Timelike Ricci curvature lower bounds via optimal transport for Orlicz-type Lorentzian costs
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2026
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| author | Ohanyan, Argam Candal, Marta Sálamo |
| author_facet | Ohanyan, Argam Candal, Marta Sálamo |
| contents | We study the optimal transport problem on globally hyperbolic spacetimes associated with Orlicz-type Lorentzian cost functions of the form $u \circ \ell$, where $u$ is a suitable monotonically increasing and concave function, and $\ell$ is the time separation. Our work encompasses and generalises the case $u(x) = u_p(x) = p^{-1}x^p$ for $p \in (0,1)$, as well as the more recent $p < 0$, which have been the only examples considered so far in the literature. A fundamental notion for our purposes is the property of $u$-separation for a pair of measures, which generalises McCann's $p$-separation and for which we are able to obtain strong duality to the full Orlicz-type optimization problem. In our main results, we characterise timelike Ricci curvature lower bounds via the convexity of the relative entropy along geodesics arising from the Orlicz-type optimal transport with cost $u \circ \ell$, which is a far-reaching generalisation of McCann's seminal work in the case $u = u_p$, $p \in (0,1)$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_22538 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Timelike Ricci curvature lower bounds via optimal transport for Orlicz-type Lorentzian costs Ohanyan, Argam Candal, Marta Sálamo Differential Geometry General Relativity and Quantum Cosmology Mathematical Physics Analysis of PDEs Metric Geometry 53B30, 53C50, 49J52, 46E30, 83C99, 49Q22 We study the optimal transport problem on globally hyperbolic spacetimes associated with Orlicz-type Lorentzian cost functions of the form $u \circ \ell$, where $u$ is a suitable monotonically increasing and concave function, and $\ell$ is the time separation. Our work encompasses and generalises the case $u(x) = u_p(x) = p^{-1}x^p$ for $p \in (0,1)$, as well as the more recent $p < 0$, which have been the only examples considered so far in the literature. A fundamental notion for our purposes is the property of $u$-separation for a pair of measures, which generalises McCann's $p$-separation and for which we are able to obtain strong duality to the full Orlicz-type optimization problem. In our main results, we characterise timelike Ricci curvature lower bounds via the convexity of the relative entropy along geodesics arising from the Orlicz-type optimal transport with cost $u \circ \ell$, which is a far-reaching generalisation of McCann's seminal work in the case $u = u_p$, $p \in (0,1)$. |
| title | Timelike Ricci curvature lower bounds via optimal transport for Orlicz-type Lorentzian costs |
| topic | Differential Geometry General Relativity and Quantum Cosmology Mathematical Physics Analysis of PDEs Metric Geometry 53B30, 53C50, 49J52, 46E30, 83C99, 49Q22 |
| url | https://arxiv.org/abs/2604.22538 |