相关论文: Black holes and Bhargava's invariant theory

We study relations between some topics in number theory and supersymmetric black holes. These relations are based on the ``attractor mechanism'' of N=2 supergravity. In IIB string compactification this mechanism singles out certain…

We define a natural counting function for BPS black holes in $K3 \times T^2$ compactification of type II string theory, and observe that it is given by a weight 3/2 mock modular form discovered by Zagier. This hints at tantalizing relations…

We consider attractor varieties arising in the construction of dyonic black holes in Calabi-Yau compactifications of IIB string theory. We show that the attractor varieties are constructed from products of elliptic curves with complex…

We use heterotic/type-II prepotentials to study quantum/classical black holes with half the $N=2, D=4$ supersymmetries unbroken. We show that, in the case of heterotic string compactifications, the perturbatively corrected entropy formula…

The theory of quadratic forms and class numbers has connections to many classical problems in number theory. Recently, class numbers have appeared in the study of black holes in string theory. We describe this connection and raise questions…

Black holes in string theory compactified on Calabi-Yau varieties a priori might be expected to have moduli dependent features. For example the entropy of the black hole might be expected to depend on the complex structure of the manifold.…

We review work done over the last years on the macroscopic and microscopic entropy of supersymmetric black holes in fourdimensional N=2 supergravity and in N=2 compactifications of string theory and M-theory. Particular emphasis is put on…

The exact entropy of two-charge supersymmetric black holes in N=4 string theories is computed to all orders using Wald's formula and the supersymmetric attractor equations with an effective action that includes the relevant higher curvature…

In these lecture notes we describe recent progress in our understanding of attractor mechanism and entropy of extremal black holes based on the entropy function formalism. We also describe precise computation of the microscopic degeneracy…

In these lecture notes, we review some recent developments on the relation between the macroscopic entropy of four-dimensional BPS black holes and the microscopic counting of states, beyond the thermodynamical, large charge limit. After a…

We review some aspects of the attractor mechanism for extremal black holes of (not necessarily supersymmetric) theories coupling Einstein gravity to scalars and Maxwell vector fields. Thence, we consider N=2 and N=8, d=4 supergravities,…

We review recent developments concerning supersymmetric black holes in string theory. After a general introduction to the laws of black hole mechanics and to black hole entropy in string theory, we discuss black hole solutions in N=2…

The entropy and the attractor equations for static extremal black hole solutions follow from a variational principle based on an entropy function. In the general case such an entropy function can be derived from the reduced action evaluated…

By making use of the entropy function formalism we study the generalized attractor equations in the four dimensional N=2 supergravity in presence of higher order corrections. This result might be used to understand a possible ensemble one…

I review some recent work (done in collaboration with G. Veneziano) which clarifies the existence of a correspondence between self-gravitating fundamental string states and Schwarzschild black holes. The main result is a detailed…

We consider a class of 4D supersymmetric black hole solutions, arising from string theory compactifications, which classically have vanishing horizon area and singular space-time geometry. String theory motivates the inclusion of higher…

We derive new algebraic attractor equations describing supersymmetric flux vacua of type IIB string theory. The first term in these equations, proportional to the gravitino mass (the central charge), is similar to the attractor equations…

We consider 5D supersymmetric black holes in string theory compactifications that partially break supersymmetry. We compactify type IIB on $T^4$ and then further compactify on a circle with a duality twist to give Minkowski vacua preserving…

Suggested correspondence between a black hole and a highly excited elementary string is explored. Black hole entropy is calculated by computing the density of states for an open excited string. We identify the square root of oscillator…

We investigate the geometry of four dimensional black hole solutions in the presence of stringy higher curvature corrections to the low energy effective action. For certain supersymmetric two charge black holes these corrections drastically…