A note on entropy of de Sitter black holes

A de Sitter black hole or a black hole spacetime endowed with a positive cosmological constant has two Killing horizons -- a black hole and a cosmological event horizon surrounding it. It is natural to expect that the total Bekenstein-Hawking entropy of such spacetimes should be the sum of the two horizons' areas. In this work we apply the recently developed formalism using the Gibbons-Hawking-York boundary term and the near horizon symmetries to derive the total entropy of such two horizon spacetimes. We construct a suitable general geometric set up for general stationary axisymmetric spacetimes with two or more than two commuting Killing vector fields in an arbitrary spacetime dimensions. This framework helps us to deal with both the horizons in an equal footing. We show that in order to obtain the total entropy of such spacetimes, the near horizon mode functions for the diffeomorphism generating vector fields have to be restricted in a certain manner, compared to the single horizon spacetimes. We next discuss specific known exact solutions belonging to the Kerr-Newman- or the Plebanski-Demianski-de Sitter families to show that they fall into the category of our general framework. We end with a sketch of further possible extensions of this work.Comment: v2, 16pp; added references and discussions, results unchange

Effect of a cosmological constant on propagation of vacuum polarized photons in stationary spacetimes

Consideration of vacuum polarization in quantum electrodynamics may affect the momentum dispersion relation for photons for a non-trivial background, due to appearance of curvature dependent terms in the effective action. We investigate the effect of a positive cosmological constant $\Lambda$ on this at one loop order for stationary $\Lambda$-vacuum spacetimes. To the best of our knowledge, so far it has been shown that $\Lambda$ affects the propagation in a time dependent black hole spacetime. Here we consider the static de Sitter cosmic string and the Kerr-de Sitter spacetime to show that there can be some non-vanishing effect due to $\Lambda$ for physical polarizations. Consistency of these results with the polarization sum rule is discussed.Comment: v2, 7pp; an error corrected in the Kerr-de Sitter part, improved presentation, main results unchange

Campaign Rhetoric and the Hide-and-Seek Game

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How Much to Make and How Much to Buy: Explaining Plural Sourcing Strategies

While many theories of the firm seek to explain when firms make rather than buy, in practice firms often make and buy the same input- they engage in plural sourcing. We argue that explaining the mix of external procurement and internal sourcing for the same input requires a consideration of complementarities across and constraints within modes of procurement. We create analytical foundations for making empirical predictions about when plural sourcing is likely to be optimal and why the optimal mix of internal and external sourcing may vary across situations. Our framework also proves useful for assessing the possible estimation biases in transaction level make-or-buy studies arising from ignoring complementarities and constraints.

Mass function and particle creation in Schwarzschild-de Sitter spacetime

We construct a mass or energy function for the non-Nariai class Schwarzschild-de Sitter black hole spacetime in the region between the black hole and the cosmological event horizons. The mass function is local, positive definite, continuous and increases monotonically with the radial distance from the black hole event horizon. We derive the Smarr formula using this mass function, and demonstrate that the mass function reproduces the two-temperature Schwarzschild-de Sitter black hole thermodynamics, along with a term corresponding to the negative pressure due to positive cosmological constant. We further give a field theoretic derivation of the particle creation by both the horizons and discuss its connection with the mass function.Comment: v3, 16pp; added references and discussions, typo corrected; accepted in Eur. Phys. J.