We investigate criteria under which one may construct the energy tensor of a null radiation field from an algebraically special vacuum metric. Spherically symmetric gravitational collapse of a star. For a distant observer, an infalling observer hits the horizon when the bh forms and evaporates. The btz black hole in \schwarzschild coordinates is described by the metric. Pdf the classical vaidya metric is transformed to the special diagonal coordinates in the case of the linear mass function allowing rather easy. Removing a coordinate singularity at the schwarzschild radius. The penrose process according to the penrose mechanism, it is possible to extract rotational energy from a kerr black hole. How do i see using a penrose diagram that two different spacetimes have a similar global and causal structure. External spacetime of a spherically symmetric and nonrotating star which is either emitting or absorbing null dust. Penrose diagram of the schwarzschildkruskal spacetime. The kerr metric is commonly expressed in one of two forms, the boyerlindquist form and the kerrschild form.
The penrose diagram for a particular spacetime is independent of what coordinates you use to describe it. This invaluable book presents gravitation and gauge fields as interrelated topics with a common physical and mathematical foundation, such as gauge theory of gravitation and other fields, giving emphasis to the physicists point of view. These conclusions are made very clear by using the penrose coordinates, which give the metric of equation 2. In this paper, we use the charged vaidya metric to obtain a candidate macroscopic penrose diagram for the formation and subsequent evaporation of a charged black hole, thereby illustrating how predictability might be retained. The time dependent geometry is resulted from collapse of a null shell where the injection takes place at the boundary time t 0. Pdf linear mass vaidya metric at the end of black hole evaporation. For a more detailed account in two spacetime dimensions see section 3. Notice that d 2 coordinates here, 1 here and 1 here, so its threedimensional. Therefore the penrose diagram is going to be the same as the standard penrose diagram for minkowski space.
What kind of global and causal structures does a penrose diagram reveal. At any rate, they are very often called carter penrose diagrams. As such, they contain some sections which are entirely absent from the audio recordings. Penrose diagram of the schwarzschild solution youtube. Likewise, the outgoing eddingtonfinkelstein coordinates are obtained by replacing t with the null coordinate. Hawking radiation appears before the horizon in term of the lightcone coordinate u. Penrose diagram for the linear mass vaidya metric with 0 diagram. Schwarzschild metric wikimili, the best wikipedia reader. Pdf we discuss the near singularity region of the linear mass vaidya metric for. Pdf linear mass vaidya metric at the end of black hole. Penrosecarter diagram of the kruskalszekeres spacetime. The notebooks are opened in readonly mode, but you can access to an interactive version by clicking on execute on binder in the top right menu to download a notebook and run it on your computer, click on ipynb or on the download button in the. Relatividad general q2 program of general relativity. The next step is to construct a penrose diagram from this system.
I added a reference to the original paper by carter that featured such a diagram. E n 2 lr n vaidya metric at the end of black hole evaporation. Roger penrose, who invented this kind of diagram in the early 1950s, himself calls them conformal diagrams. This diagram di ers from that of the kerr metric at r1, re. The penrose diagram of this spacetime is shown in fig. Penrose diagram of the schwarzschild solution and construction of the kruskal extension. 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. The kerr metric is an exact solution of the einstein field equations of general relativity. About half of the material is devoted to einsteins general. Lecture notes on general relativity columbia university. The ingoing eddingtonfinkelstein coordinates are obtained by replacing the coordinate t with the new coordinate. The notebooks are opened in readonly mode, but you can access to an interactive version by clicking on execute on binder in the top right menu.
Investigating static and dynamic nonsingular black holes core. We study a selfconsistent solution of the semiclassical einstein equation including the back reaction from the hawking radiation. Music so we have obtained this metric on antide sitter space, which covers entire space time. July 15, 2015 abstract these are the lecture notes from professor andrew stromingers physics 211r.
Causal and global structure of penrose diagrams stack exchange. These sections are in italics, allowing readers already familiar with the material to easily bypass them. The schwarzschild solution in schwarzschild coordinates. Carroll institute for theoretical physics university of california santa barbara, ca 93106. The outgoing vaidya metric r ru lightlike curves hawking radiation of null dust. Pdf on maximal analytical extension of the vaidya metric. To guarantee the continuity of the metric and the extrinsic curvature, we prove that the two solutions must be joined at a null.
External spacetime of a star that emits or receives radiation. They can be read directly in the browser by just clicking on their titles. Space time and now we want to draw a penrose carter diagram of the space. 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. Accelerated observers in minkowski space and the rindler metric. Misner, thorne, and wheeler only explain the penrose diagrams of the minkowski and schwarzchild metrics, and neither wald nor thorne and blandford have any systematic discussions of penrose diagrams at all that i could find. While the vaidya metric is an extension of the schwarzschild metric to include a pure radiation field, the kinnersley metric constitutes a further extension of the vaidya metric. The penrose diagram of the schwarzschild geometry clarifies this unexpected behavior. In this paper it is argued that a carter penrose diagram can be viewed as a di.
Black holes from a to z andrew strominger center for the fundamental laws of nature, harvard university, cambridge, ma 028, usa last updated. Penrose diagram geometries of formation and evaporation are connected at the collapsing matter shock wave. An example of computation for curved spacetime has been provided, with a conformal diagram for robertsonwalker universe. Classical fields world scientific publishing company. The penrose diagram of the completed schwarzschild manifold.
What is the general procedure for constructing the penrose. Timedependent black hole from higher dimensions introduction. 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. This diagram is obtained by patching two penrose diagrams. Jun 19, 2015 the rindler coordinates are just a different set of coordinates for describing minkowski space. Definition of a penrose diagram a penrose diagram is a kind of spacetime diagram arranged to make clear the complete causal structure of any given geometry. The kerr metric or kerr geometry describes the geometry of empty spacetime around a rotating uncharged axiallysymmetric black hole with a quasispherical event horizon. Although this diagram does not show the erospheres, i have never seen a conformal penrose d. Chapter 1 an introduction to black holes black holes belong to the most fascinating objects predicted by einsteins theory of gravitation. Although they have been studied for years,1 they still attract tremendous attention in the physics and astrophysics literature. Pdf penrose diagrams for the minkowski and schwarzschild. Global structure of evaporating black holes sciencedirect.
The goal of penrose diagrams is to nd coordinates that are bounded and preserve the light. It is named after the indian physicist prahalad chunnilal vaidya and constitutes the simplest nonstatic generalization of the nonradiative schwarzschild solution. The argument can also be run in the reverse direction. Next, we consider the correction to the hawking radiation. Our geometry is constructed by connecting flat space and the outgoing vaidya metric at the locus of the shock wave. Lecture 1 these lecture notes provide somewhat more detailed explanations than those given in. In this case, the presence of new mass term changes the thermodynamics, causal structure and penrose diagrams just up to a rescaling in the. The field bears the same relationship to the original metric as does vaidya s to schwarzschilds. Penrose diagram for the conventional model of the formation and evaporation of a black. A penrose diagram for such a model can be depicted by piling up sliced schwanschildde sitter spacetime with various mass so. Penrose diagrams for the minkowski and schwarzschild spacetimes. A penrose diagram is a kind of spacetime diagram arranged to make clear the complete causal structure of any given. Carterpenrose diagram for the global geometry of the vaidya metric in the case of a.
The schwarzschild metric is given by ds2 1 r s r dt2 1 r s r 1 dr2 r2d 2. As an example we generate a class of null radiation fields from a class of vacuum metrics without symmetry discovered by robinson and robinson. There are basically six possibilities as depicted in figure 2. In general relativity, the vaidya metric describes the nonempty external spacetime of a spherically symmetric and nonrotating star which is either emitting or absorbing null dusts. Complexity growth following multiple shocks sciencedirect. Black holes assignment 7 this assignment will be discussed in the tutorials in the week of dec. Critical phenomena in gravitational collapse of husain. Hyperbolic cosine of rho squared d rho squared hyperbolic sign of rho omega d 2.
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. It can be readily derived from the schwarzschild metric, using the newmanpenrose formalism also known as the spincoefficient formalism. The nonradiative part also corresponds to a tracefree field. We first use the cutandpaste technique to match the conformally flat solution \c0\ onto an outgoing vaidya solution. Consider semiclassical metric vaidya metric approximation pisinchen et al. Radiating collapse of a spherically symmetric spacetime. Vaidya metric, which described a black hole that is either emitting or being irradiated. These in nities are shown on the penrose diagram in figure 8. Linear mass vaidya metric at the end of black hole evaporation. It is shown that the complexification of vaidya s metric results in a metric that bears the same relation to vaidya s metric as does the kerr metric to the schwarzschild metric. On maximal analytical extension of the vaidya metric. They are an indispensable map for navigating inside a black hole. In order to prove that this is the selfconsistent solution, we first show that the weyl anomaly is canceled if we take the effects of the. Penrosecarter diagram of the antide sitter spacetime.
The classical vaidya metric is transformed to the special diagonal coordinates in. The metric on each segment between two shock waves we use 0 as the time coordinate substituting the stationary solutions for and, we obtain this is the metric of inside the black hole. Lots of calculations in general relativity susan larsen tuesday, february 03, 2015 page 1. Penroses diagram for the extended vaidya spacetime when mu. The entire spacetime can be predicted from initial conditions if boundary conditions at the singularity are known. With respect to the above coordinate system, the metric g can be expressed as a 0,2 tensor as follows.
Although they have been studied for years,1 they still attract. Lecture notes on general relativity gravity and string theory group. However, the energymomentum tensor consists of two parts. The penrose diagram of double black hole vaidya geometry. The biggest difference is that locally, the metric on a penrose diagram is conformally equivalent to the actual metric in spacetime. The entire spacetime can be predicted from initial conditions if boundary conditions at. The conformal factor is chosen such that the entire infinite spacetime is transformed into a penrose diagram of finite size. Black holes from a to z course given in spring 2015, at harvard university. The fully extended schwarzschild geometry 4 the penrose diagram. Absence of horizon in black hole formation peiming ho physics department. This metric is connected to the vaidya metric at the outermost shock wave.
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