<p>We establish the nonlinear stability to the future of tilted two-fluid Bianchi I solutions to the Einstein–Euler equations with positive cosmological constant and linear equations of state <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$p_{(\mathfrak {a})}=K_{(\mathfrak {a})}\rho _{(\mathfrak {a})}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>p</mi> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="fraktur">a</mi> <mo stretchy="false">)</mo> </mrow> </msub> <mo>=</mo> <msub> <mi>K</mi> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="fraktur">a</mi> <mo stretchy="false">)</mo> </mrow> </msub> <msub> <mi>ρ</mi> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="fraktur">a</mi> <mo stretchy="false">)</mo> </mrow> </msub> </mrow> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\mathfrak {a}\in \{1,2\}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="fraktur">a</mi> <mo>∈</mo> <mo stretchy="false">{</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo stretchy="false">}</mo> </mrow> </math></EquationSource> </InlineEquation>, where <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$\frac{1}{3}<K_{(\mathfrak {a})}<\frac{5}{7}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mfrac> <mn>1</mn> <mn>3</mn> </mfrac> <mo><</mo> <msub> <mi>K</mi> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="fraktur">a</mi> <mo stretchy="false">)</mo> </mrow> </msub> <mo><</mo> <mfrac> <mn>5</mn> <mn>7</mn> </mfrac> </mrow> </math></EquationSource> </InlineEquation>.</p>

Future Stability of Tilted Two-Fluid Bianchi I Spacetimes

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2026年7月7日

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Grigorios Fournodavlos,
Elliot Marshall,
Todd A. Oliynyk

摘要

We establish the nonlinear stability to the future of tilted two-fluid Bianchi I solutions to the Einstein–Euler equations with positive cosmological constant and linear equations of state $p_{(\mathfrak {a})}=K_{(\mathfrak {a})}\rho _{(\mathfrak {a})}$ $p_{(a)} = K_{(a)} ρ_{(a)}$ , $\mathfrak {a}\in \{1,2\}$ $a \in {1, 2}$ , where $\frac{1}{3}<K_{(\mathfrak {a})}<\frac{5}{7}$ $\frac{1}{3} < K_{(a)} < \frac{5}{7}$ .