Related papers: Siegel Modular Forms and Black Hole Entropy

Let $k$ be an odd integer $\ge 3$ and $N$ a positive integer such that $4 \mid N$. Let $\chi$ be an even Dirichlet character modulo $N$. Shimura decomposes the space of half-integral weight cusp forms $S_{k/2}(N,\chi)$ as a direct sum of…

The recent suggestion that the entropy of Schwarzschild black holes can be computed in matrix theory using near-extremal D-brane thermodynamics is examined. It is found that the regime in which this approach is valid actually describes…

For a thermodynamic system, apart from thermal fluctuations, there are also fluctuations in thermodynamic volume when the system is in contact with a volume reservoir. For the case of black holes in anti-de Sitter spacetimes, the effect of…

For $g=8,12,16$ and $24$, there is a nonzero alternating $g$-multilinear form on the ${\rm Leech}$ lattice, unique up to a scalar, which is invariant by the orthogonal group of ${\rm Leech}$. The harmonic Siegel theta series built from…

We show that the Bekenstein-Hawking entropy associated with any black hole undergoes logarithmic corrections when small thermodynamic fluctuations around equilibrium are taken into account. Thus, the corrected expression for black hole…

In the first order formalism of gravity theories, there are some theories which are not Lorentz-diffeomorphism covariant. In the framework of such theories we cannot apply the method of conserved charge calculation used in…

The study of black holes in string theory has led to the discovery of deep and surprising connections between black holes and modular forms -- which are two classical, a priori unrelated, subjects. This article explains the main physical…

Recently it has been suggested by S. Carlip that black hole entropy can be derived from a central charge of the Virasoro algebra arising as a subalgebra in the surface deformations of General Relativity in any dimension. Here it is shown…

In this paper we study the non-holomorphic strict endoscopic parts of inner cohomology spaces of a modular Siegel threefold respect to local systems. First we show that there is a non-zero subspace of the strict endoscopic part such that it…

We prove that the infinitesimal invariant of a higher Chow cycle of type (2,3-g) on a generic abelian variety of dimension g<4 gives rise to a meromorphic Siegel modular form of (virtual) weight Sym^{4}det^{-1} with bounded singularity, and…

Wald's formula for black hole entropy, applied to extremal black holes, leads to the entropy function formalism. We manipulate the entropy computed this way to express it as the logarithm of the ground state degeneracy of a dual quantum…

We argue that supersymmetric BPS states can act as efficient finite energy probes of the moduli space geometry thanks to the attractor mechanism. We focus on 4d $\mathcal{N}=2$ compactifications and capture aspects of the effective field…

The entropy of stationary black holes has recently been calculated by a number of different approaches. Here we compare the Noether charge approach (defined for any diffeomorphism invariant Lagrangian theory) with various Euclidean methods,…

Logarithmic corrections to the entropy of extremal black holes have been successfully used to accurately match degeneracies from microscopic constructions to calculations of the gravitational path integral. In this paper, we revisit the…

We study the cohomology of certain local systems on moduli spaces of principally polarized abelian surfaces with a level 2 structure. The trace of Frobenius on the alternating sum of the \'etale cohomology groups of these local systems can…

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…

String theory is used to compute the microscopic entropy for several examples of black holes in compactifications with $N=2$ supersymmetry. Agreement with the Bekenstein-Hawking entropy and the moduli-independent $N=2$ area formula is found…

Strominger and Vafa have used D-brane technology to identify and precisely count the degenerate quantum states responsible for the entropy of certain extremal, BPS-saturated black holes. Here we give a Type-II D-brane description of a class…

We prove that formal Fourier Jacobi expansions of degree 2 are Siegel modular forms. As a corollary, we deduce modularity of the generating function of special cycles of codimension 2, which were defined by Kudla. A second application is…

We study the entropy of black holes in the deformed Horava-Lifshitz gravity with coupling constant lambda. For lambda=1, the black hole resembles the Reissner-Norstrom black hole with a geometric parameter acting like the electric charge.…