Supersymmetric black holes in string theory

Mohaupt, Thomas

doi:10.1002/prop.200610382

Cited by 17 publications

(18 citation statements)

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“…µ , and purely magnetically with respect to A (2) µ and A (4) µ . Again, for extremal black holes one expects AdS 2 × S 2 near-horizon geometry (3.1) which in the present case is given by: One proceeds in the similar fashion as in section 4.…”

Section: -Charge Black Holes In D =mentioning

confidence: 99%

α′²-corrections to extremal dyonic black holes in heterotic string theory

Cvitan

Prester

Ficnar

2008

J. High Energy Phys.

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We calculate α ′2 -corrections to the entropy of the 5-dimensional 3-charge and the 4-dimensional 4-charge large extremal black holes using the low energy effective action of the heterotic string theory. In the 4-dimensional case, our results are in agreement with the microscopic statistical entropy both for the BPS and the non-BPS black holes. In the more interesting 5-dimensional case, where the direct microscopic stringy description is still unknown, our results for the BPS black holes are in agreement with the results obtained from the action supplemented with R 2 -correction obtained by supersymmetric completion of the gravitational Chern-Simons term. This agreement does not extend to the non-BPS black holes, for which we propose a different expression for the entropy. We show that the new expression is supported by certain α ′3 -order calculations, and by the arguments based on the AdS/CFT correspondence. Contents 1. Introduction: Motivation and results 1 2. D = 6 heterotic effective action 4 3. Entropy function and its expansion 7 4. 3-charge black holes in D = 5 9 5. 4-charge black holes in D = 4 13 A. Identification of charges 14 B. Near-horizon solutions 15 B.1 D = 5 3-charge extremal black holes 16 B.2 D = 4 4-charge extremal black holes 16C. On contributions from α ′2 and higher order terms in the action 18 the limit of small string coupling constant g s (free string limit), which for nw ≫ 1 is given by 1 [7,8,9] S (BP S) stat = 2π nw(N W + 4) , n > 0 .( 1.1) For n < 0 the corresponding states are non-BPS with the statistical entropy given byNote that (1.1) and (1.2) are exact in α ′ . Now, when one increases g s , it has been argued that at some point these states become black holes. While in this regime string theory becomes highly nonperturbative, it is expected that one can use low energy effective action (at least for large black holes). Indeed, in the lowest order in α ′ , the solutions which describe extremal black holes with the two electric (n and w) and the two magnetic charges (N and W ) were explicitly constructed [10]. The near-horizon effective string coupling constant is proportional to 1/|nw|, which means that one can neglect string loops for nw ≫ 1. Also, the expansion in α ′ is equivalent to the expansion in 1/|N W |. The Bekenstein-Hawking entropy is S bh(0) = 2π |nwN W |, in agreement with (1.1) and (1.2). The α ′ -corrections to the entropies were calculated in [11], with the results again in agreement with (1.1) and (1.2). Surprising results were obtained when the following two types of R 2 -corrections in the effective action were taken: (i) the supersymmetrized gravitational Chern-Simons term [12], (ii) the Gauss-Bonnet term [13]. Both of these actions give the black hole entropy in the BPS case in the exact agreement with the statistical entropy (1.1), while they do not reproduce (1.2) in the non-BPS case. These results are surprising because the full effective action contains an infinite number of additional terms, for which there is no obvious reason to produce a canceling c...

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Section: -Charge Black Holes In D =mentioning

confidence: 99%

α′²-corrections to extremal dyonic black holes in heterotic string theory

Cvitan

Prester

Ficnar

2008

J. High Energy Phys.

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“…For a large class of BPS black hole solutions, we are able to identify the black hole entropy as the logarithm of the degeneracy of states belonging to the microstates of the corresponding black hole. This prediction includes not only the leading entropy formula of Bekenstein and Hawking (see [2] for a recent review) but also all the subleading quantum gravitational corrections which was proposed in [3], building on the work of [4] (see also [5] and references there).…”

Section: Introductionmentioning

confidence: 97%

Higher derivative correction to Kaluza–Klein black hole solution

Yavartanoo

Yun

2008

Eur. Phys. J. C

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We investigate the attractor mechanism in Kaluza-Klein black hole solution in the presence of higher derivative terms. In particular, we discuss the attractor behavior of static black holes by using the effective potential approach as well as entropy function formalism. We consider different higher derivative terms with a general coupling to moduli field. For the R 2 theory, we use effective potential approach, looking for solutions which are analytic near the horizon and show that they exist and enjoy the attractor behavior. The attractor point is determined by extremization of the modified effective potential at the horizon. We study the effect of the general higher derivative corrections of R n terms. Using the entropy function we define the modified effective potential and we find the conditions to have the attractor solution. In particular for a single charged Kaluza-Klein black hole solution we show that higher derivative correction dresses the naked singularity for an appropriate coupling, and we can find the attractor solution.

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“…The work of Wald [1] has led to great progress in the understanding of the entropy of black holes. This approach is valid in theories with invariance under general coordinate invariance, and has been applied in particular to actions with gravitational higher-derivative corrections (see [2] for an overview). For extremal black holes the entropy formalism ( [3], see also [4]) can be applied.…”

Section: Introductionmentioning

confidence: 99%