We investigate the propagation of gravitational waves within the framework of Finslerian f(R, T) gravity based on a Randers-type perturbation. Starting from a generalized Finsler function, we construct the induced metric, inverse metric, Cartan tensor, and spray coefficients, leading to the corresponding Chern-Rund connection and Ricci curvature. Variation of the Finslerian action yields modified field equations, which are subsequently linearized in the high-frequency limit. The principal symbol of the resulting wave operator establishes hyperbolicity for sufficiently small Finsler couplings, thereby ensuring a well-posed Cauchy problem. From the eikonal analysis we derive a modified dispersion relation <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\omega ^2=c^2|\textbf{k}|^2[1+\alpha (\hat{n})]$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>ω</mi> <mn>2</mn> </msup> <mo>=</mo> <msup> <mi>c</mi> <mn>2</mn> </msup> <msup> <mrow> <mo stretchy="false">|</mo> <mi mathvariant="bold">k</mi> <mo stretchy="false">|</mo> </mrow> <mn>2</mn> </msup> <mrow> <mo stretchy="false">[</mo> <mn>1</mn> <mo>+</mo> <mi>α</mi> <mrow> <mo stretchy="false">(</mo> <mover accent="true"> <mi>n</mi> <mo stretchy="false">^</mo> </mover> <mo stretchy="false">)</mo> </mrow> <mo stretchy="false">]</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>, where <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\alpha (\hat{n})$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>α</mi> <mo stretchy="false">(</mo> <mover accent="true"> <mi>n</mi> <mo stretchy="false">^</mo> </mover> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> encodes anisotropic corrections from the Randers one-form and matter couplings. At subprincipal order, polarization birefringence emerges: the + and <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$\times $</EquationSource> <EquationSource Format="MATHML"><math> <mo>×</mo> </math></EquationSource> </InlineEquation> modes acquire distinct phase velocities governed by symmetric trace-free projections of <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$\nabla \beta $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">∇</mi> <mi>β</mi> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$T_{\mu \nu }$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>T</mi> <mrow> <mi>μ</mi> <mi>ν</mi> </mrow> </msub> </math></EquationSource> </InlineEquation>. Mapping these effects to observational data, we show that multi-messenger events such as GW170817 and the latest LIGO-Virgo-KAGRA runs constrain the effective Finsler couplings to the level of <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$10^{-15}$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>15</mn> </mrow> </msup> </math></EquationSource> </InlineEquation>-<InlineEquation ID="IEq7"> <EquationSource Format="TEX">$10^{-14}$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>14</mn> </mrow> </msup> </math></EquationSource> </InlineEquation>. These results establish a mathematically consistent and observationally testable framework for probing Finslerian modifications of gravity through gravitational-wave phenomenology.

Dispersion relations of gravitational waves in Finsler f(R, T) gravity

期刊论文
发表日期：

2026年5月10日

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Yousef Alipour Fakhri

摘要

We investigate the propagation of gravitational waves within the framework of Finslerian f(R, T) gravity based on a Randers-type perturbation. Starting from a generalized Finsler function, we construct the induced metric, inverse metric, Cartan tensor, and spray coefficients, leading to the corresponding Chern-Rund connection and Ricci curvature. Variation of the Finslerian action yields modified field equations, which are subsequently linearized in the high-frequency limit. The principal symbol of the resulting wave operator establishes hyperbolicity for sufficiently small Finsler couplings, thereby ensuring a well-posed Cauchy problem. From the eikonal analysis we derive a modified dispersion relation $\omega ^2=c^2|\textbf{k}|^2[1+\alpha (\hat{n})]$ $ω^{2} = c^{2} {| k |}^{2} [1 + α (\hat{n})]$ , where $\alpha (\hat{n})$ $α (\hat{n})$ encodes anisotropic corrections from the Randers one-form and matter couplings. At subprincipal order, polarization birefringence emerges: the + and $\times $ $\times$ modes acquire distinct phase velocities governed by symmetric trace-free projections of $\nabla \beta $ $\nabla β$ and $T_{\mu \nu }$ $T_{μ ν}$ . Mapping these effects to observational data, we show that multi-messenger events such as GW170817 and the latest LIGO-Virgo-KAGRA runs constrain the effective Finsler couplings to the level of $10^{-15}$ $10^{- 15}$ - $10^{-14}$ $10^{- 14}$ . These results establish a mathematically consistent and observationally testable framework for probing Finslerian modifications of gravity through gravitational-wave phenomenology.