Can the "brick wall" model present the same results in different coordinate representations?

By using the 't Hooft's "brick wall" model and the Pauli-Villars regularization scheme we calculate the statistical-mechanical entropies arising from the quantum scalar field in different coordinate settings, such as the Painlev\'{e} and Lemaitre coordinates. At first glance, it seems that the entropies would be different from that in the standard Schwarzschild coordinate since the metrics in both the Painlev\'{e} and Lemaitre coordinates do not possess the singularity at the event horizon as that in the Schwarzschild-like coordinate. However, after an exact calculation we find that, up to the subleading correction, the statistical-mechanical entropies in these coordinates are equivalent to that in the Schwarzschild-like coordinate. The result is not only valid for black holes and de Sitter spaces, but also for the case that the quantum field exerts back reaction on the gravitational field provided that the back reaction does not alter the symmetry of the spacetime.Comment: 8 pages, Phys. Rev. D in pres

Black Hole Thermodynamics and Statistical Mechanics

We have known for more than thirty years that black holes behave as thermodynamic systems, radiating as black bodies with characteristic temperatures and entropies. This behavior is not only interesting in its own right; it could also, through a statistical mechanical description, cast light on some of the deep problems of quantizing gravity. In these lectures, I review what we currently know about black hole thermodynamics and statistical mechanics, suggest a rather speculative "universal" characterization of the underlying states, and describe some key open questions.Comment: 35 pages, Springer macros; for the Proceedings of the 4th Aegean Summer School on Black Hole

Twenty-five years of Marxist Biblical criticism

In the context of a renewed interest in Marxism outside biblical studies, this article surveys and critiques the background and current status of a similar renewal in biblical studies. It begins with a consideration of the background of current studies in liberation, materialist and political theologies, and moves on to note the division between literary and social scientific uses of Marxist theories. While those who used Marxist literary methods were initially inspired by Terry Eagleton and Fredric Jameson, more recent work has begun to make use of a whole tradition of Marxist literary criticism largely ignored in biblical studies. More consistent work, however, has taken place in the social sciences in both Hebrew Bible and New Testament studies. In Hebrew Bible studies, debates focus on the question of mode of production, especially the domestic or household mode of production, while in New Testament studies, the concerns have been with reconstructing the context of the Jesus movement and, more recently, the Pauline correspondence. I close with a number of questions concerning the division into different areas of what is really a holistic approach to texts and history