BLACK HOLES: the OTHER SIDE of INFINITY General Information
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Active Galactic Nuclei: a Brief Introduction
Active Galactic Nuclei: a brief introduction Manel Errando Washington University in St. Louis The discovery of quasars 3C 273: The first AGN z=0.158 2 <latexit sha1_base64="4D0JDPO4VKf1BWj0/SwyHGTHSAM=">AAACOXicbVDLSgMxFM34tr6qLt0Ei+BC64wK6kIoPtCNUMU+oNOWTJq2wWRmSO4IZZjfcuNfuBPcuFDErT9g+hC09UC4h3PvJeceLxRcg20/W2PjE5NT0zOzqbn5hcWl9PJKUQeRoqxAAxGoskc0E9xnBeAgWDlUjEhPsJJ3d9rtl+6Z0jzwb6ETsqokLZ83OSVgpHo6754xAQSf111JoK1kTChN8DG+uJI7N6buYRe4ZBo7di129hJ362ew5NJGAFjjfm3V4m0nSerpjJ21e8CjxBmQDBogX08/uY2ARpL5QAXRuuLYIVRjooBTwZKUG2kWEnpHWqxiqE+MmWrcuzzBG0Zp4GagzPMB99TfGzGRWnekZya7rvVwryv+16tE0DysxtwPI2A+7X/UjASGAHdjxA2uGAXRMYRQxY1XTNtEEQom7JQJwRk+eZQUd7POfvboej+TOxnEMYPW0DraRA46QDl0ifKogCh6QC/oDb1bj9ar9WF99kfHrMHOKvoD6+sbuhSrIw==</latexit> <latexit sha1_base64="H7Rv+ZHksM7/70841dw/vasasCQ=">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</latexit> The power source of quasars • The luminosity (L) of quasars, i.e. how bright they are, can be as high as Lquasar ~ 1012 Lsun ~ 1040 W. • The energy source of quasars is accretion power: - Nuclear fusion: 2 11 1 ∆E =0.007 mc =6 10 W s g− -
Undergraduate Thesis on Supermassive Black Holes
Into the Void: Mass Function of Supermassive Black Holes in the local universe A Thesis Presented to The Division of Mathematics and Natural Sciences Reed College In Partial Fulfillment of the Requirements for the Degree Bachelor of Arts Farhanul Hasan May 2018 Approved for the Division (Physics) Alison Crocker Acknowledgements Writing a thesis is a long and arduous process. There were times when it seemed further from my reach than the galaxies I studied. It’s with great relief and pride that I realize I made it this far and didn’t let it overpower me at the end. I have so many people to thank in very little space, and so much to be grateful for. Alison, you were more than a phenomenal thesis adviser, you inspired me to believe that Astro is cool. Your calm helped me stop freaking out at the end of February, when I had virtually no work to show for, and a back that ached with every step I took. Thank you for pushing me forward. Working with you in two different research projects were very enriching experiences, and I appreciate you not giving up on me, even after all the times I blanked on how to proceed forward. Thank you Johnny, for being so appreciative of my work, despite me bringing in a thesis that I myself barely understood when I brought it to your table. I was overjoyed when I heard you wanted to be on my thesis board! Thanks to Reed, for being the quirky, intellectual community that it prides itself on being. -
Chapter 22 Neutron Stars and Black Holes Units of Chapter 22 22.1 Neutron Stars 22.2 Pulsars 22.3 Xxneutron-Star Binaries: X-Ray Bursters
Chapter 22 Neutron Stars and Black Holes Units of Chapter 22 22.1 Neutron Stars 22.2 Pulsars 22.3 XXNeutron-Star Binaries: X-ray bursters [Look at the slides and the pictures in your book, but I won’t test you on this in detail, and we may skip altogether in class.] 22.4 Gamma-Ray Bursts 22.5 Black Holes 22.6 XXEinstein’s Theories of Relativity Special Relativity 22.7 Space Travel Near Black Holes 22.8 Observational Evidence for Black Holes Tests of General Relativity Gravity Waves: A New Window on the Universe Neutron Stars and Pulsars (sec. 22.1, 2 in textbook) 22.1 Neutron Stars According to models for stellar explosions: After a carbon detonation supernova (white dwarf in binary), little or nothing remains of the original star. After a core collapse supernova, part of the core may survive. It is very dense—as dense as an atomic nucleus—and is called a neutron star. [Recall that during core collapse the iron core (ashes of previous fusion reactions) is disintegrated into protons and neutrons, the protons combine with the surrounding electrons to make more neutrons, so the core becomes pure neutron matter. Because of this, core collapse can be halted if the core’s mass is between 1.4 (the Chandrasekhar limit) and about 3-4 solar masses, by neutron degeneracy.] What do you get if the core mass is less than 1.4 solar masses? Greater than 3-4 solar masses? 22.1 Neutron Stars Neutron stars, although they have 1–3 solar masses, are so dense that they are very small. -
Squashing and Spaghettification in Newtonian Gravitation
Revista Brasileira de Ensino de F´ısica, vol. 42, e20200278 (2020) Artigos Gerais www.scielo.br/rbef c b DOI: https://doi.org/10.1590/1806-9126-RBEF-2020-0278 Licenc¸aCreative Commons Squashing and spaghettification in Newtonian gravitation R. R. Machado*1 , A. C. Tort2 , C. A. D. Zarro2 1Centro Federal de Educa¸c˜aoTecnol´ogicaCelso Suckow da Fonseca, Rio de Janeiro, RJ, Brasil 2Universidade Federal do Rio de Janeiro, Instituto de F´ısica,Rio de Janeiro, RJ, Brasil Received on July 06, 2020. Revised on September 07, 2020. Accepted on October 08, 2020. Action films and sci-fi novels should be common resources in classrooms since they serve as examples and references involving physical situations. This is due to the abstract nature of many physical concepts, and the lack of references in students’ daily lives makes them more difficult to be visualized or imagined. In this work we bring a discussion of how we can resort to films and literary works in order to elucidate the concepts regarding tidal forces. To this effect, we have used the action film Total Recall (2012) to present the squashing effect and the classic of juvenile literature From Earth to the Moon (1865) to discuss the effect of spaghettification in the context of Newtonian mechanics. Keywords: Newtonian gravitation, non-inertial frames, tidal forces. 1. Introduction Earth to the Moon [3], see Figure 2. On Verne’s chap- ter XXIII, he describes the Projectile-Vehicle, to which Action movies and sci-fi novels can always be resorted to we will refer as Verne’s projectile, designed to trans- whenever we look for situations, or examples, capable of port adventurous people through space; more precisely motivating our students. -
Radio Observations of the Supermassive Black Hole at the Galactic Center and Its Orbiting Magnetar
Radio Observations of the Supermassive Black Hole at the Galactic Center and its Orbiting Magnetar Rebecca Rimai Diesing Honors Thesis Department of Physics and Astronomy Northwestern University Spring 2017 Honors Thesis Advisor: Farhad Zadeh ! Radio Observations of the Supermassive Black Hole at the Galactic Center and its Orbiting Magnetar Rebecca Rimai Diesing Department of Physics and Astronomy Northwestern University Honors Thesis Advisor: Farhad Zadeh Department of Physics and Astronomy Northwestern University At the center of our galaxy a bright radio source, Sgr A*, coincides with a black hole four million times the mass of our sun. Orbiting Sgr A* at a distance of 3 arc seconds (an estimated 0.1 pc) and rotating with a period of 3.76 s is a magnetar, or pulsar⇠ with an extremely strong magnetic field. This magnetar exhibited an X-ray outburst in April 2013, with enhanced, highly variable radio emission detected 10 months later. In order to better understand the behavior of Sgr A* and the magnetar, we study their intensity variability as a function of both time and frequency. More specifically, we present the results of short (8 minute) and long (7 hour) radio continuum observations, taken using the Jansky Very Large Array (VLA) over multiple epochs during the summer of 2016. We find that Sgr A*’s flux density (a proxy for intensity) is highly variable on an hourly timescale, with a frequency dependence that di↵ers at low (34 GHz) and high (44 GHz) frequencies. We also find that the magnetar remains highly variable on both short (8 min) and long (monthly) timescales, in agreement with observations from 2014. -
Active Galactic Nuclei
Active Galactic Nuclei • Optical spectra, distance, line width • Varieties of AGN and unified scheme • Variability and lifetime • Black hole mass and growth • Geometry: disk, BLR, NLR • Reverberation mapping • Jets and blazars • AGN spectra Optical spectrum of an AGN • Variety of different emission lines • Each line has centroid, area, width • There is also continuum emission Emission lines • Shift of line centroid gives recession velocity v/c = Δλ/λ. • The width is usually characterized by the “Full Width at Half Maximum”. For a Gaussian FHWM = 2.35σ. • The line width is determined by the velocity distribution of the line emitting gas, Δv/c = σ/λ. • Area is proportional to the number of detected line photons or the line flux. • Usually characterized by “equivalent width” or range in wavelength over which integration of the continuum produces the same flux as the line. Early observations of AGN • Very wide emission lines have been known since 1908. • In 1959, Woltjer noted that if the profiles are due to Doppler motion and the gas is gravitationally bound then v2 ~ GM/r. For v ~ 2000 km/s, we have 10 r M ≥10 ( 100 pc ) M Sun • So AGN, known at the time as Seyfert galaxies, must either have a very compact and luminous nucleus or be very massive. Quasars • Early radio telescopes found radio emission from stars, nebulae, and some galaxies. • There were also point-like, or star-like, radio sources which varied rapidly these are the `quasi-stellar’ radio sources or quasars. • In visible light quasars appear as points, like stars. Quasar optical spectra Redshift of 3C273 is 0.16. -
Closed Timelike Curves, Singularities and Causality: a Survey from Gödel to Chronological Protection
Closed Timelike Curves, Singularities and Causality: A Survey from Gödel to Chronological Protection Jean-Pierre Luminet Aix-Marseille Université, CNRS, Laboratoire d’Astrophysique de Marseille , France; Centre de Physique Théorique de Marseille (France) Observatoire de Paris, LUTH (France) [email protected] Abstract: I give a historical survey of the discussions about the existence of closed timelike curves in general relativistic models of the universe, opening the physical possibility of time travel in the past, as first recognized by K. Gödel in his rotating universe model of 1949. I emphasize that journeying into the past is intimately linked to spacetime models devoid of timelike singularities. Since such singularities arise as an inevitable consequence of the equations of general relativity given physically reasonable assumptions, time travel in the past becomes possible only when one or another of these assumptions is violated. It is the case with wormhole-type solutions. S. Hawking and other authors have tried to save the paradoxical consequences of time travel in the past by advocating physical mechanisms of chronological protection; however, such mechanisms remain presently unknown, even when quantum fluctuations near horizons are taken into account. I close the survey by a brief and pedestrian discussion of Causal Dynamical Triangulations, an approach to quantum gravity in which causality plays a seminal role. Keywords: time travel; closed timelike curves; singularities; wormholes; Gödel’s universe; chronological protection; causal dynamical triangulations 1. Introduction In 1949, the mathematician and logician Kurt Gödel, who had previously demonstrated the incompleteness theorems that broke ground in logic, mathematics, and philosophy, became interested in the theory of general relativity of Albert Einstein, of which he became a close colleague at the Institute for Advanced Study at Princeton. -
Light Rays, Singularities, and All That
Light Rays, Singularities, and All That Edward Witten School of Natural Sciences, Institute for Advanced Study Einstein Drive, Princeton, NJ 08540 USA Abstract This article is an introduction to causal properties of General Relativity. Topics include the Raychaudhuri equation, singularity theorems of Penrose and Hawking, the black hole area theorem, topological censorship, and the Gao-Wald theorem. The article is based on lectures at the 2018 summer program Prospects in Theoretical Physics at the Institute for Advanced Study, and also at the 2020 New Zealand Mathematical Research Institute summer school in Nelson, New Zealand. Contents 1 Introduction 3 2 Causal Paths 4 3 Globally Hyperbolic Spacetimes 11 3.1 Definition . 11 3.2 Some Properties of Globally Hyperbolic Spacetimes . 15 3.3 More On Compactness . 18 3.4 Cauchy Horizons . 21 3.5 Causality Conditions . 23 3.6 Maximal Extensions . 24 4 Geodesics and Focal Points 25 4.1 The Riemannian Case . 25 4.2 Lorentz Signature Analog . 28 4.3 Raychaudhuri’s Equation . 31 4.4 Hawking’s Big Bang Singularity Theorem . 35 5 Null Geodesics and Penrose’s Theorem 37 5.1 Promptness . 37 5.2 Promptness And Focal Points . 40 5.3 More On The Boundary Of The Future . 46 1 5.4 The Null Raychaudhuri Equation . 47 5.5 Trapped Surfaces . 52 5.6 Penrose’s Theorem . 54 6 Black Holes 58 6.1 Cosmic Censorship . 58 6.2 The Black Hole Region . 60 6.3 The Horizon And Its Generators . 63 7 Some Additional Topics 66 7.1 Topological Censorship . 67 7.2 The Averaged Null Energy Condition . -
Spacetime Warps and the Quantum World: Speculations About the Future∗
Spacetime Warps and the Quantum World: Speculations about the Future∗ Kip S. Thorne I’ve just been through an overwhelming birthday celebration. There are two dangers in such celebrations, my friend Jim Hartle tells me. The first is that your friends will embarrass you by exaggerating your achieve- ments. The second is that they won’t exaggerate. Fortunately, my friends exaggerated. To the extent that there are kernels of truth in their exaggerations, many of those kernels were planted by John Wheeler. John was my mentor in writing, mentoring, and research. He began as my Ph.D. thesis advisor at Princeton University nearly forty years ago and then became a close friend, a collaborator in writing two books, and a lifelong inspiration. My sixtieth birthday celebration reminds me so much of our celebration of Johnnie’s sixtieth, thirty years ago. As I look back on my four decades of life in physics, I’m struck by the enormous changes in our under- standing of the Universe. What further discoveries will the next four decades bring? Today I will speculate on some of the big discoveries in those fields of physics in which I’ve been working. My predictions may look silly in hindsight, 40 years hence. But I’ve never minded looking silly, and predictions can stimulate research. Imagine hordes of youths setting out to prove me wrong! I’ll begin by reminding you about the foundations for the fields in which I have been working. I work, in part, on the theory of general relativity. Relativity was the first twentieth-century revolution in our understanding of the laws that govern the universe, the laws of physics. -
Stable Wormholes in the Background of an Exponential F (R) Gravity
universe Article Stable Wormholes in the Background of an Exponential f (R) Gravity Ghulam Mustafa 1, Ibrar Hussain 2,* and M. Farasat Shamir 3 1 Department of Mathematics, Shanghai University, Shanghai 200444, China; [email protected] 2 School of Electrical Engineering and Computer Science, National University of Sciences and Technology, H-12, Islamabad 44000, Pakistan 3 National University of Computer and Emerging Sciences, Lahore Campus, Punjab 54000, Pakistan; [email protected] * Correspondence: [email protected] Received: 21 January 2020; Accepted: 3 March 2020; Published: 26 March 2020 Abstract: The current paper is devoted to investigating wormhole solutions with an exponential gravity model in the background of f (R) theory. Spherically symmetric static spacetime geometry is chosen to explore wormhole solutions with anisotropic fluid source. The behavior of the traceless matter is studied by employing a particular equation of state to describe the important properties of the shape-function of the wormhole geometry. Furthermore, the energy conditions and stability analysis are done for two specific shape-functions. It is seen that the energy condition are to be violated for both of the shape-functions chosen here. It is concluded that our results are stable and realistic. Keywords: wormholes; stability; f (R) gravity; energy conditions 1. Introduction The discussion on wormhole geometry is a very hot subject among the investigators of the different modified theories of gravity. The concept of wormhole was first expressed by Flamm [1] in 1916. After 20 years, Einstein and Rosen [2] calculated the wormhole geometry in a specific background. In fact, it was the second attempt to realize the basic structure of wormholes. -
Page 1 of 45 “Journey to a Black Hole”
“Journey to a Black Hole” Demonstration Manual What is a black hole? How are they made? Where can you find them? How do they influence the space and time around them? Using hands-on activities and visual resources from NASA's exploration of the universe, these activities take audiences on a mind-bending adventure through our universe. 1. How to Make a Black Hole [Stage Demo, Audience Participation] (Page 3) 2. The Little Black Hole That Couldn’t [Stage Demo, Audience Participation] (Page 6) 3. It’s A Bird! It’s a Plane! It’s a Supernova! [Stage Demo] (Page 10) 4. Where Are the Black Holes? [Stage Demo, Audience Participation] (Page 14) 5. Black Holes for Breakfast [Make-and-Take…and eat!] (Page 17) 6. Modeling a Black Hole [Cart Activity] (Page 19) 7. How to Spot a Black Hole [Stage Demo, Audience Participation] (Page 25) 8. Black Hole Hide and Seek [Cart Activity] (Page 29) 9. Black Hole Lensing [Stage Demo, Audience Participation] (Page 32) 10. Spaghettification [Make-and-Take] (Page 35) Many of these activities were inspired by or adapted from existing activities. Each such write-up contains a link to these original sources. In addition to supply lists, procedure and discussion, each activity lists a supplemental visualization and/or presentation that illustrates a key idea from the activity. Although many of these supplemental resources are available from the “Inside Einstein’s Universe” web site, specific links are given, along with a brief annotated description of each resource. http://www.universeforum.org/einstein/ Note: the science of black holes may not be immediately accessible to the younger members of your audience, but each activity includes hands-on participatory aspects to engage these visitors (pre-teen and below). -
Weyl Metrics and Wormholes
Prepared for submission to JCAP Weyl metrics and wormholes Gary W. Gibbons,a;b Mikhail S. Volkovb;c aDAMTP, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK bLaboratoire de Math´ematiqueset Physique Th´eorique,LMPT CNRS { UMR 7350, Universit´ede Tours, Parc de Grandmont, 37200 Tours, France cDepartment of General Relativity and Gravitation, Institute of Physics, Kazan Federal University, Kremlevskaya street 18, 420008 Kazan, Russia E-mail: [email protected], [email protected] Abstract. We study solutions obtained via applying dualities and complexifications to the vacuum Weyl metrics generated by massive rods and by point masses. Rescal- ing them and extending to complex parameter values yields axially symmetric vacuum solutions containing singularities along circles that can be viewed as singular mat- ter sources. These solutions have wormhole topology with several asymptotic regions interconnected by throats and their sources can be viewed as thin rings of negative tension encircling the throats. For a particular value of the ring tension the geometry becomes exactly flat although the topology remains non-trivial, so that the rings liter- ally produce holes in flat space. To create a single ring wormhole of one metre radius one needs a negative energy equivalent to the mass of Jupiter. Further duality trans- formations dress the rings with the scalar field, either conventional or phantom. This gives rise to large classes of static, axially symmetric solutions, presumably including all previously known solutions for a gravity-coupled massless scalar field, as for exam- ple the spherically symmetric Bronnikov-Ellis wormholes with phantom scalar. The multi-wormholes contain infinite struts everywhere at the symmetry axes, apart from arXiv:1701.05533v3 [hep-th] 25 May 2017 solutions with locally flat geometry.