Penrose diagram for the process of black hole formation and evaporation, such that. The btz black hole di ers from the schwarzschild and kerr solutions in some important respects. The laws of black hole mechanics the energy of a kerr black hole can be changed by dropping something in it and can even by decreased by a trick called the penrose process. The kerr solution welcome to the infn roma home page. Penrose diagram of kerr black hole the penrose diagram of the kerr geometry starts out the same as the schwarzschild diagram, but. The precursors to the penrose diagrams were kruskalszekeres diagrams. This diagram allows us to qualitatively understand the fundamental properties of the black hole. Looking at the penrosediagram for the rotating kerrblack hole just one illustrating picture at the end i come up the following question. This happens through the penrose process in the black hole s ergosphere, an area just outside its event horizon. Angular momentum of a black hole a x m, where m is the black hole mass and a is a parameter. Schwarzschild and kerr solutions of einsteins field. Each of such asymptotic region admits a black hole and white hole event horizons.
I know that alain riazuelo has computed similar videos, e. Penrose diagram for the eternal schwarzschild hole we now do a similar transformation 32,37 for the black hole metric. The carter penrose diagram of a static bh obtained from kruskal coordinates as representated in fig. So the point of this page is to demonstrate what the kerr black hole and its intriguing features look like. There are basically six possibilities as depicted in figure 2. Mit lectures on the geometry and analysis of black hole. Rotating black holes in penrose diagrams physics forums.
The penrose diagram adds to kruskal and szekeres diagram the conformal crunching of the. In that case a rotating black hole gradually reduces to a schwarzschild black hole, the minimum configuration from which no further energy can be extracted, although the kerr black hole s rotation velocity will never quite reach zero. Black holes from a to z course given in spring 2015, at harvard university. An example of computation for curved spacetime has been provided, with a conformal diagram for robertsonwalker universe.
Regions iii and iv are the extension of the kruskal diagram, often interpreted as another, perhaps ctional, universe connected to the rst by a wormhole. Pdf analogue physics became very popular in recent decades. Analysis of the topology of the kerr metric nasaads. We rst discuss the singularities of the kerr solution, and the interpretation of the associated parameters contained therein. The properties of the ergosphere and energy extraction by penrose process in a rotating nonkerr black hole are investigated. Schwarzschild and kerr solutions of einsteins field equation an introduction christian heinicke 1. All structured data from the file and property namespaces is available under the creative commons cc0 license. In theoretical physics, a penrose diagram is a twodimensional diagram capturing the causal. The penrose diagram of schwarzschild geometry we can add the electric charge qor the angular momentum jto get kerr black hole or reissnernordstr. So in minkowski space, what does a particle moving look like in a penrose diagram. Black holes kim griest department of physics, university of california, san diego, ca 92093 abstract introduction to einsteins general theory of relativity as applied especially to black. If the accretion disk is close to the black hole, the xray colors from the iron will be spread out by the immense gravity of the black hole. Schwarzschild and kerr solutions of einsteins field equation. Then we continue with the definition of the kruskalszekeres coordinates which cover the entire black hole spacetime.
Penrose diagrams for the minkowski and schwarzschild. It is shown that the ergosphere is sensitive to the deformation. The rotating black hole syed ali raza may 24, 2012 1 abstract in this project we explore some of the properties of space time near a spinning black hole. This has critical implications for the behavior of accretion disks in particular it causes the inner portion of the disk to align with the holes spin, since each orbit precesses around the hole at a di. Carterpenrose diagrams and black holes ewa felinska the basic introduction to the method of building penrose diagrams has been presented, starting with obtaining a penrose diagram from minkowski space. Penrose diagrams for the minkowski and schwarzschild spacetimes. The axes assigned with t and r in the diagram correspond to t and x used in section 4. My intention was to introduce the subject of black hole thermodynamics starting at the beginning, at a level suitable for anyone. In 1963, new zealand mathematician roy kerr proposed the first realistic theory for a rotating black hole. The problem with using a kerr black hole as a means of travel, through time or otherwise, is that you never know where youre going to end up. Penrose diagrams are often used to illustrate the hypothetical einsteinrosen bridge connecting two separate universes in the maximally extended schwarzschild black hole solution.
Algorithms for the explicit computation of penrose diagrams. The conformal diagram for minkowski spacetime contains a number of. We do this by wickrotating our time coordinates as t. With the use of these coordinates we define penrosecarter diagram for the schwarzschild black hole. The kerr metric or kerr geometry describes the geometry of empty spacetime around a rotating uncharged axiallysymmetric black hole with a quasispherical event horizon. Files are available under licenses specified on their description page. Analogous properties describe spacetime near other stellar spinning objects like earth and the sun too. Region iii is the white hole, and region iv is another asymptotically. Penrose diagrams university of north carolina at wilmington. Could a rotating black hole be used to travel through time. Above we see a penrose diagram representing a coordinate extension 1 for a charged or rotating black hole.
The black hole region for a given asymptotic region corresponds to the white hole for the next asymptotic region. The second wavy black singularity next to region iv is sometimes called a white hole since future pointing worldlines diverge from the region. The schwarzschild metric has a singularity at r rs where 0g00 and g11 however, we have already seen that a free falling observer acknowledges a smooth motion without any peculiarity when he passes the horizon. Examples of penrose diagrams for some types of black holes will be. The region inside this triangle is the penrose diagram. The biggest difference is that locally, the metric on a penrose diagram is conformally. The association of the surface area of a black hole with its entropy is discussed and it is shown that with the introduction of quantum mechanics black holes cease to be black and can radiate. Penrose diagram for the kerr black hole physics forums. The kerr metric is an exact solution of the einstein field equations of general relativity. Looking at the penrose diagram for the rotating kerr black hole just one illustrating picture at the end i come up the following question. Mar, 2020 black hole in m87 black hole at the centre of the massive galaxy m87, about 55 million lightyears from earth, as imaged by the event horizon telescope eht. This image was the first direct visual evidence of a supermassive black hole and its shadow. Transformations for the cpds for the reisnernordstrom metric are analyzed. Pdf rotating nonkerr black hole and energy extraction.
A penrose diagram is a kind of spacetime diagram arranged to make clear the. Penrose diagram of a kerr black hole 51 because a rotating, kerrtype black hole has four different spacetime regions and a ring singularity, the penrose diagram for this spacetime is more complicated. The penrose diagram of the kerr geometry for a rotating black hole looks like the. Penrose diagram of a kerr black hole 51 net texts, inc. The penrose diagram of the maximally extended extremal kerr spacetime is shown in fig. Could a kerr black hole be used to travel through time. The penrose diagram in figure 2, which shows the internal structure of a kerr black hole, makes this clear. Penrose diagram of a kerr black hole 51 because a rotating, kerr type black hole has four different spacetime regions and a ring singularity, the penrose diagram for this spacetime is more complicated.
Although this diagram does not show the erospheres, i have never seen a conformal penrose d. Pdf quantum analogue of a kerr black hole and the penrose. Penrose diagrams, kerr black holes yacine aliha moud penrose diagrams our goal here is to have a visual representation of an in nite spacetime with a nite coordinate range, while preserving its causal structure. Schwarzschild black hole solution depends on mass only. Penrose diagram for the eternal schwarzschild hole we now do a similar transformation 32,37 for the black hole metric 23, getting ds. Penrose diagrams of charged and rotating black holes. The use of different coordinate systems, maximal extensions and penrose diagrams is explained. The degree to which the iron feature is spread out red wing reveals how close the accretion disk is to the black hole. Carter penrose diagrams and black holes ewa felinska the basic introduction to the method of building penrose diagrams has been presented, starting with obtaining a penrose diagram from minkowski space.
However, stephen hawking calculated that black holes actually radiate quantum. All this information is from this great site for penrose diagrams by andrew hamilton, who seems to do a lot of work with black holes based on his site. Because this distance depends on the black holes spin, the spin rate. This happens through the penrose process in the black holes ergosphere, an area just outside its event horizon. Dec 01, 20 all this information is from this great site for penrose diagrams by andrew hamilton, who seems to do a lot of work with black holes based on his site.
As the frefo approaches the event horizon, his signals are pulled toward the black hole and take ever longer to reach the fido. Due to the lack of analytical transformations for the carter penrose diagrams cpds for the kerr metric, the topology of the kerr bh is studied by analytical investigation of the equations of motion. The penrose diagram of the kerr geometry for a rotating black hole looks like the penrose diagram of the reissnernordstrom geometry for a charged black hole, except that it is possible to pass through the disk bounded by the ring singularity of the rotating black hole to an antiverse. Although the classical behavior of the btz black hole has not been. These are the lecture notes from professor andrew stromingers physics 211r. It is the rst half of a survey of black holes focusing on the deep puzzles they present concerning the relations between general relativity, quantum mechanics and thermodynamics. Minkowski space has no gravitational force acting on a particle so it moves along a straight line. Penrosecarter diagram for the schwarzschild black hole. Removing a coordinate singularity at the schwarzschild radius. In that case a rotating black hole gradually reduces to a schwarzschild black hole, the minimum configuration from which no further energy can be extracted, although the kerr black holes rotation velocity will never quite reach zero. It allows simulating inaccessible physical phenomena, such as black holes, in the. Before we close, we investigate the problem of precession of an inclined circular orbit around kerr.
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