Course: Relativistic Astrophysics

Section outline

Select section General

General
- Select activity Announcements
  
  Forum
  
  Announcements Forum
- Select activity EPTA Results 29 June 2023
  
  Kaltura Video Resource
  
  EPTA Results 29 June 2023 Kaltura Video Resource
Select section Lecture Timetable

Lecture Timetable
- Select activity Lecture Timetable
  
  File
  
  Lecture Timetable File
Select section Supporting Material

Supporting Material
- Select activity Shapiro & Teukolsky: black holes
  
  File
  
  Shapiro & Teukolsky: black holes File
- Select activity Introduction to lensing
  
  File
  
  Introduction to lensing File
- Select activity GW notes Carroll
  
  File
  
  GW notes Carroll File
- Select activity Cliff Will, tests of GR with pulsars
  
  File
  
  Cliff Will, tests of GR with pulsars File
- Select activity Notes on BH astrophysics
  
  File
  
  Notes on BH astrophysics File
- Select activity Yoshida 2006: seed BH formation from PopIII stars
  
  File
  
  Yoshida 2006: seed BH formation from PopIII stars File
- Select activity Pringle 1981: theory of accretion disks
  
  File
  
  Pringle 1981: theory of accretion disks File
- Select activity Loeb 2006: hierarchical growth and first halo formation
  
  File
  
  Loeb 2006: hierarchical growth and first halo formation File
- Select activity Questions and answers
  
  Forum
  
  Questions and answers Forum
  
  In this forum you can ask any question/clarification and provide any feedback about the course.
  When starting a discussion, you can open a specific thread for that, and when asking something specific, always refer to the lecture where the topic is treated.
- Select activity Exam information
  
  Forum
  
  Exam information Forum
  
  Regarding the exam, the modality will be the following.
  The exam is exclusively oral and, unless new restrictions are issued, in person. Exams usually take place in my office (U2, second floor, room 2012)
  The exam will last about 1 hour and is structured as follows:
  - the first 15-20 minutes will be dedicated to a topic of your choice. Don't overrun, I won't let you talk for an hour about what you want, if after 15 minutes you haven't got to the point and you messed around, I will stop you and evaluate you for what you have been able to expose. So prepare a topic from start to end, describing premises, the physics and the mathematics of the various steps, up to the conclusions. I might interrupt you for questions and clarifications along the way.
  - in the rest of the exam I will ask you 2-3 questions always on the topics of the course, also trying to challenge you to critically think about things, to evaluate your level of understanding of the physics on which the different topics are based.
  Exams sessions for the period January-April are already available. However, the sessions are mostly define for the purpose of registering the grades. So please register to the session and send me an email and we'll agree on a date and time that meet the needs of both your and my schedule.
  I'd say that's it, if you have any questions, don't hesitate to contact me.
  Alberto
Select section Lecture I: Introduction. Plan of the course and curved geometries

Lecture I: Introduction. Plan of the course and curved geometries
- Select activity Plan of the lecture course
  
  Kaltura Video Resource
  
  Plan of the lecture course Kaltura Video Resource
- Select activity Lecture1.2: curved geometries and the metric tensor
  
  Kaltura Video Resource
  
  Lecture1.2: curved geometries and the metric tensor Kaltura Video Resource
Select section Lecture II: Vectors and Tensors, Equivalence Principle and Geodsesic Equation

Lecture II: Vectors and Tensors, Equivalence Principle and Geodsesic Equation
- Select activity Lecture2.1: transformations and operations with vectors and tensors
  
  Kaltura Video Resource
  
  Lecture2.1: transformations and operations with vectors and tensors Kaltura Video Resource
- Select activity The strong equivalence principle and the geodesic equation
  
  Kaltura Video Resource
  
  The strong equivalence principle and the geodesic equation Kaltura Video Resource
Select section Lecture III: Riemann tensor, stress energy tensor and principle of general covariance: Einstein's equations

Lecture III: Riemann tensor, stress energy tensor and principle of general covariance: Einstein's equations
- Select activity Lecture3.1: the Riemann tensor
  
  Kaltura Video Resource
  
  Lecture3.1: the Riemann tensor Kaltura Video Resource
- Select activity Lecture3.2: Stress energy tensor. The principle of general covariance and Einstein's equations
  
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  Lecture3.2: Stress energy tensor. The principle of general covariance and Einstein's equations Kaltura Video Resource
Select section Lecture IV: The Newtonian limit of GR, symmetries and killing vectors

Lecture IV: The Newtonian limit of GR, symmetries and killing vectors
- Select activity Lecture4.1: The Newtonian limit of General Relativity
  
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  Lecture4.1: The Newtonian limit of General Relativity Kaltura Video Resource
- Select activity Lecture4.2: Killing vector fields, symmetries and conserved quantities
  
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  Lecture4.2: Killing vector fields, symmetries and conserved quantities Kaltura Video Resource
Select section Lecture V: The Schwarzschild solution

Lecture V: The Schwarzschild solution
- Select activity Lecture5.1: Derivation of the Schwarzschild solution
  
  Kaltura Video Resource
  
  Lecture5.1: Derivation of the Schwarzschild solution Kaltura Video Resource
- Select activity Lecture5.2: real and apparent singularities: the concept of horizon
  
  Kaltura Video Resource
  
  Lecture5.2: real and apparent singularities: the concept of horizon Kaltura Video Resource
Select section Lecture VI: Kruskal extension, proper vs coordinate time and gravitational redshift

Lecture VI: Kruskal extension, proper vs coordinate time and gravitational redshift
- Select activity Lecture6.1: The Kruskal extension to the Schwarzschild metric
  
  Kaltura Video Resource
  
  Lecture6.1: The Kruskal extension to the Schwarzschild metric Kaltura Video Resource
- Select activity Lecture6.2: Proper vs coordinate time, gravitational redshift
  
  Kaltura Video Resource
  
  Lecture6.2: Proper vs coordinate time, gravitational redshift Kaltura Video Resource
Select section Lecture VII: Geodesic equations in the Schwarzschild metric

Lecture VII: Geodesic equations in the Schwarzschild metric
- Select activity Lecture7.1: Derivation of geodesic equations from a variational principle
  
  Kaltura Video Resource
  
  Lecture7.1: Derivation of geodesic equations from a variational principle Kaltura Video Resource
- Select activity Lecture7,2: Geodesic equations for massive and massless particles in Schwarzschild
  
  Kaltura Video Resource
  
  Lecture7,2: Geodesic equations for massive and massless particles in Schwarzschild Kaltura Video Resource
Select section Lecture VIII: trajectories of massless particles in Schwarzschild: deflection of light

Lecture VIII: trajectories of massless particles in Schwarzschild: deflection of light
- Select activity Lecture8.1: Qualitative study of photon trajectories in the Schwarzschild metric
  
  Kaltura Video Resource
  
  Lecture8.1: Qualitative study of photon trajectories in the Schwarzschild metric Kaltura Video Resource
- Select activity Lecture8.2: Light bending, a perturbative derivation
  
  Kaltura Video Resource
  
  Lecture8.2: Light bending, a perturbative derivation Kaltura Video Resource
Select section Lecture IX: the Shapiro delay

Lecture IX: the Shapiro delay
- Select activity Lecture9.1: mathematical derivation of the Shapiro delay
  
  Kaltura Video Resource
  
  Lecture9.1: mathematical derivation of the Shapiro delay Kaltura Video Resource
- Select activity Lecture9.2: the Shapiro delay in the solar system. NOTE: last 20m are out of focus. Please look at the video from last year!…
  
  Kaltura Video Resource
  
  Lecture9.2: the Shapiro delay in the solar system. NOTE: last 20m are out of focus. Please look at the video from last year!… Kaltura Video Resource
Select section Lecture X: orbit of massive particles and radial infall

Lecture X: orbit of massive particles and radial infall
- Select activity Lecture10.1: qualitative description of massive particle motion in the Schwarzschild metric
  
  Kaltura Video Resource
  
  Lecture10.1: qualitative description of massive particle motion in the Schwarzschild metric Kaltura Video Resource
- Select activity Lecture10.2: radial infall
  
  Kaltura Video Resource
  
  Lecture10.2: radial infall Kaltura Video Resource
Select section Lecture XI: perielion precession of bound orbits of celestial bodies

Lecture XI: perielion precession of bound orbits of celestial bodies
- Select activity Lecture11.1: derivation of perielion precession and application to the orbit of Mercury
  
  Kaltura Video Resource
  
  Lecture11.1: derivation of perielion precession and application to the orbit of Mercury Kaltura Video Resource
- Select activity Lecture11.2: introduction to gravitational lensing
  
  Kaltura Video Resource
  
  Lecture11.2: introduction to gravitational lensing Kaltura Video Resource
Select section Lecture XII: light deflection and Shapiro delay from a variational principle: introduction to lensing

Lecture XII: light deflection and Shapiro delay from a variational principle: introduction to lensing
- Select activity Lecture12.1: a variational principle for light bending and Shapiro delay
  
  Kaltura Video Resource
  
  Lecture12.1: a variational principle for light bending and Shapiro delay Kaltura Video Resource
- Select activity Lecture12.2: light deflection from extended mass distributions and the lensing equation
  
  Kaltura Video Resource
  
  Lecture12.2: light deflection from extended mass distributions and the lensing equation Kaltura Video Resource
Select section Lecture XIII: Gravitational lensing, Eintsein ring, point-like lenses, multiple images and examples

Lecture XIII: Gravitational lensing, Eintsein ring, point-like lenses, multiple images and examples
- Select activity Lecture13.1: lens critical density and Einstein ring
  
  Kaltura Video Resource
  
  Lecture13.1: lens critical density and Einstein ring Kaltura Video Resource
- Select activity Lecture13,2: point-like lenses, magnification, multiple images and astrophysical applications
  
  Kaltura Video Resource
  
  Lecture13,2: point-like lenses, magnification, multiple images and astrophysical applications Kaltura Video Resource
Select section Lecture XIV: Kerr metric, definition and properties

Lecture XIV: Kerr metric, definition and properties
- Select activity Lecture14.1: more applications of weak lensing. Far field limit of the metric of a compact object
  
  Kaltura Video Resource
  
  Lecture14.1: more applications of weak lensing. Far field limit of the metric of a compact object Kaltura Video Resource
- Select activity Lecture14.2: Kerr metric, definition and general properties
  
  Kaltura Video Resource
  
  Lecture14.2: Kerr metric, definition and general properties Kaltura Video Resource
Select section Lecture XV: structure of a Kerr black hole

Lecture XV: structure of a Kerr black hole
- Select activity Lecture15.1: horizons, ZAMO and frame dragging
  
  Kaltura Video Resource
  
  Lecture15.1: horizons, ZAMO and frame dragging Kaltura Video Resource
- Select activity Lecture15.2: ergosphere and singularity
  
  Kaltura Video Resource
  
  Lecture15.2: ergosphere and singularity Kaltura Video Resource
Select section Lecture XVI: geodesic motion in the Kerr metric

Lecture XVI: geodesic motion in the Kerr metric
- Select activity Lecture16.1: massless particles, effective potential, light rings and Penrose process
  
  Kaltura Video Resource
  
  Lecture16.1: massless particles, effective potential, light rings and Penrose process Kaltura Video Resource
- Select activity Lecture16.2: massive particles, ISCO and radiative efficiency
  
  Kaltura Video Resource
  
  Lecture16.2: massive particles, ISCO and radiative efficiency Kaltura Video Resource
Select section Lecture XVII: solutions with matter, the TOV equations

Lecture XVII: solutions with matter, the TOV equations
- Select activity Lecture17.1: solving Einstein's equations with matter, general considerations
  
  Kaltura Video Resource
  
  Lecture17.1: solving Einstein's equations with matter, general considerations Kaltura Video Resource
- Select activity Lecture17.2: Tolman-Oppenheimer-Volkoff (TOV) equations
  
  Kaltura Video Resource
  
  Lecture17.2: Tolman-Oppenheimer-Volkoff (TOV) equations Kaltura Video Resource
Select section Lecture XVIII: the Schwarzschild solution, relativistic instability and maximum mass

Lecture XVIII: the Schwarzschild solution, relativistic instability and maximum mass
- Select activity Lecture18.1: The Schwarzschild solution for a relativistic star with constant energy density
  
  Kaltura Video Resource
  
  Lecture18.1: The Schwarzschild solution for a relativistic star with constant energy density Kaltura Video Resource
- Select activity Lecture18.2: relativistic instability and maximum mass of neutron and regular stars
  
  Kaltura Video Resource
  
  Lecture18.2: relativistic instability and maximum mass of neutron and regular stars Kaltura Video Resource
Select section Lectrue XIX: gravitational waves. Linear theory and general considerations

Lectrue XIX: gravitational waves. Linear theory and general considerations
- Select activity Lecture19.1: linearization of Einstein equations. Plane wave solution in vacuum and its properties
  
  Kaltura Video Resource
  
  Lecture19.1: linearization of Einstein equations. Plane wave solution in vacuum and its properties Kaltura Video Resource
- Select activity Lecture19.2: TT gauge, plus and cross polarization and detection principle
  
  Kaltura Video Resource
  
  Lecture19.2: TT gauge, plus and cross polarization and detection principle Kaltura Video Resource
Select section Lecture XX: gravitational waves from binary systems, strain amplitude and GW luminosity

Lecture XX: gravitational waves from binary systems, strain amplitude and GW luminosity
- Select activity Lecture20.1: GW equations with source term: slow motion approximation and solution for a binary system
  
  Kaltura Video Resource
  
  Lecture20.1: GW equations with source term: slow motion approximation and solution for a binary system Kaltura Video Resource
- Select activity Lecture20.2: GW luminosity and inclination-polarization averaged strain
  
  Kaltura Video Resource
  
  Lecture20.2: GW luminosity and inclination-polarization averaged strain Kaltura Video Resource
Select section Lecture XXI: binary evolution under GW emission, standard sirens and the zoology of binary GW sources

Lecture XXI: binary evolution under GW emission, standard sirens and the zoology of binary GW sources
- Select activity Lecture21.1: binary evolution under GW emission: orbital shrinking and measurement of binary period derivative
  
  Kaltura Video Resource
  
  Lecture21.1: binary evolution under GW emission: orbital shrinking and measurement of binary period derivative Kaltura Video Resource
- Select activity Lecture21.2: standard sirens (incomplete for technical problem, check recording from last year below)
  
  Kaltura Video Resource
  
  Lecture21.2: standard sirens (incomplete for technical problem, check recording from last year below) Kaltura Video Resource
- Select activity Lecture21.2bis: binary evolution and stanadard sirens (from 2020-2021)
  
  Kaltura Video Resource
  
  Lecture21.2bis: binary evolution and stanadard sirens (from 2020-2021) Kaltura Video Resource
- Select activity Lecture21.2bisbis: the binary gravitational wave source zoology (from 2020-2021)
  
  Kaltura Video Resource
  
  Lecture21.2bisbis: the binary gravitational wave source zoology (from 2020-2021) Kaltura Video Resource
Select section Lecture XXII: testing general relativity with pulsars in binary systems: setting the stage

Lecture XXII: testing general relativity with pulsars in binary systems: setting the stage
- Select activity Lecture22.1: pulsars in binaries, introduction to the concept of timing.
  
  Kaltura Video Resource
  
  Lecture22.1: pulsars in binaries, introduction to the concept of timing. Kaltura Video Resource
- Select activity Lecture22.2: pulsars in binaries: definition of the binary orbital elements.
  
  Kaltura Video Resource
  
  Lecture22.2: pulsars in binaries: definition of the binary orbital elements. Kaltura Video Resource
Select section Lecture XXIII: constructing a timing model for a pulsar in a relativistic binary

Lecture XXIII: constructing a timing model for a pulsar in a relativistic binary
- Select activity Lecture23.1: constructing a timing model; connection between proper and coordinate time
  
  Kaltura Video Resource
  
  Lecture23.1: constructing a timing model; connection between proper and coordinate time Kaltura Video Resource
- Select activity Lecture23.2: derivation of the Einstein delay
  
  Kaltura Video Resource
  
  Lecture23.2: derivation of the Einstein delay Kaltura Video Resource
Select section Lecture XXIV: full timing model, tests of general relativity and notable systems

Lecture XXIV: full timing model, tests of general relativity and notable systems
- Select activity Lecture24.1: propagation effects: Shapiro and Roemer delays
  
  Kaltura Video Resource
  
  Lecture24.1: propagation effects: Shapiro and Roemer delays Kaltura Video Resource
- Select activity Lecture24.2: full timing model, post Keplerian parameters and tests of GR (Hulse-Taylor pulsar and 'binary pulsar)'
  
  Kaltura Video Resource
  
  Lecture24.2: full timing model, post Keplerian parameters and tests of GR (Hulse-Taylor pulsar and 'binary pulsar)' Kaltura Video Resource
Select section Lecture XXV: massive black hole cosmic history: general framework

Lecture XXV: massive black hole cosmic history: general framework
- Select activity Lecture25.1: massive black hole in galaxy centers, observational facts
  
  Kaltura Video Resource
  
  Lecture25.1: massive black hole in galaxy centers, observational facts Kaltura Video Resource
- Select activity Lecture25.2: hierarchical clustering framework. Seed black hole formation in high redshift dark matter halos
  
  Kaltura Video Resource
  
  Lecture25.2: hierarchical clustering framework. Seed black hole formation in high redshift dark matter halos Kaltura Video Resource
Select section Lecture XXVI: growing black holes, spherical and disk-like accretion

Lecture XXVI: growing black holes, spherical and disk-like accretion
- Select activity Lecture26.1: possible routs to MBH growth, Bondi (spherical) accretion
  
  Kaltura Video Resource
  
  Lecture26.1: possible routs to MBH growth, Bondi (spherical) accretion Kaltura Video Resource
- Select activity Lecture26.2: adding angular momentum: disk accretion, radiative efficiency, Eddington limit and exponential mass growth
  
  Kaltura Video Resource
  
  Lecture26.2: adding angular momentum: disk accretion, radiative efficiency, Eddington limit and exponential mass growth Kaltura Video Resource
Select section Lecture XXVII: growing black holes, mass and spin evolution, Soltan argument and scaling relations

Lecture XXVII: growing black holes, mass and spin evolution, Soltan argument and scaling relations
- Select activity Lecture27.1: exponential growth and spin evolution. The problem of Quasars at z=7
  
  Kaltura Video Resource
  
  Lecture27.1: exponential growth and spin evolution. The problem of Quasars at z=7 Kaltura Video Resource
- Select activity Lecture27.2: the importance of radiatively efficient accretion: Soltan argument, mechanical feedback and M-sigma relation.
  
  Kaltura Video Resource
  
  Lecture27.2: the importance of radiatively efficient accretion: Soltan argument, mechanical feedback and M-sigma relation. Kaltura Video Resource
Select section Lecture XVIII: massive black hole binary dynamics

Lecture XVIII: massive black hole binary dynamics
- Select activity Lecture28.1: the phases of MBHB formation and evolution. Definition of the final parsec problem
  
  Kaltura Video Resource
  
  Lecture28.1: the phases of MBHB formation and evolution. Definition of the final parsec problem Kaltura Video Resource
- Select activity Lecture28.2: solving the final parsec problem: binary hardening in a stellar background
  
  Kaltura Video Resource
  
  Lecture28.2: solving the final parsec problem: binary hardening in a stellar background Kaltura Video Resource