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 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 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 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 16
The Hubble Expansion
The observational characteristics of the Universe coupled
with theoretical interpretation to be discussed further in
subsequent chapters, allow us to formulate a standard picture of the nature of our Universe.
16.1
The Stan
Chapter 17
Energy and Matter in the Universe
The history and fate of the Universe ultimately turn on
how much matter, energy, and pressure it contains, since
these components of the stressenergy tensor couple to
gravity and determine how self-gravitation
Chapter 18
Friedmann Cosmologies
Let us now consider solutions of the Einstein equations
that may be relevant for describing the large-scale structure of the Universe and its evolution following the big
bang. To do so, we must rst make a choice for the fo
Chapter 19
Evolution of the Universe
In the preceding Chapter we demonstrated that the Friedmann equations correspond to the Einstein equations
when the metric takes the RobertsonWalker form. In this
chapter we consider solutions of the Friedmann equation
Chapter 20
The Big Bang
The Universe began life in a very hot, very dense state
that we call the big bang. In this chapter we apply the
Friedmann equations to the early Universe in an attempt
to understand the most important features of the big bang
model
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 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 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 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 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 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 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
7.1
CHAPTER 7. CURVED SPACETIME AND GENERAL COVARIANCE
Covariance and Poin
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 21
Beyond the Classical Big Bang
The big bang is our standard model for the origin of the Universe and
has been for almost half a century. This place in well earned.
At a broader conceptual level, all of modern cosmology rests
on observations (fo