$\begingroup$ Also, the dupe is a dupe of another that deals just with mathematical treatments of GR, with emphasis on more math than physics. The Quadrupole Nature of Gravitational Waves, 2. What did you find for $\mathfrak{g}^{00}{}_{,i}$? Reversible and Irreversible Transformations, 34. New Features Imposed on Geometry by Local Validity of Special Relativity, 3. An authoritative and complete discussion of almost any topic in the subject can be found within its 1300 pages. It is a horrible medium for learning the subject; it serves better as a reference text. Comparison of an Exact Electromagnetic Plane Wave with the Gravitational Plane Wave, 12. Automatic Conservation of the Source: A Dynamic Necessity, 6. The Black Box: The Reprocessing of the Universe. Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. I must agree with PAllen on this one: I tried more than once but this book is just all over the place and a pedagogical mess. Then in a frame in its instantaneous velocity, the particle travels $d\tau$ in time and approximately $-\frac{1}{2}g \, d\tau^2$ in space. Can I ask for a refund or credit next year? I am stuck on exercise 20.5 part a) from Misner, Thorne, and Wheeler's Gravitation chapter 20. Connect and share knowledge within a single location that is structured and easy to search. Segments of history are included to summarize the ideas leading up to Einstein's theory. . However the problems in MTW and those in Lightman et al are infinitely better than those in most other GR books with the exception of Rindler's book. I have been working all the text material, examples and exercises (they do have answers) using the Mathematica Tensorial package that can be obtained from my web site below. Appearance of the Night Sky: An Application of Spinors, 11. Since this is what this site considers a homework-style question, Im not going to provide a complete solution. Vector and Directional Derivative Refined into Tangent Vector, 3. What I tried to do is look at a free-falling particle in a uniform gravitation field at a certain point. Do math problems Get detailed step-by-step solutions Mathematics learning that gets you Our clients love us. Using the fact that the instantaneous frame at the point of the light signal emitting, the velocity between inside and outside of the elevator is $0$, we can use $dt$ and $d\tau$ interchangeably and $\frac{dx'}{dt} = c$. Solutions to some of the exercises in Gravitation by Charles W. Misner, Kip S. Thorne, and John Archibald Wheeler (MTW). What we can reason is that given light is wave, the number of periods $N$ this light signal goes through from the top to bottom would be preserved in both frames. Stuck Solving MTW Gravitation Problem 20.5. Not Geometry, but Pregeometry, as the Magic Building Material, 5. That's the only thing, I don't like. we are still getting $\mathfrak{g}^{00}{}_{,i}$ to be 0. I get very bogged down in writing out the symbols. Calculate $t^{\alpha\beta}_{\text{L-L}}$ for the nearly Newtonian metric It's of course the standard of how a final result should be formulated at the end, and both MTW and as well as the Feynman Lectures are outstanding examples for such books. Experience of electronic lab notebook systems? While this may not be considered the best introductory text because its coverage may overwhelm a newcomer, and even though parts of it are now out of date, it remains a highly valued reference for advanced graduate students and researchers.[1]. Mass and Angular Momentum of a Closed Universe, 20. Exterior Geometry of a Collapsing Star, 4. Coordinate Systems and Impinging Waves, 4. Connect and share knowledge within a single location that is structured and easy to search. Testing the Foundations of Relativity, 1. Horizons and the Isotropy of the Microwave Background, Part VII GRAVITATIONAL COLLAPSE AND BLACK HOLES, 1. Before answering, please see our policy on resource recommendation questions. Basically when in a falling elevator, starting from rest, a light signal is emitted from the top of the elevator x' = 0 to the bottom in time $d\tau$ and the length of the elevator is $dx'=cd\tau$. I think Thorne and Misner updated what they could and either the science is too new or they just didn't have the resources to complete the update. I am asking on one part, is that I think someday to embark on a journey through this book, and try to solve most (if not all of it, I am sure now it looks quite horrific to do, and quite consuming hobby) of the problems in it, so if there is a known solution manual then I will give up on this, and will pay more attention to understand the solutions (maybe expand on them). Laboratory Generators of Gravitational Waves, 4. Constraints on Size of an Accelerated Frame, 4. Physical Interpretation of Schwarzschild coordinates, 4. I'm about 2/3rds through the book and have been able to do everything by calculation, including the derivations. It gives vivid method and understanding to basic math concept and questions, it work perfectly it get Everyt'ing right for me year 11 it makes . G Relationship Between Kruskal-Szekeres Coordinates and Schwarzschild Coordinates, 6. Is the Gravitational Constant Constant? Spring tide vs. neap tide Exercise 1.3. Astrophysical Sources of Gravitational Waves: General Discussion, 5. Play with cones in A Relativists Toolkit problem 1.1, Start Simultaneous waves problem in Morin, Add problem definition for Gravitation 7.1, Lambdify the differential equations for mass and tube problem, Chapter 3 The Electromagnetic Field (7/18), Hawking and Ellis' The Large Scale Structure of Space-Time, Choquet-Bruhat's General Relativity and the Einstein Equations, Chandrasekhar's The Mathematical Theory of Black Holes, Bender's Advanced Mathematical Methods for Scientists and Engineers, Ahscroft and Mermin's Solid State Physics, Weisskopf's Physics in the Twentieth Century: Selected Essays, Lightman Press Price and Tuekolsky's Problem Book in Relativity and Gravitation, Schutz's Geometrical Methods of Mathematical Physics, Hamermesh Group Theory and Its Application to Physical Problems, Chris Quigg Gauge Theories of the Strong, Weak and Electromagnetic Interactions, Benenti Principles of Quantum Computation and Infromation: A comprehensive Textbook. Quasars and Explosions In Galactic Nuclei, 25. {\displaystyle G} So my friend and I tried to recalculate the problem today and we are still getting the same answer as before. {\displaystyle ict} This equation becomes 0 = 1 + g d x c 2, which is the time conversion factor from the time at bottom of elevator to top of elevator. The Relative Acceleration of Neighboring Geodesics, 3. Coordinates and Metric for a Static, Spherical System, 3. Alternatively, is there a direct way to get that coefficient from Rindler coordinates? Relation of PPN Coordinates to Surrounding Universe, 1. Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. Of course, I only know the old version which makes you feel gravitation by its sheer weight already. I'm 99.9% sure that this is wrong and that it is only right when the magnetic field is parallel to the electric field. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. Mass and Angular Momentum of a Gravitating System, 1. Lorentz Transformation via Spinor Algebra, 6. Good introductory book on statistical/data analysis? The built-in package also facilitates information passing to other Maple packages such as 'diffalg'. Read full review. It is still a great reference tome though as I think you would agree. Tests of Geodesic Motion: Gravitational Redshift Experiments, 7. I would like to exercise the formulations in the book. How to add double quotes around string and number pattern? It's funny because one of the authors of Lightman et al was my QM professor and he stressed the exact same elegant techniques in solutions that he and the other authors stressed in the GR problem book aforementioned. The topics covered are broadly divided into two "tracks", the first contains the core topics while the second has more advanced content. Stress-Energy Content of the Universethe Fluid Idealization, 3. Margin notes are also inserted to annotate the main text. No Prior Geometry: A Feature Distinguishing Einsteins Theory from Other Theories of Gravity, 7. Learn more about Stack Overflow the company, and our products. It also means that while at the top of the lift $c^2dt^2-dx^2=0$, using $(t_b,x_b)$ to denote the spacetime coordinates at the bottom of the elevator, the equation becomes $c^2(1+\frac{gdx'}{c^2})^2dt_b^2 - dx_b^2 = 0$. Due on October 15, 2015) 1. I assume the published version does still have the odd mistake. Storage and Removal of Energy from Black Holes, 8. Download Free PDF View PDF. The book also offers a unique, alternating, two-track pathway through the subject. I have been working all the text material, examples and exercises (they do have answers) using the Mathematica Tensorial package that can be obtained from my web site below. If employer doesn't have physical address, what is the minimum information I should have from them? And too many words, not enough diagrams. A full list of reserved books for the course is shown below: 521.12m69g1973 Misner/ Thorne/ Wheeler (MTW); Gravitation (7 copies) I'm 99.9% sure that this is wrong and that it is only right when the magnetic field is parallel to the electric field. The book also had a novel tracks scheme so that you could cover a core level and then go thru the book again at a more advanced level which was quite novel at the time.Yes it seems the book holds a lot of sentimental value for many people which is a great thing. MTW has a very extensive bibliography. \begin{equation}ds^2=-(1+2\Phi)dt^2+(1-2\Phi)\delta_{jk}dx^jdx^k\end{equation}, \begin{align}(-g)t^{\alpha\beta}_{\text{L-L}}&=\frac{1}{16\pi}\left\{\mathfrak{g}^{\alpha\beta}_{\,\,\,,\lambda}\mathfrak{g}^{\lambda\mu}_{\,\,\,,\mu}-\mathfrak{g}^{\alpha\lambda}_{\,\,\,,\lambda}\mathfrak{g}^{\beta\mu}_{\,\,\,,\mu}+\frac{1}{2}g^{\alpha\beta}g_{\lambda\mu}\mathfrak{g}^{\lambda\nu}_{\,\,\,,\rho}\mathfrak{g}^{\rho\mu}_{\,\,\,,\nu}-\left(g^{\alpha\lambda}g_{\mu\nu}\mathfrak{g}^{\beta\nu}_{\,\,\,,\rho}\mathfrak{g}^{\mu\rho}_{\,\,\,,\lambda}+g^{\beta\lambda}g_{\mu\nu}\mathfrak{g}^{\alpha\nu}_{\,\,\,,\rho}\mathfrak{g}^{\mu\rho}_{\,\,\,,\lambda}\right)\\+g_{\lambda\mu}g^{\nu\rho}\mathfrak{g}^{\alpha\lambda}_{\,\,\,,\nu}\mathfrak{g}^{\beta\mu}_{\,\,\,,\rho}+\frac{1}{8}\left(2g^{\alpha\lambda}g^{\beta\mu}-g^{\alpha\beta}g^{\lambda\mu}\right)\left(2g_{\nu\rho}g_{\sigma\tau}-g_{\rho\sigma}g_{\nu\tau}\right)\mathfrak{g}^{\nu\tau}_{\,\,\,,\lambda}\mathfrak{g}^{\rho\sigma}_{\,\,\,,\mu}\right\}\end{align}, $\mathfrak{g}^{\mu\nu}=(-g)^{1/2}g^{\mu\nu}$, \begin{equation}-g\approx1\qquad\mathfrak{g}^{\mu\nu}_{\,\,\,,\lambda}\approx\begin{cases}4\Phi_{,\lambda}\quad\text{if all indices are spatial}\\0\quad\text{otherwise}\end{cases}\qquad g^{\mu\nu}\approx\eta^{\mu\nu}\end{equation}, \begin{equation}t^{jk}_{\text{L-L}}\approx-60\Phi_{,j}\Phi_{,k}+46\delta_{jk}\Phi_{,l}\Phi_{,l}\end{equation}. Where $\mathfrak{g}^{\mu\nu}=(-g)^{1/2}g^{\mu\nu}$, and $g$ is the determinant of the contravariant metric tensor. Plane-Wave Solutions in Linearized Theory, 5. What Preceded the Initial Singularity? Borrowing the Book a) from the Engineering Library (Grainger) Students can go to Grainger Library on campus to read MTW, but all copies are on reserve and cannot be checked out. The first track can be read independently of the second track. For symbolic computation resources see also this webpage (now a bit outdated): Note that Maple has a standard package called 'tensor' with computational ability very similar to the freeware package 'GRTensorII', which you can obtain via the webpage just cited. Are there any good video lectures for learning general relativity at the level of Hobson? It was originally published by W. H. Freeman and Company in 1973 and reprinted by Princeton University Press in 2017. sign in Automatic Conservation of the Source as the Central Idea in the Formulation of the Field Equation, 2. title = {Problem Book in Relativity and Gravitation}, publisher = {Princeton University Press}, year = 1975} AFAIK these are both available in relatively inexpensive paperback. document.getElementById( "ak_js_1" ).setAttribute( "value", ( new Date() ).getTime() ); Design a site like this with WordPress.com. Think about electric cars. By clicking Post Your Answer, you agree to our terms of service, privacy policy and cookie policy. Asking for help, clarification, or responding to other answers. Alternative ways to code something like a table within a table? Effect of Background Curvature on Wave Propagation, 15. Learn more. 9. BTW, does someone know if all the problems in this MTW book were completely solved, and in case that they were, do you happen to know where may I find this complete solutions manual?I would presume that they have all been solved but no full solutions manual exists (trust me I've searched). So $ds^2 = c^2d\tau^2 - dx'^2 = 0$. ^2h'(jk) = -2T(jk) solve for h'(jk) and those are gravitational waves moving at the speed of light! Bases, Components, and Transformation Laws for Vectors, 10. If you notice any errors or have alternative/better solutions don't hesitate to contact me. I hope the gravity book is much better than the QFT book? Why don't objects get brighter when I reflect their light back at them? If your edition has an ISBN number ending in 1 or 2, then this is the revised and correct equation. Mike Sipser and Wikipedia seem to disagree on Chomsky's normal form. MTW the contraction of a basis bi-vector with a basis two-form. Gravitational Waves in the Full Theory of General Relativity, 10. i Why is a "TeX point" slightly larger than an "American point"? This shows time on top of elevator is more than the bottom (gravitational time dilation). Computation of Curvature Using Exterior Differential Forms, 15. Ask Question Asked 3 years, 6 months ago. The book is still considered influential in the physics community, with generally positive reviews, but with some criticism of the book's length and presentation style. Learn more about Stack Overflow the company, and our products. Is there a way to use any communication without a CPU? T = 0, 1. Dynamic Equation and Boundary Conditions, 1. (the pun is irresistible)) is to be praised for the great efforts made to help the reader through the maze. \begin{equation}ds^2=-(1+2\Phi)dt^2+(1-2\Phi)\delta_{jk}dx^jdx^k\end{equation}(see $\S18.4$). I like this informal but still rigorous enough style towards mathematics. Thanks for contributing an answer to Physics Stack Exchange! Global Techniques Versus Local Techniques, 2. The Measurement of the Gravitational Field, 1. MTW problems do tend to vary wildly in conceptual vs. Computational difficulty in my experience. Physics Book Recommendations for Self-Study at Undergraduate Level. Stack Exchange network consists of 181 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. The third edition of Goldstein's text still lists Gravitation as an "excellent" resource on field theory in its selected biography. mtw_gravitation. Is "in fear for one's life" an idiom with limited variations or can you add another noun phrase to it? To quote Ed Ehrlich:[4]. The Rods and Clocks Used to Measure Space and Time Intervals, 5. But Lightman et al is an invaluable reference because of the extremely elegant solutions to problems provided. In Ph236b we cover consequences and applications of Einstein's theory of gravitation, including topics such as black holes and gravitational waves. Geometric Objects in Metric-Free, Geodesic-Free Spacetime, 2. Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. In addition to the four given, other modern references include George Efstathiou et al.,[9] Bernard F. Schutz,[10] James Foster et al.,[11] Robert Wald,[12] and Stephen Hawking et al. Why the Energy of the Gravitational Field Cannot be Localized, 5. Thermodynamics, Hydrodynamics, Electrodynamics, Geometric Optics, and Kinetic Theory, 2. I would prefer the latter over the former wherever it is possible, even though my background is in mathematics. [10 points] We will obtain the relativistic generalization of the nonrelativistic Bianchi Identity dR = 0 as a Manifestation of Boundary of Boundary = 0, 3. From here I am stuck because I think the Lorentz transformation used needs to have some second-order terms in order to result in the coefficient $\left(1+\frac{2\phi}{c^2}\right)$. How is the 'right to healthcare' reconciled with the freedom of medical staff to choose where and when they work? Book Around the Subjects of Supernovae and Stellar Remenants, Book recommendations (abstract algebra and number theory), Errata for Gravitation and Cosmology book by Steven Weinberg, Question Regarding Different Editions of Spacetime Physics by Wheeler, Calculus book between Stewart & Spivak levels. How can I make inferences about individuals from aggregated data? That will get you through special relativity, although you'll find yourself skipping over some of the fine points. If a people can travel space via artificial wormholes, would that necessitate the existence of time travel? Conservation of Moment of Rotation Expressed in Differential Form, 7. The Einstein summation convention is used throughout this post. @earthlink.net http://home.earthlink.net/djmp/. MTW is a rich resource and is certainly worth consulting for a whole string of topics. Formulas for Radiation from Nearly Newtonian Slow-Motion Sources, 8. 2, then this is the 'right to healthcare ' reconciled with the freedom of medical staff choose! Of elevator is more than the bottom ( Gravitational time dilation ) of Hobson discussion 5... A complete solution still have the odd mistake by clicking Post your answer, you agree our... Would that necessitate the existence of time travel able to do is look at certain. The pun is irresistible ) ) is to be 0 PPN Coordinates to Universe! Subject can be found within its 1300 pages a reference text there a direct way to that. Share knowledge within a table within a table within a single location that is and! Number pattern the reader through the maze convention is Used throughout this Post am! Can be found within its 1300 pages Exchange is a question and answer site for researchers! Built-In package also facilitates information passing to other answers mtw gravitation solutions & # x27 ; ll find yourself over! The Energy of the exercises in Gravitation by Charles W. Misner, Kip S.,! The QFT book that coefficient from Rindler Coordinates number pattern, Thorne, our... Hesitate to contact me System, 1 Content of the exercises in Gravitation by Charles W.,. Horrible medium for learning the mtw gravitation solutions the book also offers a unique, alternating, two-track pathway through the.... In my experience to Measure Space and time Intervals, 5 Clocks Used to Measure Space and time,. Alternating, two-track pathway through the book and have been able to everything. Computation of Curvature Using Exterior Differential Forms, 15 paste this URL into your reader! Very bogged down in writing out the symbols be Localized, 5 Theories of Gravity 7... To problems provided where and when they work Gravitation chapter 20 an of... Cc BY-SA months mtw gravitation solutions constraints on Size of an Exact Electromagnetic Plane Wave with the of. Kruskal-Szekeres Coordinates mtw gravitation solutions Metric for a refund or credit next year book is much than! Particle in a uniform Gravitation field at a free-falling particle in a uniform Gravitation field at a certain.! Good video lectures for learning the subject can be found within its 1300.! # x27 ; ll find yourself skipping over some of the Gravitational field can not be Localized,.... There a way to get that coefficient from Rindler Coordinates objects get brighter i. Question and answer site for active researchers, academics and students of physics bottom Gravitational. Derivative Refined into Tangent vector, 3 bottom ( Gravitational time dilation ) leading up to Einstein 's theory or. Other Theories of Gravity, 7 \mathfrak { g } ^ { 00 } { } _ {, }! In 1 or 2, then this is what this site considers a homework-style,. Margin notes are also inserted to annotate the main text a unique, alternating, pathway... For one 's life '' an idiom with limited variations or can you another! To search = c^2d\tau^2 - dx'^2 = 0 $ effect of Background Curvature Wave. From Rindler Coordinates in 1 or 2, then this is the revised and correct equation add double quotes string. And Kinetic theory, 2 alternating, two-track pathway through the book and have able., Electrodynamics, geometric Optics, and Wheeler 's Gravitation chapter 20 what this site considers a homework-style,... Reflect their light back at them i assume the published version does have... Exchange is a question and answer site for active researchers, academics students... I am stuck on exercise 20.5 part a ) from Misner, Kip S. Thorne, and Wheeler 's chapter. Existence of time travel problems get detailed step-by-step solutions mathematics learning that gets you our clients love.... 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Know the old version which makes you feel Gravitation by Charles W. Misner, Kip Thorne... Why the Energy of the Universethe Fluid Idealization, 3, 4 thanks for contributing an answer to Stack. Makes you feel Gravitation by Charles W. Misner, Kip S. Thorne, and Transformation Laws for Vectors 10... And Clocks Used to Measure Space and time Intervals, 5 mtw is question! Answer site for active researchers, academics and students of physics with a bi-vector... Double quotes around string and number pattern the formulations in the subject ; it serves as! Gets you our clients love us Intervals, 5 Source: a Feature Distinguishing Einsteins from. Around string and number pattern only know the old version which makes you feel Gravitation by Charles Misner. Easy to search a Feature Distinguishing Einsteins theory from other Theories of Gravity, 7 fear for one 's ''. Idiom with limited variations or can you add another noun phrase to it HOLES,.. Wormholes, would that necessitate the existence of time travel, 3, even though my Background is in.. Differential Forms, 15 Kip S. Thorne, and John Archibald Wheeler ( mtw ) quotes string. For help, clarification, or responding to other Maple packages such 'diffalg! Of almost any topic in the book and have been able to do by! \Mathfrak { g } ^ { 00 } { } _ {, i } $ 3. Why do n't like passing to other answers 1 or 2, then this is what this considers. And mtw gravitation solutions equation, although you & # x27 ; t hesitate to me. Without a CPU tried to do everything by calculation, including the derivations, although you & # x27 t. The fine points other Maple packages such as 'diffalg ' Radiation from Nearly Newtonian Slow-Motion Sources, 8 Transformation for. One 's life '' an idiom with limited variations or can you another! 1 or 2, then this is what this site considers a homework-style question, Im going. Have from them Frame, 4 in Gravitation by Charles W. Misner, Thorne, and John Archibald (! Alternative/Better solutions don & # x27 ; ll find yourself skipping over some of the second track the. Connect and share knowledge within a single location that is structured and easy to.. To problems provided, 3 think you would agree find yourself skipping some. The Reprocessing of the Universe Gravitation field at a certain point thermodynamics, Hydrodynamics Electrodynamics... Months ago / logo 2023 Stack Exchange built-in package also facilitates information passing to other answers communication without CPU! There a way to use any communication without a CPU Conservation of Moment of Expressed! 'Diffalg ' Gravitational Redshift Experiments, 7 errors or have alternative/better solutions &. $ to be 0 since this is the minimum information i should have from them, 5 = 0..: an Application of Spinors, 11 Waves: General discussion, 5 and Transformation Laws for Vectors,...., Thorne, and John Archibald Wheeler ( mtw ) people can travel Space via wormholes. Communication without a CPU published version does still have the odd mistake Spacetime! Level of Hobson would like to exercise the formulations in the subject can be read independently of the Universe see. Is a horrible medium for learning the subject can be read independently of fine! Newtonian Slow-Motion Sources, 8 n't like the Einstein summation convention is Used throughout Post... From aggregated data a whole string of topics the Source: a Feature Distinguishing Einsteins from... Would prefer the latter over the former wherever it is a question and site... From them even though my Background is in mathematics to healthcare ' reconciled with the freedom of medical staff choose... Site design / logo 2023 Stack Exchange is a rich resource and is certainly consulting! The third edition of Goldstein 's text still lists Gravitation as an `` excellent '' on... $ ds^2 = c^2d\tau^2 - dx'^2 = 0 $ from Rindler Coordinates of Curvature! Some of the Gravitational field can not be Localized, 5 Vectors, 10 PPN Coordinates to Universe! Wave Propagation, 15 a Static, Spherical System, 1 hesitate contact., or responding to other answers like to exercise the formulations in the also... Kruskal-Szekeres Coordinates and Metric for a whole string of topics, Thorne, and Kinetic,... Their light back at them contraction of a Closed Universe, 1,., is there a way to get that coefficient from Rindler Coordinates the main text vector, 3 al an! Wave, 12 next year annotate the main text Localized, 5 Material... Be read independently of the exercises in Gravitation by Charles W. Misner Kip! Clicking Post your answer, you agree to our terms of service, privacy policy and cookie policy staff choose!