The Linet-Tian solution with a positive cosmological constant in four and higher dimensions

Linear stability of the Linet - Tian solution with positive cosmological constant

The purpose of this paper is to extend the analysis of gravitational instability of the Linet - Tian solution to the case $Λ> 0$. A fundamental difference brought about by $Λ>0$, as compared to $Λ<0$ is in the structure of the resulting space time. Associated with each of the two commuting Killing vectors $\partial_ϕ$, and $\partial_{z}$, there is a curvature singularity that has the same characteristics as that associated to $\partial_ϕ$ in the Levi - Civita metric, and we show that there is an isometry relating these singularities that reduces the effective parameter space of the metrics. In…

Cylindrically and toroidally symmetric solutions with a cosmological constant

Cylindrical-like coordinates for constant-curvature 3-spaces are introduced and discussed. This helps to clarify the geometrical properties, the coordinate ranges and the meaning of free parameters in the static vacuum solution of Linet and Tian. In particular, when the cosmological constant is positive, the spacetimes have toroidal symmetry. One of the two curvature singularities can be removed by matching the Linet-Tian vacuum solution across a toroidal surface to a corresponding region of the dust-filled Einstein static universe. Some other properties and limiting cases of these space-times…

Cylindrically symmetric static solutions of the Einstein field equations for elastic matter

The Einstein field equations are derived for a static cylindrically symmetric spacetime with elastic matter. The equations can be reduced to a system of two nonlinear ordinary differential equations and we present analytical and numerical solutions satisfying the dominant energy conditions. Furthermore, we show that the solutions can be matched at a finite radius to suitable $Λ$-vacuum exteriors given by the Linet-Tian spacetime.

Cylindrical solutions in metric f(R) gravity

We study static cylindrically symmetric vacuum solutions in Weyl coordinates in the context of the metric f(R) theories of gravity. The set of the modified Einstein equations is reduced to a single equation and it is shown how one can construct exact solutions corresponding to different $f(R)$ models. In particular the family of solutions with constant Ricci scalar ($R=R_{0}$) is found explicitly which, as a special case (R=0), includes the exterior spacetime of a cosmic string. Another new solution with constant, non-zero Ricci scalar is obtained and its possible relation to the Linet-Tian so…

Cylindrical Solutions in Modified f(T) Gravity

We investigate static cylindrically symmetric vacuum solutions in Weyl coordinates in the framework of f(T) theories of gravity, where T is the torsion scalar. The set of modified Einstein equations is presented and the fourth coming equations are established. Specific physical expressions are assumed for the algebraic function f(T) and solutions are obtained. Moreover, general solution is obtained with finite values of u(r) on the axis r = 0, and this leads to a constant torsion scalar. Also, cosmological constant is introduced and its relation to Linet-Tian solution in GR is commented.

A preliminary forecast for cosmological parameter estimation with gravitational-wave standard sirens from TianQin

TianQin is a space-based gravitational-wave observatory scheduled to be launched in the 2030s. In this work, we make a preliminary forecast for the cosmological parameter estimation with the gravitational-wave standard siren observation from TianQin. We simulate the standard siren data of TianQin based on its 5-year observation after the completion of construction. In the simulation, three models for the population of massive black hole binary (MBHB), i.e., pop III, Q3nod, and Q3d, are considered to predict the event numbers of MBHB mergers. We find that: (i) among the three MBHB models, the Q…

Constraining the cosmological parameters using gravitational wave observations of massive black hole binaries and statistical redshift information

Space-borne gravitational wave detectors like TianQin are expected to detect GW signals emitted by the mergers of massive black hole binaries. Luminosity distance information can be obtained from GW observations, and one can perform cosmological inference if redshift information can also be extracted, which would be straightforward if an electromagnetic counterpart exists. In this paper, we concentrate on the conservative scenario where the EM counterparts are not available, and comprehensively study if cosmological parameters can be inferred through a statistical approach, utilizing the non-u…

通过推断极端质量比旋近的形成通道改进宇宙学约束

Improving the Cosmological Constraints by Inferring the Formation Channel of Extreme-mass-ratio Inspirals

本文提出利用引力波定位信息推断极端质量比旋近（EMRIs）的形成通道，从而更精确提取红移分布。结合TianQin、LISA及星系巡天的模拟观测，显著提升了对哈勃常数和暗能量状态方程的约束精度，并提出统计方法估计AGN中产生的EMRIs比例，进一步改进宇宙学参数约束。

A note on constant curvature solutions in cylindrically symmetric metric $f(R)$ Gravity

In the previous work we introduced a new static cylindrically symmetric vacuum solutions in Weyl coordinates in the context of the metric f(R) theories of gravity\cite{1}. Now we obtain a 2-parameter family of exact solutions which contains cosmological constant and a new parameter as $β$. This solution corresponds to a constant Ricci scalar. We proved that in $f(R)$ gravity, the constant curvature solution in cylindrically symmetric cases is only one member of the most generalized Tian family in GR. We show that our constant curvature exact solution is applicable to the exterior of a string. …