The constant curvature (CC) black holes are higher dimensional generalizations of Banados-Teitelboim-Zanelli black holes. Is the event horizon of an extremal black-hole … 2\pi = r_+ \Delta t_E + r_-\Delta \phi, \ \ \ \ 0 = r_+\Delta \phi - r_- \Delta t_E 19 κ {\displaystyle \kappa } cannot go to zero is analogous to the third law of thermodynamics, which states that the entropy of a system at absolute zero is a well defined constant. Is this vanishing of the hawking temperature something one always sees when taking a BH to exremal limits? Obviously the Hawking temperature is then $$. We also calculate the Hawking temperature of the BTZ black hole in massive gravity. As the study of the statistical mechanics of black-body radiation led to the advent of the theory of quantum mechanics, the effort to understand the statistical mechanics of black holes has had a deep impact upon the understanding of quantum gravity, leading to the formulation of the holographic principle. In the thermodynamic system, the entropy plays a central role in studying the thermodynamic properties, and thermodynamic evolution takes place in such a way that entropy never decreases. Rev. becomes In euclidean coordinates the $ r_- $ is still the value given above but purely imaginary. Does this mean there is no restriction on $T_H$ and the $\tau$ periodicity is free? The statistical explanation of entropy was rst provided by Carlip [7] and the basic points are spelled out in the recent paper [8]. Schwarzschild BH) is you expand the Wick rotated metric ($t\to i\tau$) around the solution where $g_{\tau\tau}$ vanishes, find the metric is actually flat at this point, and impose $\tau$-periodicity such that there is no conical singularity at the horizon. $$ Stating that. which for $r\to r_+$ ($r'\to 0$) becomes black holes in 3d gravity with negative cosmological constant. ds_{E}^2 = \frac{ (r^2-r_+^2)(r^2+r_-^2)}{l^2r}dt_E^2 + \frac{l^2 r^2}{(r^2-r_+^2)(r^2+r_-^2)} dr^2 + r^2(d\phi + \frac{i r_+ r_-}{l r^2} dt_E)^2 About periodicity of coordinates given a metric. The BTZ black hole di ers from the Schwarzschild and Kerr solutions in some im-portant respects: it is asymptotically anti-de Sitter rather than asymptotically flat, and has no curvature singularity at the origin. The BTZ black hole is a solution of dimensional gravity with negative cosmological constant and the metric is given by where and are lapse and shift functions; where and . Confusion with inversion and descending, example with guitar shape. These corrections stem from the space non-commutativity. Or is my way to calculate it somehow not applicable to BTZ horizons? Since the discovery of the BTZ black holes, many works have been done on the classical and quantum properties of BTZ black holes. Rev. , the Hawking temperature of the BTZ black hole in massive gravity can be calculated as (20) T H = r + 2 l 2 π − Q 2 2 π r +, which is the same as the case of the charged BTZ black hole given in Section 3.1. Use MathJax to format equations. Hawking temperature in the eternal BTZ black hole: an example of holography in AdS spacetime L. Ortíz 1 , 2 , 3 General Relativity and Gravitation volume 45 , pages 427 – 448 ( 2013 ) Cite this article (e.g Gukov 03, appendix A, Kraus 06, around Fig. paper we show that Robinson-Wilczek method can also be applied to a rotating BTZ black holes. We investigate the effect of noncommutativity and quantum corrections to the temperature and entropy of a BTZ black hole based on a Lorentzian distribution with the generalized uncertainty principle (GUP). I think I found a coordinate transformation that shines more light on this. g_{tt} =\frac{J^2}{4r_\pm^2} horizons. The former spacetime is the dominant saddle point for low-temperature BTZ black holes, while the latter holographically captures the physics on high-temperature BTZ black hole backgrounds. Furthermore $\phi'$ is not periodic. What does this line from Reverse Gravity mean? For the case of 2 d CFT, the reduced geometry is the BTZ black hole or the thermal AdS as expectation. To determine the Hawking radiation in the tunneling formalism, we apply the Hamilton-Jacobi method by using the Wentzel-Kramers-Brillouin (WKB) approach. $$ Nonetheless, it is clearly a black hole: Can you ride Hawking radiation away from a black hole? In order By continuing you agree to the use of cookies. D, 70, 044027 Banados M. et al., 1993, Phys. This can also be used simply to break supersymmetry and get a non supersymmetric zero temperature theory. (a) Compute the area of the black hole horizon to find the entropy. To learn more, see our tips on writing great answers. Copyright © 2021 Elsevier B.V. or its licensors or contributors. We, later on, endow charges and rotations to the same black hole and rederive all the expressions once again. Hmm thats funny, extremal mass indicates the smallest possible mass, so this would imply a non extremal BH radiates Hawking radiation and shrinks up to its extremal mass and not further (since it does not radiate in the extremal case). Abstract. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. D, 48, 1506 Asking for help, clarification, or responding to other answers. $$ $$ Voting system with two votes as a defense against fear of voting for a loser - is it anywhere in the world? Title: Hawking temperature in the eternal BTZ black hole: an example of Holography in AdS spacetime. Entanglement Entropy for the Charged BTZ Black Hole In this paper we investigate quantum entanglement in the context of three-dimensional (3D) AdS gravity, in particular of the charged Banados-Teitelboim-Zanelli (BTZ) black hole [1], using the AdS3/CFT2 correspondence. Rev. Viewed 1k times 4. Fermions in BTZ Black Hole Space-Time. Is using strings as keys for reference to other tables bad in terms of memory usage? Published by Elsevier B.V. https://doi.org/10.1016/j.physletb.2020.135788. Rev. Why does imaginary periodic time of the Rindler space of black hole give Hawking temperature? No response after PhD interview with good feedback + follow-up emails. The BTZ black holes [13, 15] are solutions of the Einstein field equations with cosmological constant in three dimensions. In this letter we compute the corrections to the horizons, the horizon area and Hawking temperature of a BTZ black hole. Up to which rating is my strategy in the opening is applicable? 1. Rev. Properties Euclidean BTZ is hyperbolic solid torus. Why is ~/.zprofile always sourced on every interactive session? In fact, the black hole can be nucleated at the Hawking temperature; however, the soliton can be formed at any temperature as long as M = −1. Rev. To determine the Hawking radiation in the tunneling formalism, we apply the Hamilton-Jacobi method by using the Wentzel-Kramers-Brillouin (WKB) approach. with Let us now consider the noncommutative BTZ black hole in therotating regime ðJ ≠0Þ. The same hold in 4-dim. D, 70, 044027 Banados M. et al., 1993, Phys. It was first revealed by the classical theory of general relativity (GR) that the area of the event horizon of a black hole never decreases [1]. $$ $$ t'_E = r_+ t_E + r_-\phi, \ \ \ \phi' = r_+ \phi - r_-t_E, \ \ \ r'^2= \frac{r^2-r_+^2}{r_+^2+r_-^2} It only takes a minute to sign up. At this point, we are prepared to go further. $$ Partially reducing the BTZ black hole gives us the finite temperature version. 3 Off-shell free energy By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy. So the periodicity of $t_E'$ is $\Delta t_E'=2\pi$, and of $\phi'$ is $\Delta \phi'=0$. $$ The Hawking radiation of BTZ black hole is investigated based on generalized uncertainty principle effect by using Hamilton-Jacobi method and Dirac equation. A SIMPLE DERIVATION OF FINITE-TEMPERATURE CFT CORRELATORS FROM THE BTZ BLACK HOLE Satoshi Ohyaa,b a Department of Physics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Pohraniční 1288/1, 40501 Děčín, Czech Republic An artist's depiction of two blac © 2020 The Authors. This is because a system at zero temperature … D 99, 044042 (2019)]. temperature is modified due to the presence of the noncom-mutative parameter θ. which under the coordinate transformation ds^2 = - N^2 dt^2 + N^{-2} dr^2 +r^2(d\phi + N^\phi dt)^2 We use cookies to help provide and enhance our service and tailor content and ads. The mass of the black hole when is uncharged, nonspinning represents the entropic energy content that can't be extracted, and seems to be purely thermal. (14) In terms of this entropy, the corresponding thermodynamic fundamental equation and the temperature for the CR-BTZ black hole are given respectively by 2 2 πQ2 S 2πJ S M= + − ln , (15) 4πl S 2 4π and 8π 2 J 2 πQ2 ∂M S T = = − − . How Was "Feast" Pronounced in Early Modern English? There was a clear indication that thermodynamic principles can be incorporated into the analysis of black holes. Ask Question Asked 5 years, 9 months ago. site design / logo © 2021 Stack Exchange Inc; user contributions licensed under cc by-sa. We study the evaporation of two-dimensional black holes in JT gravity from a three-dimensional point of view. It disappears when the temperature of a rotat-ing BTZ black hole becomes absolute zero. Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. did you verify if on the extremal limit that temperature goes to zero? 2004, Phys. Authors: L. Ortíz (Submitted on 20 Oct 2011 , last revised 21 Jun 2013 (this version, v3)) Abstract: We review the relation between AdS spacetime in 1+2 dimensions and the BTZ black hole. D 99, 044042 (2019)]. Thus, it confirms Nernst theorem, and hence, can be regarded as the Planck absolute entropy of a rotating BTZ black hole. Authors: L. Ortíz (Submitted on 20 Oct 2011 , last revised 21 Jun 2013 (this version, v3)) Abstract: We review the relation between AdS spacetime in 1+2 dimensions and the BTZ black hole. We show that in non-commutative case, non-rotating BTZ black hole in … In the context ofblackholethermodynamics,theentropyisproportional toareaoftheeventhorizon[1–5].Quantummechanically $$ We investigate the effect of noncommutativity and quantum corrections to the temperature and entropy of a BTZ black hole based on a Lorentzian distribution with the generalized uncertainty principle (GUP). Idea. (BTZ) showed in 1992 that (2+1)-dimensional gravity has a black hole solution [8]. necessary for understanding the black hole evaporation process purely in terms of the boundary theory. no intuition, but it seems to be consistent with other calculations of temperatures for spinning and charged black holes, actually, there is an intuitive reason: extremality means that a large part of the mass of the black hole can be extracted via the Penrose or the Blandford-Znajek process, so it is in some sense on a ordered state that can be reverted without increasing the entropy. In this paper, we study the Hawking temperature of the BTZ black hole based on the purely topological method proposed by Robson, Villari, and Biancalana (RVB) [Phys. black hole is the temperature of the boundary theory. $$ (14) In terms of this entropy, the corresponding thermodynamic fundamental equation and the temperature for the CR-BTZ black hole are given respectively by u00132 u0012 u00132 πQ2 u0012 S 2πJ S M= + − ln, (15) 4πl S 2 4π and 8π 2 J 2 πQ2 u0012 u0013 ∂M S T = = − −. We … The Hawking temperature of the charged rotating BTZ black hole can be accurately derived by this topological method. D 99, 044042 (2019)]. So the time periodicity becomes $\beta =\Delta t_E = \frac{2\pi l r_+}{r_+^2+r_-^2}$ whilst also setting a fixed periodicity for $\phi$. At this point, we are prepared to go further. rev 2021.4.16.39093. 2. We also calculate the Hawking temperature of the BTZ black hole in massive gravity. horizons. The solution is parameterized by the mass and angular momentum of the black hole and they obey the conditions, and . angular momentum of the rotating black hole. Instead of looking for a conical singularity in $g_{tt}$ alone I must look at conical singularities in any part of the metric (apart from $g_{rr}$) First of all the metric can be expressed in terms of $r_\pm$ and Wick rotated $t\to it_E$ such that 2004, Phys. Entanglement Entropy for the Charged BTZ Black Hole In this paper we investigate quantum entanglement in the context of three-dimensional (3D) AdS gravity, in particular of the charged Banados-Teitelboim-Zanelli (BTZ) black hole [1], using the AdS3/CFT2 correspondence. $$ Thanks for contributing an answer to Physics Stack Exchange! 2. Thus, it confirms Nernst theorem, and hence, can be regarded as the Planck absolute entropy of a rotating BTZ black hole. Now the perscription I learned to find a Hawking Temperature at a horizon (e.g. The metric of the BTZ Black Hole is given by Determine the off - diagonal elements of covariance matrix, given the diagonal elements. Connect and share knowledge within a single location that is structured and easy to search. It disappears when the temperature of a rotat-ing BTZ black hole becomes absolute zero. The $g_{rr}$ component of the metric is singular at points where $N^2=0$, yielding the horizons $r_\pm$ The best answers are voted up and rise to the top, Physics Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us. The same effect was observed for the area of the event horizon of black … Hawking Temperature of the BTZ Black Hole. 8. Finally, we analyze the global and local thermal stability of the system and we found that the specific heat of the black hole is positive for all possible values of z, and at the self-dual temperature T s = 1 2 π (1 z) z z + 1, there is a Hawking-Page phase transition between the BTZ black hole and thermal AdS 3 spacetime. We first analyze the effect of quantum corrections (motivated from string theory and loop quantum gravity) on various thermodynamic variables for uncharged and stationary BTZ black hole. Rev. 2. In this paper, we study the Hawking temperature of the BTZ black hole based on the purely topological method proposed by Robson, Villari, and Biancalana (RVB) [Phys. B. Sathiapalan BTZ black-hole and Luttinger Liquids In the BTZ black hole it is not hard to show the extremal condition, angular momentum parameter a equals mass a = m, is zero temperature. B. Sathiapalan BTZ black-hole and Luttinger Liquids N^2 = -M+ \frac{r^2}{l^2} + \frac{J^2}{4 r^2}, \ \ \ \ \ \ N^\phi = -\frac{J}{2r} ds_E^2 = \frac{r'^2}{l^2} dt_E'^2 +\frac{l^2}{1+r'^2} dr'^2 + (1+r'^2)d\phi'^2 The Hawking temperature of the charged rotating BTZ black hole can be accurately derived by this topological method. T_H = \frac{r_+^2+r_-^2}{2\pi l r_+} Is there any intuition on why this is the case? Could New Jersey Really Ban Pennsylvania Drivers? The Euclidean BTZ black hole is a hyperbolic 3-manifold homeomorphic to (the interior of) the hyperbolic solid torus, hence to the knot complement of the unknot in the 3-sphere. Student put my name in the acknowledgement section despite the fact I have never talked to him, Movie about a homicidal monster that lives in a cave, who is actually a woman's son. Isn't this hard to match with the fact that hawking radiation should lead to the vanishing of BH's instead of bringing them to this non radiating extremal state? ScienceDirect ® is a registered trademark of Elsevier B.V. ScienceDirect ® is a registered trademark of Elsevier B.V. Topological approach to derive the global Hawking temperature of (massive) BTZ black hole. Extremal black holes have vanishing surface gravity. D, 48, 1506 r_\pm = \sqrt{ \frac{Ml^2}{2}\left( 1 \pm \sqrt{1-\left(\frac{J}{Ml}\right)^2} \right)} Ah, I was not complete enough in my euclidean description but in fact it does. Because the metric function of the BTZ black hole in massive gravity has a mass term, the corresponding Hawking temperature cannot be derived unless an integral constant is added. Making statements based on opinion; back them up with references or personal experience. In order temperature is then the inverse Hawking temperature of the charged rotating BTZ hole... We apply the Hamilton-Jacobi method by using the truncated entanglement renormalization network, the numerator out. 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