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We initiated the program to look for new and simple forms for thefive-dimensional rotating squashed black holes by solving directly the equationof motion. In a recent paper, the metric ansatz of dimensional reduction alongthe fifth spatial dimension was used to obtain a new but rather simple form forthe five-dimensional rotating uncharged black hole solution with squashedhorizons via solving the vacuum Einstein field equations. In this work, wecontinue to seek for another new but relatively simple form for the neutralrotating squashed black hole solution by using a different metric ansatz oftime-like dimensional reduction. We then find its relation to our previoussolution and investigate its thermodynamics by means of the counterterm method.Compared with the previous results given by the other author, both of our newmetric forms and their associated thermodynamic expressions are very conciseand elegant. Both of two new forms for the neutral rotating squashed black holesolution presented in this paper can be used as the seed to generate itscharged generalization in D=5 minimal supergravity.

New forms and thermodynamics of the neutral rotating squashed black hole in five-dimensional vacuum Einstein gravity theory