Holes without Mass and Entropy in Lovelock Gravity 
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Introduction
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With the development of string theory, supergravity and brane world scenarios, over the past years, gravity theories have been widely studied in higher dimensions. In the low-energy approximation, Einstein general relativity naturally arises from string theories. As corrections from massive states of string theories and from loop expansions in string theories, some higher derivative curvature terms also appear in the low-energy effective action of string theories [@Zwie; @Lowenergylimit]. Therefore it is of great interest to discuss potential roles of those higher derivative terms in various aspects, for example, in black hole physics and early universe. Indeed, there exist a lot of works on higher derivative gravity theories in the literature.

In this paper we focus on a class of special higher derivative gravity theory, namely, Lovelock gravity [@Love], which is a natural generalization of general relativity in higher dimensions in the sense that the equations of motion of Lovelock gravity do not contain more than second order derivatives with respect to metric, as the case of general relativity. The Lagrangian of $D$-dimensional Lovelock gravity consists of the dimensionally extended Euler densities $$\label{1eq1} {\cal L} = \sum^p_{k=0}c_k {\cal L}_k,$$ where 