Chapter 15
Observational Evidence for Black
Holes
By denition an isolated black hole should be a difcult
object to observe directly. However, if black holes exist
they should often be accreting surrounding matter and interacting gravitationally with their
Chapter 14
Black Holes as Central Engines
Black holes imply a fundamental modication of our understanding of space and time. But at a more mundane
level they also are of great practical importance in astronomy because they can be extremely efcient sources
Chapter 13
Rotating Black Holes
The Schwarzschild solution, which is appropriate outside
a spherical, non-spinning mass distribution, was discovered in 1916. It was not until 1963 that a solution corresponding to spinning black holes was discovered by New
Chapter 12
Quantum Black Holes
Classically, the fundamental structure of curved spacetime ensures that nothing can escape from within the
Schwarzschild event horizon. That is an emphatically deterministic statement. But what about quantum mechanics, which
Chapter 11
Lecture: Spherical Black Holes
One of the most spectacular consequences of general relativity is the
prediction that gravitational elds can become so strong that they can
effectively trap even light.
Space becomes so curved that there are no p
Chapter 10
Neutron Stars and General Relativity
Neutron stars are relevant to our discussion of general relativity on
two levels.
They are of considerable intrinsic interest because their quantitative description requires solution of the Einstein equatio
Chapter 9
Lecture: The Schwarzschild
Spacetime
One of the simplest solutions to the Einstein equations
corresponds to a metric that describes the gravitational
eld exterior to a static, spherical, uncharged mass without angular momentum and isolated from
Chapter 8
Lecture: General Theory of
Relativity
We shall now employ the central ideas introduced in the previous two
chapters:
The metric and curvature of spacetime
The principle of equivalence
The principle of general covariance
to construct the gener
Chapter 7
Curved Spacetime and General
Covariance
In this chapter we generalize the discussion of preceding chapters to extend covariance to more general curved
spacetimes.
145
146
CHAPTER 7. CURVED SPACETIME AND GENERAL COVARIANCE
7.1 Covariance and Poin
Chapter 6
Lecture: Principle of Equivalence
The general theory of relativity rests upon two principles that are in
fact related:
The principle of equivalence
The principle of general covariance
6.1 Inertial and Gravitational Mass
1. The inertial mass is
Chapter 5
Lecture: Lorentz Invariant
Dynamics
In the preceding chapter we introduced the Minkowski
metric and covariance with respect to Lorentz transformations between inertial systems. This was shown to lead to
the basic properties of special relativity
Chapter 4
Lecture: Lorentz Covariance
To go beyond Newtonian gravitation we must consider,
with Einstein, the intimate relationship between the curvature of space and the gravitational eld.
Mathematically, this extension is bound inextricably
to the geom
Chapter 3
Covariance and Tensor Notation
The term covariance implies a formalism in which the
laws of physics maintain the same form under a specied
set of transformations.
EXAMPLE: Lorentz covariance implies equations that are
constructed in such a way t
Chapter 1
Introduction
General relativity is a theory of gravity that represents a
radical new view of space and time.
It supercedes Newtonian mechanics and Newtonian
gravity.
It reduces to those theories in the limit of velocities
that are small with r
Chapter 2
Coordinate Systems and
Transformations
A physical system has a symmetry under some operation
if the system after the operation is observationally indistinguishable from the system before the operation.
Example: A perfectly uniform sphere has a
s
Chapter 14
Supernovae
Supernovae represent the catastrophic death of certain stars. They are
among the most violent events in the Universe,
They typically produce about 1053 erg, with a large fraction of
this energy released in the rst second of the expl
Chapter 14
Nova Explosions and X-Ray Bursts
Some stars appear to increase their brightness suddenly
at visible (and other) wavelengths by very large amounts
over a period of days, and then slowly dim back to obscurity over a matter of months.
The increas
Chapter 12
Accreting Binary Systems
Observation suggests that more than half of the stars are binaries.
When the components of a binary are well separated, they largely
behave as isolated stars unless there are strong winds.
However, if the semimajor ax
Chapter 11
White Dwarfs and Neutron Stars
Red giants will eventually consume all their accessible nuclear fuel.
After ejection of the envelope, the cores of these stars
shrink to the very hot, very dense objects that we call
white dwarfs.
An even more d
Chapter 10
Stellar Pulsations and Variability
One commonplace of modern astronomy that would have
been highly perplexing for ancient astronomers is that
many stars vary their light output by detectable amounts
over time.
In some cases these variations ar
Chapter 9
Red Giant Evolution
Life on the main sequence is characterized by the stable
burning of hydrogen to helium under conditions of hydrostatic equilibrium.
While the star is on the main sequence the inner composition is changing, but there is littl
Chapter 8
The Sun: Life and Times on the
Main Sequence
In the preceding chapter we considered the collapse of a
protostar to the main sequence In this chapter we examine
the nature of life on the main sequence for such a star.
The essence of life on the
Chapter 7
Formation of Stars
Substantial direct and indirect information indicates that
stars are born in nebulae.
Basics are well understood, many details are not.
We shall have to gloss over various sticky points with
assumptions that will be justied
Chapter 6
Energy Transport in Stars
In the stars
Most energy production in stars takes place in the
deep interior where density and temperatures are
high, but
Most electromagnetic energy that we see coming
from stars is radiated from the photosphere, wh
Chapter 5
Stellar Energy Production
Stars have three primary sources of energy:
1. Heat left over from earlier processes,
2. Gravitational energy,
3. Thermonuclear energy.
We shall see that
Gravitational energy plays an important role in various stages o
Chapter 4
Hydrostatic Equilibrium
A fundamental property of main sequence stars like our
Sun is their stability over long periods of time.
In the case of the Sun, the geological record indicates
that it has been emitting energy at its present rate for
se
Chapter 1
Some Properties of Stars
This chapter is assigned reading for review.
1
2
CHAPTER 1. SOME PROPERTIES OF STARS
Chapter 2
The HertzsprungRussell Diagram
This chapter is assigned reading for review.
3
4
CHAPTER 2. THE HERTZSPRUNGRUSSELL DIAGRAM
Cha