arXiv Open Access 2009

Morse theory of causal geodesics in a stationary spacetime via Morse theory of geodesics of a Finsler metric

Erasmo Caponio Miguel Angel Javaloyes Antonio Masiello

Lihat Sumber

Abstrak

We show that the index of a lightlike geodesic in a conformally standard stationary spacetime is equal to the index of its spatial projection as a geodesic of a Finsler metric associated to the spacetime. Moreover we obtain the Morse relations of lightlike geodesics connecting a point to an integral line of the standard timelike Killing vector field by using Morse theory on the associated Finsler manifold. To this end, we prove a splitting lemma for the energy functional of a Finsler metric. Finally, we show that the reduction to Morse theory of a Finsler manifold can be done also for timelike geodesics.

Topik & Kata Kunci

math.DG gr-qc

Penulis (3)

Erasmo Caponio

Miguel Angel Javaloyes

Antonio Masiello

Format Sitasi

APA MLA BibTeX

Caponio, E., Javaloyes, M.A., Masiello, A. (2009). Morse theory of causal geodesics in a stationary spacetime via Morse theory of geodesics of a Finsler metric. https://arxiv.org/abs/0903.3519

Akses Cepat

Lihat di Sumber

Informasi Jurnal

Tahun Terbit: 2009
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓