More on long string dynamics in gravity on<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>AdS</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>: Spinning strings and rotating BTZ black holes

Kim, Jihun; Porrati, Massimo

doi:10.1103/physrevd.91.124061

Cited by 8 publications

(7 citation statements)

References 25 publications

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“…Such additional states were proposed in [86] to account for the lack of holomorphic factorization and other problems of the torus partition function of Euclidean Λ < 0 pure gravity in 3D. In [87,88] the classical dynamics of long string was studied beyond the probe approximation. It was shown that in the limit that their tension is Planckian, T ∼ G −2 , their collapse generate only heavy states with any mass above the "Seiberg bound" M = (c − 1)/12l = 1/8G − 1/12l.…”

Section: Scattered Last Remarksmentioning

confidence: 99%

On a canonical quantization of 3D Anti de Sitter pure gravity

Kim

Porrati

2015

J. High Energ. Phys.

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We perform a canonical quantization of pure gravity on AdS 3 using as a technical tool its equivalence at the classical level with a Chern-Simons theory with gauge group SL(2, R) × SL(2, R). We first quantize the theory canonically on an asymptotically AdS space -which is topologically the real line times a Riemann surface with one connected boundary. Using the "constrain first" approach we reduce canonical quantization to quantization of orbits of the Virasoro group and Kähler quantization of Teichmüller space. After explicitly computing the Kähler form for the torus with one boundary component and after extending that result to higher genus, we recover known results, such as that wave functions of SL(2, R) Chern-Simons theory are conformal blocks. We find new restrictions on the Hilbert space of pure gravity by imposing invariance under large diffeomorphisms and normalizability of the wave function. The Hilbert space of pure gravity is shown to be the target space of Conformal Field Theories with continuous spectrum and a lower bound on operator dimensions. A projection defined by topology changing amplitudes in Euclidean gravity is proposed. It defines an invariant subspace that allows for a dual interpretation in terms of a Liouville CFT. Problems and features of the CFT dual are assessed and a new definition of the Hilbert space, exempt from those problems, is proposed in the case of highly-curved AdS 3 .

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Section: Scattered Last Remarksmentioning

confidence: 99%

On a canonical quantization of 3D Anti de Sitter pure gravity

Kim

Porrati

2015

J. High Energ. Phys.

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“…Still lacking is the study of the thermodynamics and the entropy of the extremal BTZ ring case, that might emulate the direct calculation of the entropy of an extremal BTZ black hole. For other studies related to the properties of matter systems, in particular, rotational properties in BTZ backgrounds see [14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Thermodynamics of extremal rotating thin shells in an extremal BTZ spacetime and the extremal black hole entropy

2017

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In a (2+1)-dimensional spacetime with a negative cosmological constant, the thermodynamics and the entropy of an extremal rotating thin shell, i.e., an extremal rotating ring, are investigated. The outer and inner regions with respect to the shell are taken to be the Bañados-Teitelbom-Zanelli (BTZ) spacetime and the vacuum ground state anti-de Sitter (AdS) spacetime, respectively. By applying the first law of thermodynamics to the extremal thin shell, one shows that the entropy of the shell is an arbitrary well-behaved function of the gravitational area A+ alone, S = S(A+). When the thin shell approaches its own gravitational radius r+ and turns into an extremal rotating BTZ black hole, it is found that the entropy of the spacetime remains such a function of A+, both when the local temperature of the shell at the gravitational radius is zero and nonzero. It is thus vindicated by this analysis, that extremal black holes, here extremal BTZ black holes, have different properties from the corresponding nonextremal black holes, which have a definite entropy, the Bekenstein-Hawking entropy S(A+) = A + 4G , where G is the gravitational constant. It is argued that for extremal black holes, in particular for extremal BTZ black holes, one should set 0 ≤ S(A+) ≤ A + 4G , i.e., the extremal black hole entropy has values in between zero and the maximum Bekenstein-Hawking entropy A + 4G . Thus, rather than having just two entropies for extremal black holes, as previous results have debated, namely, 0 and A + 4G , it is shown here that extremal black holes, in particular extremal BTZ black holes, may have a continuous range of entropies, limited by precisely those two entropies. Surely, the entropy that a particular extremal black hole picks must depend on past processes, notably on how it was formed. A remarkable relation between the third law of thermodynamics and the impossibility for a massive body to reach the velocity of light is also found. In addition, in the procedure, it becomes clear that there are two distinct angular velocities for the shell, the mechanical and thermodynamic angular velocities. We comment on the relationship between these two velocities. In passing, we clarify, for a static spacetime with a thermal shell, the meaning of the Tolman temperature formula at a generic radius and at the shell.

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“…Moreover, the BTZ black hole can be formed via gravitational collapse of matter shells in a (2+1)-dimensional spacetime reproducing anew what happens in the 3+1 world. For instance, thin shell, i.e., thin ring, collapse to a BTZ black hole has been studied in [19][20][21], and spinning string dynamics in a (2+1)-dimensional AdS background has also been shown to give rise to a rotating BTZ black hole [22]. Mechanical properties of a stationary shell in a BTZ background and its quasistatic collapse up to its own gravitational radius were displayed in [23].…”

Section: Introductionmentioning

confidence: 99%

Thermodynamics of rotating thin shells in the BTZ spacetime

et al. 2015

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We investigate the thermodynamic equilibrium states of a rotating thin shell, i.e., a ring, in a (2+1)-dimensional spacetime with a negative cosmological constant. The inner and outer regions with respect to the shell are given by the vacuum anti-de Sitter and the rotating Bañados-TeitelbomZanelli spacetimes, respectively. The first law of thermodynamics on the thin shell, together with three equations of state for the pressure, the local inverse temperature and the thermodynamic angular velocity of the shell, yields the entropy of the shell, which is shown to depend only on its gravitational radii. When the shell is pushed to its own gravitational radius and its temperature is taken to be the Hawking temperature of the corresponding black hole, the entropy of the shell coincides with the Bekenstein-Hawking entropy. In addition, we consider simple ansätze for the equations of state, as well as a power-law equation of state where the entropy and the thermodynamic stability conditions can be examined analytically.

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More on long string dynamics in gravity onAdS3: Spinning strings and rotating BTZ black holes

Cited by 8 publications

References 25 publications

On a canonical quantization of 3D Anti de Sitter pure gravity

On a canonical quantization of 3D Anti de Sitter pure gravity

Thermodynamics of extremal rotating thin shells in an extremal BTZ spacetime and the extremal black hole entropy

Thermodynamics of rotating thin shells in the BTZ spacetime

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