Black hole entropy as T-duality invariant

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Abstract
We study the Euler numbers and entropies of nonextremal intersecting D-branes in ten dimensions. We use surface gravity to constrain the compactification radii. We correctly obtain the integer valued Euler numbers for these radii. Moreover, the entropies are found to be invariant under T-duality transformation. In the extremal limit, we obtain the finite entropies only for two intersecting D-branes. We observe that these entropies are proportional to the product of the charges of each D-brane. We further study the entropies of the boosted metrics. We find that their entropies can be interpreted in term of the microscopic states of D-branes.