A nontrivial torsion appears, and the deformed equations of motion are found to fit nicely into the framework of the einstein. Research article fermion fields in btz black hole spacetime and entanglement entropy dharmveersinghandsanjaysiwach department of physics, centre of advanced studies, banaras hindu university, varanasi, india. If we can explain this entropy in such a simple setting, it may take us a. In particular, when the latter is large, they reproduce the bulk shockwave. Thermodynamic curvature of the charged btz black hole in. The book has been awarded with harvey awards for best. The leading term is the standard bekensteinhawking area law and subleading term corresponds to first quantum corrections in black hole entropy. Symmetry free fulltext global embeddings of btz and. Part iv duality between charged btz black hole and. Using an orbifold description of the euclidean btz black hole, we show that there is a special relation between the spectrum and the truncated heat kernel of this black hole with the patterson. Upper and lower bounds for the radial size of the orbits are given in all cases and the possibility of passing from one black hole exterior spacetime to another is discussed using penrose diagrams. Btz m, where mis a simple manifold, and their entropies and greybody factors can be obtained from the btz black hole directly 419 or by duality 2022.
We consistently construct the offshell free energies of the black hole and the soliton by properly taking into account the conical space. Free download or read online black hole pdf epub book. In order to remove the usual problems with the ctcs, those regions in the btz geometry are cut out of the global ads 3. There are two schemes for analyzing the thermodynamic behavior of the charged btz black hole. Abstract for the threedimensional btz black hole we consider a selberg type zeta function. Isnt this hard to match with the fact that hawking radiation should lead to the vanishing of bhs instead of bringing them to this non radiating.
In the large c limit, w elds are a weekly coupled description of h cg as gas of coherent particles on ads 3. Horizon fluff a semiclassical approach to btz black. When i calculate the euclidean action, i always get an. Quantum fluctuations of a btz black hole in massive.
The btz black hole in schwarzschild coordinates is described by the metric. Hawking temperature of the btz black hole stack exchange. Pdf the cosmological constant and the black hole equation of state. The book was published in multiple languages including english, consists of 368 pages and is available in hardcover format. Scrambling time from local perturbations of the eternal btz. Pdf quantum liouville theory and btz black hole entropy. In one case, the charged btz black hole is superentropic 51, 52, that the reverse isoperimetric inequality is violated. Following on from this, we invoke a precise mathematical theorem of hyperbolic geometry, due to sullivan 19, 20, to establish a no hair theorem for the btz black hole 21. Thermal fluctuations to the thermodynamics of a non. Research article phase transitions of the btz black hole in. Upper and lower bounds for the radial size of the orbits are given in all cases and the possibility of passing from one blackhole exterior spacetime to another is discussed using penrose diagrams. We consider the hawkingpage phase transition between the btz black hole of m. Btz black hole spacetime and construct the entanglement thermodynamics for. It reproduces the bekensteinhawking entropy and also the logarithmic corrections to it.
On the other hand, a schwarzschild black hole in asymptotic antide sitter space would tunnel into the thermal soliton solution known as. Quantum fluctuations of a btz black hole in massive gravity. If one introduces the mass of a conical singularity, a transition between the nonrotating btz black hole and thermal ads space is also possible. Scrambling time from local perturbations of the eternal. Btz black hole and quantum hall e ect in the bulkboundary dynamics y. Black hole remnant in asymptotic antide sitter space pdf. In particular, when the latter is large, they reproduce the bulk shockwave propagation along the btz horizon description. A natural guess is that black hole entropy should be associated with horizon degrees of freedom. Pdf thermodynamics of btz black hole and entanglement entropy. Charged rotating btz black holes in noncommutative spaces. In order to remove the usual problems with the ctcs, those regions in. Probing the btz black hole with test fields internet archive.
We study the entanglement entropy of fermion fields in btz black hole spacetime and calculate prefactor of the leading and subleading terms and logarithmic divergence term of the entropy using the discretized model. Firstly, we show that there is no such embedding for 4d rnads black hole in 6d flat ambient space, completing the classification which we started earlier. The btz black hole di ers from the schwarzschild and kerr solutions in some important respects. An asymptotically ads charged btz black hole in a massive theory of gravity has also been constructed 25. Hawkingpage phase transition in btz black hole revisited. A zeta function for the btz black hole international. It has become vital to understand btz black hole thermodynamics from. We notice that there exist two critical points between which the gibbs free energy is negative. We emphasize the conceptual utility of our formula for discussing 1n corrections to strongly coupled. We indicate how special values of its logarithm correspond to certain thermodynamic quantities associated with the. Phase transition between the btz black hole and ads space.
The case of zero cosmological constant corresponding to the interior region of a black hole is analyzed in detail. Several e orts have been made to generalize the gaugegravity proposal for non ads. More precisely, it corresponds to an orbifold of the universal covering space of ads 3. Horizon fluff a semiclassical approach to btz black hole. I want to calculate the mass and entropy of nonrotating btz black hole using euclidean method. From the figure, we can see that the gibbs free energy is zero for a btz black hole in thermal equilibrium. We start with a charged rotating btz solution and obtain deformed gauge fields, vielbeins, and spin connections. For the threedimensional btz black hole we consider a selberg type zeta function. Then we construct an explicit embedding of nonspinning btz black hole in 6d. In this paper, we investigate properties of rainbow btz black holes in the scenario with the freefall ff orthonormal frame. Lee hodgkinson university of nottingham relativity and grstatic, stationary and inertial unruhdewitt detectors onavitation. Complete geodesics of both types exist in the rotating black hole background, but not in the spinless case. Btz is a monotonically increasing positive function of the temperature, as the case of any chernsimons black hole in odd dimensions 15. Pdf black hole book by charles burns free download 368.
A hole is nothing, and if it is black, we cant even see it. Must switch smoothly, obtain response function in regulator free form, then take sharp switching limit. We indicate how special values of its logarithm correspond to certain thermodynamic quantities associated with. Fermion fields in btz black hole spacetime and entanglement. The mass and angular momentum of the black hole is. The righthand side is written in terms of the thermofield state formed by two copies of the outsidehorizon r 1 portion of the schwarzschild view of the btz black hole.
In particular, for the simplest extremal black hole, i. Charged rotating btz black holes in noncommutative spaces and. The main characters of this sequential art, graphic novels story are. A semiclassical approach to btz black hole microstates hamid r. We study the problem of construction of global isometric embedding for spherically symmetric black holes with negative cosmological constant in various dimensions. The first edition of the novel was published in 1995, and was written by charles burns. On the btz black hole and the spinning cosmic string. If we can explain this entropy in such a simple setting, it may take us a long way towards understanding the general problem. We have found that the btz bh has thermodynamic geometries similar to that of the. This solution of the einstein field equations in three spacetime dimensions shares many of the characteristics of the kerr black hole.
Mar 27, 2015 we provide a holographic description in terms of a free falling particle in the eternal btz black hole that exactly matches our cft calculations. We provide a holographic description in terms of a free falling particle in the eternal btz black hole that exactly matches our cft calculations. The lefthand side is the generating functional of the bulk or boundary correlators of the btz black hole discussed above, with any bulk sources being analytic in z. In this section, we obtain the free fall ff rainbow btz black hole and then calculate. The solution of a remnant was suggested for the black hole ground state after surface gravity is corrected for the loop quantum effect. This result shows that the btz black hole can be parametrized by at most two parameters, its. Hawkingpage phase transition in btz black hole revisited inspire.
Research article phase transitions of the btz black hole in new massive gravity yunsoomyung institute of basic science and department of computer simulation, inje university, gimhae, republic of korea. For a generic btz black hole solution, however, the quotient leads to closed timelike curves ctcs in some regions of the space, which happen to fall behind the inner horizon of the black hole geometry. Thermodynamics of btz black holes in gravitys rainbow. Static, stationary and inertial unruhdewitt detectors on. In this section, we obtain the free fall ff rainbow btz black hole and then calculate its hawking temperature via the hamiltonjacobi method. We assumed some basic \bohrtype quantization on central charge and the di cit angle. Complete geodesics of both types exist in the rotating blackhole background, but not in the spinless case.
Btz black hole and quantum hall e ect in the bulkboundary. We introduce a set of scalar fields as test fields to study the dynamical behaviors of the btz banadosteitelboimzanelli black hole. Quantum fields on btz black holes white rose university. Research article phase transitions of the btz black hole. Holography of the btz black hole, inside and out pdf. In one scheme, the charged btz black hole is superentropic, while in the another, it is not. Thermal fluctuations to the thermodynamics of a nonrotating. Research article fermion fields in btz black hole space. In this paper, we investigate the thermodynamic curvature of the charged banadosteitelboimzanelli btz black hole and the relationship between thermodynamic curvature and reverse isoperimetric inequality. Static,stationaryandinertialunruhdewittdetectors onthebtzblackhole lee hodgkinson 1 university of nottingham april 1, 2012 1incollaborationwithjormalouko lee hodgkinson university of nottinghamstatic, stationary and inertial unruhdewitt detectors on the btz black holeapril 1, 2012 1.
Yesif that black hole represents the most extreme state of matter possible, if it represents the possible end of the universe, if it represents the. However, it is not clear if this chiral cft captures any of the dynamics around an extremal black hole 6. Banadosteitelboimzanelli btz black holes are constructed by orbifolding ads3 geometry by boost transformations of its o2,2 isometry group. However, when the small statistical fluctuations around equilibrium are considered, we get a nonzero gibbs free energy. Pdf thermodynamics of btz black holes in gravitys rainbow. Ruppeiner theory of black hole thermodynamics jan e aman 1, james bedford2. In this system, there exists a mass gap so that there does not seem to exist a continuous thermodynamic phase transition. Part iv duality between charged btz black hole and luttinger liquids 91. Afshar 9th crete regional meeting on string theory kolymbari july 11, 2017. We indicate how special values of its logarithm correspond to certain thermodynamic quantities associated with the black hole. Research article fermion fields in btz black hole spacetime. Holography of the btz black hole, inside and out pdf paperity.