Entropy function for 4-charge extremal black holes in type IIA superstring theory

We calculate near-horizon solutions for four-dimensional 4-charge and fivedimensional 3-charge black holes in heterotic string theory from the part of the tendimensional tree-level effective action which is connected to gravitational Chern-Simons term by supersymmetry. We obtain that the entropies of large black holes exactly match the α ′ -exact statistical entropies obtained from microstate counting (D = 4) and AdS/CFT correspondence (D = 5). Especially interesting is that we obtain agreement for both BPS and non-BPS black holes, contrary to the case of R 2 -truncated (four-derivative) actions (D-dimensional N = 2 off-shell supersymmetric or Gauss-Bonnet) were used, which give the entropies agreeing (at best) just for BPS black holes. The key property of the solutions, which enabled us to tackle the action containing infinite number of terms, is vanishing of the Riemann tensor R M N P Q obtained from torsional connection defined with Γ = Γ − 1 2 H. Moreover, if every monomial of the remaining part of the effective action would contain at least two Riemanns R M N P Q , it would trivially follow that our solutions are exact solutions of the full heterotic effective action in D = 10. The above conjecture, which appeared (in this or stronger form) from time to time in the literature, has controversial status, but is supported by the most recent calculations of ). Agreement of our results for the entropies with the microscopic ones supports the conjecture. As for small black holes, our solutions in D = 5 still have singular horizons.

Section: Additional Terms In the Actionmentioning

confidence: 92%

α′-exact entropies for BPS and non-BPS extremal dyonic black holes in heterotic string theory from ten-dimensional supersymmetry

Prester

Terzić

2008

“…It is well known that after dimensional reduction, the extremal black hole in Type II string theory has AdS 2 as part of its near horizon geometry rather than AdS 3 . It has already been noticed in [10] and [11] that although the entropy function could give the correct entropy in lower dimensions, not all the moduli fields could take definite values. In this section we first do the dimensional reduction down to six and five dimensions, keeping the BTZ part of the near horizon metric invariant, then we find that the same results for the entropy can be obtained while some of the moduli fields do not take definite values.…”

Section: Entropy Function In Lower Dimensionsmentioning

confidence: 99%

Entropy function for non-extremal black holes in string theory

Cai

Pang

2007

Self Cite

We generalize the entropy function formalism to five-dimensional and four-dimensional non-extremal black holes in string theory. In the near horizon limit, these black holes have BTZ metric as part of the spacetime geometry. It is shown that the entropy function formalism also works very well for these non-extremal black holes and it can reproduce the Bekenstein-Hawking entropy of these black holes in ten dimensions and lower dimensions.

“…The Sen entropy function framework is applicable for this exercise in spite of the non standard horizon geometry, with certain modifications. The corrected entropy actually depends on a parameter which involves field redefinitions for the higher derivative terms [24]. This essentially happens for the D2-D6-NS5-P system because the supergravity configuration admits a near horizon geometry involving AdS 3 and S 2 with different radii (unlike the D1-D5-P system considered later).…”

Section: Four Charged Black Holes In D = 10mentioning

confidence: 99%

“…The α′ corrected entropy for the four charged extremal black hole may now be computed using the Wald formula and the Sen entropy function extremisation framework. An explicit computation gives the corrected entropy as [24] …”

Section: Four Charged Black Holes In D = 10mentioning

confidence: 99%

Thermodynamic geometry and extremal black holes in string theory

Sarkar

Sengupta

Tiwari

2008

We study a generalisation of thermodynamic geometry to degenerate quantum ground states at zero temperatures exemplified by charged extremal black holes in type II string theories. Several examples of extremal charged black holes with non degenerate thermodynamic geometries and finite but non zero state space scalar curvatures are established. These include black holes described by D1-D5-P and D2-D6-NS5-P brane systems and also two charged small black holes in Type II string theories. We also explore the modifications to the state space geometry and the scalar curvature due to the higher derivative contributions and string loop corrections as well as an exact entropy expression from quantum information theory. Our construction describes state space geometries arising out of a possible limiting thermodynamic characterisation of degenerate quantum ground states at zero temperatures.