Tianye Liu

collaborators

2 papers

gr-qc2025

Creating a Universe from Nothing as an Alternative to the Cosmological Principle

Philip D. Mannheim, Daniel A. Norman, Tianye Liu

In the cosmological Robertson-Walker geometry required of the cosmological principle both the Weyl tensor $C^{I^¼ I^» I^½ I^º}$ and the Bach tensor $W^{Î¼Î½}=[2\nabla_Îº\nabla_Î»-R_{Î»Îº}…

math-ph2025

Properties of associated Legendre conical functions

Daniel A. Norman, Philip D. Mannheim, Tianye Liu

We present some new properties of associated Legendre conical functions of the first and second kind, $P_{- 1/2 + i I ¨ }^{- 1/2 - K} (I ¨ )$ and $Q_{- 1/2 + i I ¨ }^{- 1/2 - K} (I ¨ )$ . In particular w…