does anyone know good books and/or other sources of information regarding black hole mathematics/physics? Currently I'm reading the black hole wars by Leonard Susskind; it seems to be a collection of general explanations rather than a mathematical resource.
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I’m studying a PhD in Theoretical Physics (quantum field theory, to be specific), but I would like to learn more about black holes (and related areas. Does anyone have any suggestions for textbooks/available notes on these subjects for people without much background in them? Obviously I’m very comfortable with mathematics and physics in general so I’m not looking for “pop science” material.
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I am only an interested layman in cosmology and GR. In recent years, we have learned that black holes indeed exist in the universe and that almost all galaxies contain massive black holes in their centers. Black holes, in essence only devour other (stellar) matter and they also swallow each other as has been demonstrated by the gravitational wave discoveries. Is it possible that black holes eventually will "eat" most or even all normal and dark matter of the universe? And could this, and a merging of black holes, lead to a situation where all the universe ends up being a few or even only one black hole?
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I want to learn some advanced topics in GR, such as . However nearly no textbooks on GR contain this area, such as Wald, MTW, Hawking, Carroll and  Zee's. Can anyone recommend some textbooks or papers giving the elaboration in detail?
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Can someone suggest a textbook that treats general relativity from a rigorous mathematical perspective? Ideally, such a book would   Prove all theorems used. Use modern "mathematical notation" as opposed to "physics notation", especially with respect to linear algebra and differential geometry. Have examples that illustrate both computational and theoretical aspects. Have a range of exercises with varying degrees of difficulty, with answers.   An ideal text would read a lot more like a math book than a physics book and would demand few prerequisites in physics. Bottom line is that I would like a book that provides an axiomatic development of general relativity clearly and with mathematical precision works out the details of the theory.  Addendum (1): I did not intend to start a war over notation. As I said in one of the comments below, I think indicial notation together with the summation convention is very useful. The coordinate-free approach has its uses as well and I see no reason why the two can't peacefully coexist. What I meant by "mathematics notation" vs. "physics notation" is the following: Consider, as an example, one of the leading texts on smooth manifolds, John Lee's Introduction to Smooth Manifolds. I am very accustomed to this notation and it very similar to the notation used by Tu's Introduction to Manifolds, for instance, and other popular texts on differential geometry. On the other hand, take Frankel's Geometry of Physics. Now, this is a nice book but it is very difficult for me to follow it because 1) Lack of proofs and 2)the notation does not agree with other math texts that I'm accustomed to. Of course, there are commonalities but enough is different that I find it really annoying to try to translate between the two...  Addendum (2):  For the benefit of future readers, In addition to suggestions below, I have found another text that also closely-aligns with the criteria I stated above. It is, Spacetime: Foundations of General Relativity and Differential Geometry by Marcus Kriele. The author begins by discussing affine geometry, analysis on manifolds, multilinear algebra and other underpinnings and leads into general relativity at roughly the midpoint of the text. The notation is also fairly consistent with the books on differential geometry I mentioned above.
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I'm looking for good book recommendations for preparing for the International Physics Olympiad. As stated on the , the topics covered are about the same as those in the first year or two of a physics degree:        Mechanics: kinematics, dynamics, celestial mechanics, hydrodynamics   Electromagnetism: Maxwell's equations, circuits, matter in EM fields   Waves: damped/driven harmonic oscillators, waves, interference and diffraction, geometrical optics   Modern: special relativity, matter waves, particle and nuclear physics   Thermodynamics: laws of thermodynamics, heat engines, phase transitions      However, there's less of an emphasis on complicated calculations, and more of an emphasis on problem solving and insight. For example, multivariable calculus is almost never used; instead many questions can be elegantly solved by symmetry. I'm looking for textbooks or problem books to bring me to this level, starting from the level of high school physics.
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I'm not a physicist but I'm interested in , and I do not know how to start learning about it. What would be a good book to read to start learning about this topic?
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I was wondering if you could tell me about some self-learning resources for linear model theories. My professor has been using "A First Course in Linear Model Theory, Ravishanker and Dey. Publisher: CRC." I found this kinda difficult. My major is mathematics. Thank you so much for your time!
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Black hole theory involves space (or space-time), itself, being sucked into the black-hole, with the event horizon marking the point at which space/space-time is moving faster than the speed of light. I find it really hard to picture how this could be happening while objects maintained a reasonable stable orbit around black holes. If we take the stars that orbit the super massive black hole at the centre of the Milky Way, the orbital dynamics are used to calculate the mass of the black hole, in the normal way. In other words not taking account of the fact space is rushing at some speed inwards toward the black-hole.  I appreciate I'm missing some knowledge here. That's the motivation for asking the question.
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I am looking for a textbook that treats the subject of Special Relativity from a geometric point of view, i.e. a textbook that introduces the theory right from the start in terms of 4-vectors and Minkowski tensors, instead of the more traditional "beginners" approach. Would anyone have a recommendation for such a textbook ?  I already have decent knowledge of the physics and maths of both SR and GR ( including vector and tensor calculus ), but would like to take a step back and expand and broaden my intuition of the geometry underlying SR, as described by 4-vectors and tensors. What I do not need is another "and here is the formula for time dilation..." type of text, of which there are thousands out there, but something much more geometric and in-depth.  Thanks in advance.
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There are no book recommendations for Astrophysics here. I will write my own answer, but I am also interested in what are others' views on the question (I will NOT mark my own answer as the best one).
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I've taken up self-study of math. (How smart can that be?) I've just about finished a course in real analysis which spent a lot of time on metric spaces and some time revisiting calculus.  I was thinking of trying abstract algebra. I would appreciate any book recommendations.  Thanks in advance.  Andrew
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I am almost finishing Gilbert Strang's book "An introduction to linear algebra" (plus video lectures at MIT OCW). First and foremost, I would like to suggest this course for everyone. It has been incredibly illuminating.   I would like to continue studying linear algebra, with particular focus on different properties of matrices and the transition to more general linear spaces (I am a physicist so Hilbert spaces and etc. are of particular interest).   Does anyone have a a good recommendation of books/resources/etc.?
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I'm interested in learning physics. I do realize that the subject is large and that it would be easier if I had a specific area of interest. However, I do not. I suppose I want to learn about the fundamentals of it all; the axioms that combine all physics fields. Or, in other words, a high school physics class.   Specifically, a book or series of videos would be helpful. I looked over MIT and unfortunately the material wasn't for me. I don't mean to be "picky" so I am not completely ruling out any resource just yet.   Thanks in advance.
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I'm interested in learning how to use geometry and topology in physics. Could anyone recommend a book that covers these topics, preferably with some proofs, physical applications, and emphasis on geometrical intuition? I've taken an introductory course in real analysis but no other higher math.
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How would you explain string theory to non-physicists such as myself? I'm especially interested in how plausible is it and what is needed to successfully prove it?
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I'm interested in reading Dr. Peter Woit's article, Quantum field theory and representation theory: a sketch .  What math and physics background would be needed?  (A list of topics from the two fields would be more than sufficient.)  With great appreciation and regards.
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How exactly does time slow down near a black hole? I have heard this as a possible way of time traveling, and I do understand that it is due in some way to the massive gravity around a black hole, but how exactly does that massive gravity slow down time?