Carlo Rovelli

Quantum gravity

You'll probably know about the difficulty of quantising gravity, and of the arguments over the viability of String Theory as a solution. But what alternatives are there? Well the main contender is Loop Quantum Gravity (LQG). Carlo Rovelli's book Quantum Gravity gives a research level treatment of this subject. The first part of the book looks at general relativity, classical mechanics and quantum theory, including quantum field theory. However, these chapters don't try to teach the reader these subjects. Rather they provide a new way of looking at them for readers who have already devoted some time to studying them.

The second part of the book gets on to Loop Quantum Gravity itself, showing the importance of background independence - rather than being given, space and time emerge as consequences of the theory. There is a chapter on the applications of the subject, such as quantum cosmology and black hole entropy. The book concludes with appendices looking at the history of LQG and at its philosophical implications. There is no doubt that this book requires a lot of prior knowledge, but I feel that it would be very useful to anyone wishing to learn about LQG, as it has plenty of recommendations of books which will give you this knowledge, and so it maps out a path for those wishing to study the subject.

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Hardcover 455 pages
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Published: 2004 Cambridge University Press

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Hardcover 455 pages
ISBN: 0521837332
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Weight:2.25 lbs

Published: 2004 Cambridge University Press

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Hardcover 455 pages
ISBN: 0521837332
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Published: 2004 Cambridge University Press

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Product Description
Quantum gravity poses the problem of merging quantum mechanics and general relativity, the two great conceptual revolutions in the physics of the twentieth century. The loop and spinfoam approach, presented in this book, is one of the leading research programs in the field. The first part of the book discusses the reformulation of the basis of classical and quantum Hamiltonian physics required by general relativity. The second part covers the basic technical research directions. Appendices include a detailed history of the subject of quantum gravity, hard-to-find mathematical material, and a discussion of some philosophical issues raised by the subject. This fascinating text is ideal for graduate students entering the field, as well as researchers already working in quantum gravity. It will also appeal to philosophers and other scholars interested in the nature of space and time.

Product Description

Quantum gravity poses the problem of merging quantum mechanics and general relativity, the two great conceptual revolutions in the physics of the twentieth century. The loop and spinfoam approach, presented in this book, is one of the leading research programs in the field. The first part of the book discusses the reformulation of the basis of classical and quantum Hamiltonian physics required by general relativity. The second part covers the basic technical research directions. Appendices include a detailed history of the subject of quantum gravity, hard-to-find mathematical material, and a discussion of some philosophical issues raised by the subject. This fascinating text is ideal for graduate students entering the field, as well as researchers already working in quantum gravity. It will also appeal to philosophers and other scholars interested in the nature of space and time.

Good books on Quantum Gravity ****
I'm a new comer to quantum gravity. Although I only have some background in classical mechanics and relativity , I thought the books is quite approachable as most of the terms are explained cearly following the logical reasioning. A side note: Besides string and loop quantum gravity, the book also mentioned differernt version of theoretical framework such as tiwster theory and Euclidean quantum gravity. Its quite disappointing that the book didn't go into detail of each theory and possibly give a comparison between different theory.

Good books on Quantum Gravity ****

I'm a new comer to quantum gravity. Although I only have some background in classical mechanics and relativity , I thought the books is quite approachable as most of the terms are explained cearly following the logical reasioning. A side note: Besides string and loop quantum gravity, the book also mentioned differernt version of theoretical framework such as tiwster theory and Euclidean quantum gravity. Its quite disappointing that the book didn't go into detail of each theory and possibly give a comparison between different theory.

A change in paradigm *****
This is a excellent book. Dr. Rovelli is attempting a rare exercise in that he is trying to substantially change a physicists view of the world. This book is equal parts philosphy and mathematics and tries to instill in the reader an intuition that most books never achieve. The book is not for someone who likes to be given an equation or model and then is shown how to "turn the crank" to obtain an answer or those who think the theory is finished as long as you constrain yourself to stay away from the pathologies. (Think Standard Model and a single photon that has the energy density of a black hole. ) Most present day theories have these pathologies, patches and inconsistencies precisely because they were built from previous approximate theories and then were modified when problems showed up. This book starts with a clean sheet of paper and asks, "What should a relativistic quantum theory of gravity look like?' "What are the mathematical structures that are needed and how do they fit together to give us a consistent view of the world?" Indeed the book goes back through classical mechanics and quantum just to show what the mathematical structures do in each of these early theories. The philosophical basis, the "why is this important", for the combination of quantum ideas and the philosophy of relativism is very well laid out in this book. That is what I was seeking, "the why". Theories that throw another constraint on the space of solutions, or add more symmetry just to fix problems that pop up means that they have serious flaws in their basic foundations that need to be addressed differently. Dr. Rovelli shows that loop quantum gravity has the same clean sparseness as it's foundations and is very appealing. The discrete quantization of volume and area is a major sucess. If you like having your world view changed, a new paradigm, I highly recommend this book.

A change in paradigm *****

This is a excellent book. Dr. Rovelli is attempting a rare exercise in that he is trying to substantially change a physicists view of the world. This book is equal parts philosphy and mathematics and tries to instill in the reader an intuition that most books never achieve. The book is not for someone who likes to be given an equation or model and then is shown how to "turn the crank" to obtain an answer or those who think the theory is finished as long as you constrain yourself to stay away from the pathologies. (Think Standard Model and a single photon that has the energy density of a black hole. ) Most present day theories have these pathologies, patches and inconsistencies precisely because they were built from previous approximate theories and then were modified when problems showed up. This book starts with a clean sheet of paper and asks, "What should a relativistic quantum theory of gravity look like?' "What are the mathematical structures that are needed and how do they fit together to give us a consistent view of the world?" Indeed the book goes back through classical mechanics and quantum just to show what the mathematical structures do in each of these early theories. The philosophical basis, the "why is this important", for the combination of quantum ideas and the philosophy of relativism is very well laid out in this book. That is what I was seeking, "the why". Theories that throw another constraint on the space of solutions, or add more symmetry just to fix problems that pop up means that they have serious flaws in their basic foundations that need to be addressed differently. Dr. Rovelli shows that loop quantum gravity has the same clean sparseness as it's foundations and is very appealing. The discrete quantization of volume and area is a major sucess. If you like having your world view changed, a new paradigm, I highly recommend this book.

Good LQG book, but title is deceptive ***
I have to start by saying that I think the title is very deceptive. This is hardly a book on quantum gravity, more accurately it's a book on one approach to quantum gravity, namely loop quantum gravity. No other approaches to quantum gravity are seriously considered. Even the current leading candidate for providing a quantum theory of gravity, i.e. string theory, is only presented as a straw man to show how poorly it fares (in the author's mind) compared to loop quantum gravity. The book begins with a brief discussion on general issues in quantum gravity and by presenting some background in general relativity. He contends that it is wrong to approach quantum gravity by treating general relativity as just another field theory. Two central themes of his approach to quantum gravity seem to be that one should not ignore the fact that general relativity is a theory of spacetime and the correct way to approach finding the quantum theory of gravity (although I don't believe he uses these exact words) is to quantize spacetime. This will lead to spacetime having a discrete structure and will provide a cutoff that will remove the ultraviolet divergences of quantum field theory (this is somewhat different from the way they are removed in string theory). While I agree both of these ideas have a lot of intuitive appeal, it's clear that the jury is still out. The treatment of general relativity focuses mainly on things that will be useful for developing loop quantum gravity. This includes formulating it in terms of connections (instead of the metric) and presenting it in the Hamiltonian form. I found it a bit odd that he included discussions of "Newton's bucket" and Mach's principle(s), while they have some historical importance, it seems unlikely (to me anyway) that these will provide any important insights going forward. After providing some background in quantum mechanics and quantum field theory he goes on to develop loop quantum gravity. The presentation is clear, the most up-to-date I've come across. One of the results that is of most interest is his outline of the calculation of black hole entropy by counting states. The degrees of freedom are given by quantum fluctuations of the horizon. The result, up to an undetermined multiplicative constant, is the Bekenstein entropy. This is presented as an impressive accomplishment of loop quantum gravity. The string theory calculation is dismissed (in a footnote) as having only been done for the unphysical case of an extremal black hole. Rather than just taking the author's word for it, I'd suggest reading the string theory derivation, for example in Polchinski's book "String Theory" Volume II chapter 14. Then decide which, if either, is more impressive, but there are a couple of things to note. One the string theory calculation that the author refers to gets the multiplicative factor right. Another, which the author ignores or is unaware of, is that Polchinski gives a qualitative argument that string theory gets the entropy of the Schwarzschild black hole correct to within an undetermined multiplicative factor. I thought the appendix that covered the history of quantum gravity great. One could argue that anybody that has a realistic chance of understanding the material in the book would need a fairly strong background in general relativity and quantum field theory. Such readers would easily recognize that this book hardly provides a balanced perspective. Even so, I wish the book had a more appropriate title. As a book on loop quantum gravity I think it's pretty good and rates about four stars. As a book on quantum gravity I don't see how it could rate more than one or two stars.

Good LQG book, but title is deceptive ***

I have to start by saying that I think the title is very deceptive. This is hardly a book on quantum gravity, more accurately it's a book on one approach to quantum gravity, namely loop quantum gravity. No other approaches to quantum gravity are seriously considered. Even the current leading candidate for providing a quantum theory of gravity, i.e. string theory, is only presented as a straw man to show how poorly it fares (in the author's mind) compared to loop quantum gravity.

The book begins with a brief discussion on general issues in quantum gravity and by presenting some background in general relativity.

He contends that it is wrong to approach quantum gravity by treating general relativity as just another field theory. Two central themes of his approach to quantum gravity seem to be that one should not ignore the fact that general relativity is a theory of spacetime and the correct way to approach finding the quantum theory of gravity (although I don't believe he uses these exact words) is to quantize spacetime. This will lead to spacetime having a discrete structure and will provide a cutoff that will remove the ultraviolet divergences of quantum field theory (this is somewhat different from the way they are removed in string theory). While I agree both of these ideas have a lot of intuitive appeal, it's clear that the jury is still out.

The treatment of general relativity focuses mainly on things that will be useful for developing loop quantum gravity. This includes formulating it in terms of connections (instead of the metric) and presenting it in the Hamiltonian form. I found it a bit odd that he included discussions of "Newton's bucket" and Mach's principle(s), while they have some historical importance, it seems unlikely (to me anyway) that these will provide any important insights going forward.

After providing some background in quantum mechanics and quantum field theory he goes on to develop loop quantum gravity. The presentation is clear, the most up-to-date I've come across.

One of the results that is of most interest is his outline of the calculation of black hole entropy by counting states. The degrees of freedom are given by quantum fluctuations of the horizon. The result, up to an undetermined multiplicative constant, is the Bekenstein entropy. This is presented as an impressive accomplishment of loop quantum gravity. The string theory calculation is dismissed (in a footnote) as having only been done for the unphysical case of an extremal black hole. Rather than just taking the author's word for it, I'd suggest reading the string theory derivation, for example in Polchinski's book "String Theory" Volume II chapter 14. Then decide which, if either, is more impressive, but there are a couple of things to note. One the string theory calculation that the author refers to gets the multiplicative factor right. Another, which the author ignores or is unaware of, is that Polchinski gives a qualitative argument that string theory gets the entropy of the Schwarzschild black hole correct to within an undetermined multiplicative factor.

I thought the appendix that covered the history of quantum gravity great.

One could argue that anybody that has a realistic chance of understanding the material in the book would need a fairly strong background in general relativity and quantum field theory. Such readers would easily recognize that this book hardly provides a balanced perspective. Even so, I wish the book had a more appropriate title. As a book on loop quantum gravity I think it's pretty good and rates about four stars. As a book on quantum gravity I don't see how it could rate more than one or two stars.

A book for those ``who are able to think" *****
It could be that LQG isn't as popular in the physics community as it deserves to bebecause a lot of people don't appreciate an important aspect of classical GR (covered in part I of Rovelli's book). Below I give a quick and easy argument whichuses only the very basics of GR making it accessible to anyone and also rather difficult to dismiss. The hope is that by giving this argument the browser will see that there may actually be something to LQG and have a look at this book. Ok. In 1912, while developing GR, Einstein realised something he found rather alarming. Here's one version of the argument: it starts with an utterly straightforward mathematical observation. Here is written the SHO differential equation twice Eq(1) d^2 f(x) / dx^2 + f(x) = 0 and Eq(2) d^2 g(y) / dy^2 + g(y) = 0 except in Eq(1) the independent variable is x and in Eq(2) the independent variable is y. Once we find out that a solution to Eq(1) is f(x) = cos x, we immediately know that g(y) = cos y solves Eq(2). This observation combined with general covariance has profound implications for GR. Assume pure gravity first. Say we have two coordinate systems, x-coordinates and y-coordinates. General covariance demands the equations of motion have the same form in both coordinate systems, that is, we have exactly the same differential equation to solve in both coordinate systems except in one the independent variable is x and in the other the independent variable is y. Once we find a metric function g_{ab}(x) that solves the EQM in the x-coordinates we immediately know (by exactly the same reasoning as above) that the same function written as a function of y solves the EOM in the y-coordinates. As both metric functions have the same functional form but belong to different coordinate systems, they impose different spacetime geometries. Thus we have generated a second DISTINCT solution! Now comes the problem. Say the two coordinate systems coincide at first, but at some point after t=0 we allow them to differ. We then have two solutions, they both have the same initial conditions yet they impose different spacetime geometries. The conclusion is that GR does NOT determine the proper-time between spacetime points! Bummer! The argument I have given (or rather a refinement of it) is what's known as Einstein's hole argument. It is straightforward to include matter - we have a larger set of differential equations but they still have the same form in all coordinates systems, the same argument applies and again we obtain two solutions with the same initial conditions which impose different spacetime geometries. It is very important to note that we could not have generated these extra distinct solutions if spacetime were fixed and non-dynamical, and so the resolution (background independence) only comes about when we allow spacetime to be dynamical. We can interpret these extra distinct solutions as follows. For simplicity we first assume there is no matter. Define a metric function g'_{ab} whose value at P is given by the value of g_{ab} at P_0, i.e. g'_{ab}(P) = g_{ab}(P_0). Now consider the coordinate system which assigns to P the same coordinate values that P_0 has in the x-coordinates. We then have g'_{ab} (y_0=u_0,y_1=u_1, y_2=u_2, y_3=u_3) = g_{ab} (x_0=u_0,x_1=u_1, x_2=u_2 , x_3=u_3), where u_0,u_1,u_2,u_3 range over the permissible coordinate values. But this is precisely the condition that the two metric functions have the same functional form! We see that the new solution is generated by dragging the original metric function over the spacetime manifold while keeping the coordinate lines `attached' (it is important to realise that we are not performing a coordinate transformation here). This is what's known as an active diffeomorphsm (coordinate transformations are called passive diffeomorphisms). It should be easy to see that when we have matter present, simultaneously performing an active diffeomorphism on the gravitational and matter fields generates the new distinct solution. It was only in 1915 when Einstein finally resolved the hole argument that GR was born. The resolution (mainly taken from Rovelli's book) is: as GR does not determine the distance between spacetime points, how the gravitational and matter fields are located over spacetime, and so the values they take at spacetime points, can have no physical meaning. What GR does determine are the mutual relations that exist between the gravitational field and the matter fields (i.e. the value the gravitational field takes where the matter field takes such and such value). From these mutual relations we can form a notion of matter being located with respect to the gravitational field and vice-versa, (see Rovelli's book for exposition). What Einstein discovered was that physical entities are located with respect to one another only and not with respect to the spacetime manifold. This is what background independence is! And what Einstein was referring to when he made his remark "beyond my wildest expectations". We learnt from SR that position and motion only have meaning relative to an inertial frame; GR teaches us that there are no background geometric reference systems at all, position and motion have become completely relative! LQG people regard background independence as a central tenet in their approach to quantizing gravity - a classical symmetry that ought to be preserved by the quantum theory if we are to be truly quantizing geometry(=gravity). One immediate consequence is that LQG is UV-finite because small and large distances are gauge equivalent. A less immediate consequence is that the theory can be formulated at a level of rigour of mathematical physics, which is nothing to sneeze at in the absence of experimental guidance. Perturbative string theory (as well as a number of non-perturbative developments) is not background independent, the scattering matrix they calculate is not invariant under active diffeomorphisms. Of the end of 2005 Rovelli et al have put together the formulism to calculate background independent scattering amplitudes (this is no easy task!). Rovelli has obtained Newton's law from the fully non-perturbative quantum theory. However it is still early days and this result is not yet convincing established. To finish off, we should see this book on more shelves and in more book stores!! Also, look out for another LQG book by Thomas Thiemann and Peter Woit's book in April.

A book for those ``who are able to think" *****

It could be that LQG isn't as popular in the physics community as it deserves to bebecause a lot of people don't appreciate an important aspect of classical GR (covered in part I of Rovelli's book). Below I give a quick and easy argument whichuses only the very basics of GR making it accessible to anyone and also rather difficult to dismiss. The hope is that by giving this argument the browser will see that there may actually be something to LQG and have a look at this book.

Ok. In 1912, while developing GR, Einstein realised something he found rather alarming. Here's one version of the argument: it starts with an utterly straightforward mathematical observation. Here is written the SHO differential equation twice Eq(1) d^2 f(x) / dx^2 + f(x) = 0 and Eq(2) d^2 g(y) / dy^2 + g(y) = 0 except in Eq(1) the independent variable is x and in Eq(2) the independent variable is y. Once we find out that a solution to Eq(1) is f(x) = cos x, we immediately know that g(y) = cos y solves Eq(2). This observation combined with general covariance has profound implications for GR. Assume pure gravity first. Say we have two coordinate systems, x-coordinates and y-coordinates. General covariance demands the equations of motion have the same form in both coordinate systems, that is, we have exactly the same differential equation to solve in both coordinate systems except in one the independent variable is x and in the other the independent variable is y. Once we find a metric function g_{ab}(x) that solves the EQM in the x-coordinates we immediately know (by exactly the same reasoning as above) that the same function written as a function of y solves the EOM in the y-coordinates. As both metric functions have the same functional form but belong to different coordinate systems, they impose different spacetime geometries. Thus we have generated a second DISTINCT solution! Now comes the problem. Say the two coordinate systems coincide at first, but at some point after t=0 we allow them to differ. We then have two solutions, they both have the same initial conditions yet they impose different spacetime geometries. The conclusion is that GR does NOT determine the proper-time between spacetime points! Bummer! The argument I have given (or rather a refinement of it) is what's known as Einstein's hole argument. It is straightforward to include matter - we have a larger set of differential equations but they still have the same form in all coordinates systems, the same argument applies and again we obtain two solutions with the same initial conditions which impose different spacetime geometries. It is very important to note that we could not have generated these extra distinct solutions if spacetime were fixed and non-dynamical, and so the resolution (background independence) only comes about when we allow spacetime to be dynamical. We can interpret these extra distinct solutions as follows. For simplicity we first assume there is no matter. Define a metric function g'_{ab} whose value at P is given by the value of g_{ab} at P_0, i.e. g'_{ab}(P) = g_{ab}(P_0). Now consider the coordinate system which assigns to P the same coordinate values that P_0 has in the x-coordinates. We then have g'_{ab} (y_0=u_0,y_1=u_1, y_2=u_2, y_3=u_3) = g_{ab} (x_0=u_0,x_1=u_1, x_2=u_2 , x_3=u_3), where u_0,u_1,u_2,u_3 range over the permissible coordinate values. But this is precisely the condition that the two metric functions have the same functional form! We see that the new solution is generated by dragging the original metric function over the spacetime manifold while keeping the coordinate lines `attached' (it is important to realise that we are not performing a coordinate transformation here). This is what's known as an active diffeomorphsm (coordinate transformations are called passive diffeomorphisms). It should be easy to see that when we have matter present, simultaneously performing an active diffeomorphism on the gravitational and matter fields generates the new distinct solution.

It was only in 1915 when Einstein finally resolved the hole argument that GR was born. The resolution (mainly taken from Rovelli's book) is: as GR does not determine the distance between spacetime points, how the gravitational and matter fields are located over spacetime, and so the values they take at spacetime points, can have no physical meaning. What GR does determine are the mutual relations that exist between the gravitational field and the matter fields (i.e. the value the gravitational field takes where the matter field takes such and such value). From these mutual relations we can form a notion of matter being located with respect to the gravitational field and vice-versa, (see Rovelli's book for exposition). What Einstein discovered was that physical entities are located with respect to one another only and not with respect to the spacetime manifold. This is what background independence is! And what Einstein was referring to when he made his remark "beyond my wildest expectations". We learnt from SR that position and motion only have meaning relative to an inertial frame; GR teaches us that there are no background geometric reference systems at all, position and motion have become completely relative! LQG people regard background independence as a central tenet in their approach to quantizing gravity - a classical symmetry that ought to be preserved by the quantum theory if we are to be truly quantizing geometry(=gravity). One immediate consequence is that LQG is UV-finite because small and large distances are gauge equivalent. A less immediate consequence is that the theory can be formulated at a level of rigour of mathematical physics, which is nothing to sneeze at in the absence of experimental guidance.

Perturbative string theory (as well as a number of non-perturbative developments) is not background independent, the scattering matrix they calculate is not invariant under active diffeomorphisms. Of the end of 2005 Rovelli et al have put together the formulism to calculate background independent scattering amplitudes (this is no easy task!). Rovelli has obtained Newton's law from the fully non-perturbative quantum theory. However it is still early days and this result is not yet convincing established.

To finish off, we should see this book on more shelves and in more book stores!! Also, look out for another LQG book by Thomas Thiemann and Peter Woit's book in April.

Clarity and Precision Prevail *****
I'm experiencing some hesitation as this is hands down the most advanced book that I have ever 'reviewed' and, in fact, ever read. I have only completed Part 1 -"Relativistic Foundations" as I have to go deeper into Differential Geometry before proceeding into Part II - "Loop Quantum Gravity." Part 1 is a pretty amazing, often philosophical introduction both describing the problem that QG is trying to approach (the contradictions between QFT and GR)and laying the foundation for LQG. It becomes clear (slowly) that our notions of space and time need serious overhauling before we can understand what LQG is all about. String theory doesn't have this problem as it more or less uses our 20th century notions of space and time as its framework. Sure, it adds a few dimensions and curls some up but it's pretty much still the same old space and time. LQG does not use this framework and rather seems to work towards a physics without time. Rovelli does a masterful job in Part 1 of slowly, clearly and precisely helping the reader to make this transition. Most memorable to me is his discusson of the ten meanings of time where he demonstrates that we have already stripped time of many of its seemingly inherent properties ('flowing', 'measured' to name 2). He just proposes stripping off a few others! I'm looking forward to Part II.

Clarity and Precision Prevail *****

I'm experiencing some hesitation as this is hands down the most advanced book that I have ever 'reviewed' and, in fact, ever read. I have only completed Part 1 -"Relativistic Foundations" as I have to go deeper into Differential Geometry before proceeding into Part II - "Loop Quantum Gravity." Part 1 is a pretty amazing, often philosophical introduction both describing the problem that QG is trying to approach (the contradictions between QFT and GR)and laying the foundation for LQG. It becomes clear (slowly) that our notions of space and time need serious overhauling before we can understand what LQG is all about. String theory doesn't have this problem as it more or less uses our 20th century notions of space and time as its framework. Sure, it adds a few dimensions and curls some up but it's pretty much still the same old space and time. LQG does not use this framework and rather seems to work towards a physics without time. Rovelli does a masterful job in Part 1 of slowly, clearly and precisely helping the reader to make this transition. Most memorable to me is his discusson of the ten meanings of time where he demonstrates that we have already stripped time of many of its seemingly inherent properties ('flowing', 'measured' to name 2). He just proposes stripping off a few others! I'm looking forward to Part II.

Excellent Review *****
This is an excellent introduction to quantum gravity. It introduces all of the concepts well, and covers all of the important work that has been done. Although the focus is on loop quantum gravity and spinfoams, it provides ample coverage of general relativity and quantum mechanics and the problems with different proposals for quantum gravity. I will be keeping this book on my desk and referencing it often!

Excellent Review *****

This is an excellent introduction to quantum gravity. It introduces all of the concepts well, and covers all of the important work that has been done.

Although the focus is on loop quantum gravity and spinfoams, it provides ample coverage of general relativity and quantum mechanics and the problems with different proposals for quantum gravity.

I will be keeping this book on my desk and referencing it often!