du
(
Shing-Tung Yau Center, Southeast University
)
Lecture 25: Binary system bound by scalar field
Yuchen Du
(
Shing-Tung Yau Center, Southeast University
)
13:00 - 14:30
Room: 1502
In this lecture, we will explicitly work out two examples where gravitational waves are generated from circular motions. In the first example, we will consider two point masses interacting through a scalar field. Through this example, we will see how the different parts we have learned so far come into play just at the right place to form a complete physical picture.
14:30
Lecture 26: Gravitationally-bound binary system
-
Yuchen Du
(
Shing-Tung Yau Center, Southeast University
)
Lecture 26: Gravitationally-bound binary system
Yuchen Du
(
Shing-Tung Yau Center, Southeast University
)
14:30 - 16:00
Room: 1502
In the second example, we will consider two point masses interacting through gravity. Through the knowledge we have learned from the first example, we can see that we have to go beyond the linear order to correctly calculate the gravitational waves generated.
Sunday, 22 March 2026
Monday, 23 March 2026
Tuesday, 24 March 2026
Wednesday, 25 March 2026
Thursday, 26 March 2026
Friday, 27 March 2026
Saturday, 28 March 2026
Sunday, 29 March 2026
Monday, 30 March 2026
Tuesday, 31 March 2026
Wednesday, 1 April 2026
Thursday, 2 April 2026
Friday, 3 April 2026
Saturday, 4 April 2026
Sunday, 5 April 2026
Monday, 6 April 2026
Tuesday, 7 April 2026
Wednesday, 8 April 2026
Thursday, 9 April 2026
Friday, 10 April 2026
Saturday, 11 April 2026
13:00
Lecture 27: Quadrupole radiation: radiated power, radiated angular momentum and radiation reaction
-
Yuchen Du
(
Shing-Tung Yau Center, Southeast University
)
Lecture 27: Quadrupole radiation: radiated power, radiated angular momentum and radiation reaction
Yuchen Du
(
Shing-Tung Yau Center, Southeast University
)
13:00 - 14:30
Room: 1502
In this lecture, we finish our discussion of leading-order GW by computing the radiated power, radiated angular momentum, and discussing its backreaction on the binary system.
14:30
Lecture 28: Mass octupole and current quadrupole
-
Yuchen Du
(
Shing-Tung Yau Center, Southeast University
)
Lecture 28: Mass octupole and current quadrupole
Yuchen Du
(
Shing-Tung Yau Center, Southeast University
)
14:30 - 16:00
Room: 1502
In this lecture, we discuss the subleading order of GW, generated by the mass octupole and current quadrupole of the source. This serves as a warm-up for the upcoming discussion on systematic multipole expansion next week.
Sunday, 12 April 2026
Monday, 13 April 2026
Tuesday, 14 April 2026
Wednesday, 15 April 2026
Thursday, 16 April 2026
Friday, 17 April 2026
Saturday, 18 April 2026
Sunday, 19 April 2026
Monday, 20 April 2026
Tuesday, 21 April 2026
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Monday, 27 April 2026
Tuesday, 28 April 2026
Wednesday, 29 April 2026
Thursday, 30 April 2026
Friday, 1 May 2026
Saturday, 2 May 2026
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