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Register a new userLectures on the Microscopic Modeling of the 5-dim. Black Hole of IIB String Theory and the $D_1-D_5$ System
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Authors
Spenta R. Wadia
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In these notes we review the theory of the microscopic modeling of the 5-dim. black hole of type IIB string theory in terms of the $D1-D5$ brane system. The emphasis here is more on the brane dynamics rather than on supergravity solutions. We present a discussion of the low energy brane dynamics and account for black hole thermodynamics and Hawking radiation rates. These considerations are valid in the regime of supergravity due to the non-renormalization of the low energy dynamics in this model.
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The strongly coupled dynamics of black hole formation in bulk AdS is conjectured to be dual to the thermalization of a weakly interacting CFT on the boundary for low $N$ which, for $Ntoinfty$, becomes strongly coupled. We search for this thermalization effect by utilizing the D1D5 CFT to compute effective string interactions for $N=2$. This is done by turning on a marginal deformation of the theory which twists together or untwists effective strings. For a system to thermalize, the initial state, which is far from thermal, must redistribute its energy via interactions until a thermal state is achieved. In our case, we consider excited states of the effective strings. We compute splitting amplitudes for 1) one excitation going to three excitations and 2) two excitations going to four excitations using two insertions of the deformation. Scenario 1) corresponds to a single particle moving in AdS. Scenario 2) corresponds to two particles moving and colliding in AdS. We find that the `1 to 3 amplitude has terms which oscillate with time, $t$, where $t$ is the duration of the two deformations. We find that the `2 to 4 amplitude has similar oscillatory terms as well as secular terms which grow like $t^2$. For this case the growth implies that for large $t$ the excitations in the initial state, which carry a given energy, prefer to redistribute themselves amongst lower energy modes in the final state. This is a key feature of thermalization. Albeit in a simplified setting, we therefore argue that we have identified the thermalization vertex in the D1D5 CFT, which after repeated applications, should lead to thermalization. This ultimately maps to two particles colliding and forming a black hole in AdS, which in our case, is a fuzzball.
We briefly review the microscopic modeling of black holes as bound states of branes in the context of the soluble D1-D5 system. We present a discussion of the low energy brane dynamics and account for black hole thermodynamics and Hawking radiation rates. These considerations are valid in the regime of supergravity due to the non-renormalization of the low energy dynamics in this model. Using Maldacena duality and standard statistical mechanics methods one can account for black hole thermodynamics and calculate the absorption cross section and the Hawking radiation rates. Hence, at least in the case of this model black hole, since we can account for black hole properties within a unitary theory, there is no information paradox.
We give an elementary introduction to classical and quantum bosonic string theory.
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We present a new supersymmetric, asymptotically flat, black hole solution to five-dimensional U(1)^3-supergravity which is regular on and outside an event horizon of lens space topology L(2,1). The solution has seven independent parameters and uplifts to a family of 1/8-supersymmetric D1-D5-P black brane solutions to Type IIB supergravity. The decoupling limit is asymptotically AdS(3) x S^3 x T^4, with a near-horizon geometry that is a twisted product of the near-horizon geometry of the extremal BTZ black hole and L(2,1) x T^4, although it is not (locally) a product space in the bulk. We show that the decoupling limit of a special case of the black lens is related to that of a black ring by spectral flow, thereby supplying an account of its entropy. Analogous solutions of U(1)^N-supergravity are also presented.
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