Isothermal Plasma Waves in Gravitomagnetic Planar Analogue

Plane symmetric analogue of NUT space

In this article on the basis of a new definition of spacetime symmetry, which is in accordance with the symmetry of the curvature invariants, we investigate exact vacuum solutions of Einstein field equations corresponding to both static and stationary plane symmetric spacetimes using the concepts of the (1+3)-decomposition or threading formalism. Demanding the presence of a plane symmetric gravitomagnetic field we find a family of two parameter (m and l) solutions, every member of which being the plane symmetric analogue of NUT space.

Pseudo-Schwarzschild Spherical Accretion as a Classical Black Hole Analogue

We demonstrate that a spherical accretion onto astrophysical black holes, under the influence of Newtonian or various post-Newtonian pseudo-Schwarzschild gravitational potentials, may constitute a concrete example of classical analogue gravity naturally found in the Universe. We analytically calculate the corresponding analogue Hawking temperature as a function of the minimum number of physical parameters governing the accretion flow. We study both the polytropic and the isothermal accretion. We show that unlike in a general relativistic spherical accretion, analogue white hole solutions can n…

Effects of Schwarzschild Geometry on Isothermal Plasma Wave Dispersion

The behavior of isothermal plasma waves has been analyzed near the Schwarzschild horizon. We consider a non-rotating background with non-magnetized and magnetized plasmas. The general relativistic magnetohydrodynamical equations for the Schwarzschild planar analogue spacetime with an isothermal state of the plasma are formulated. The perturbed form of these equations is linearized and Fourier analyzed by introducing simple harmonic waves. The determinant of these equations in each case leads to a complex dispersion relation, which gives complex values of the wave number. This has been used to …

A Liquid Model Analogue for Black Hole Thermodynamics

We are able to characterize a 2--dimensional classical fluid sharing some of the same thermodynamic state functions as the Schwarzschild black hole. This phenomenological correspondence between black holes and fluids is established by means of the model liquid's pair-correlation function and the two-body atomic interaction potential. These latter two functions are calculated exactly in terms of the black hole internal (quasilocal) energy and the isothermal compressibility. We find the existence of a ``screening" like effect for the components of the liquid.

欧拉-科特韦格涡流：一种流体力学的类比于薛定谔和克莱因-戈尔登方程的模型

Euler-Korteweg vortices: A fluid-mechanical analogue to the Schrödinger and Klein-Gordon equations

本文通过假设无旋涡的角动量等于约化普朗克常数并引入科特韦格表面张力，推导出描述欧拉-科特韦格涡流动量和连续方程的复波方程，并在引入均匀对流时得到薛定谔方程的弱场近似，同时推导出克莱因-戈尔登方程的波方程。

Energy Formula for Newman-Unti-Tamburino class of Black Holes

We compute the \emph{surface energy~(${\cal E}_{s}^{\pm}$), the rotational energy~(${\cal E}_{r}^{\pm}$) and the electromagnetic energy~(${\cal E}_{em}^{\pm}$)} for Newman-Unti-Tamburino~(NUT) class of black hole having the event horizon~(${\cal H}^{+}$) and the Cauchy horizon~(${\cal H}^{-}$). Remarkably, we find that the \emph{mass parameter can be expressed as sum of three energies i. e. $M={\cal E}_{s}^{\pm}+{\cal E}_{r}^{\pm}+{\cal E}_{em}^{\pm}$}. It has been \emph{tested} for Taub-NUT black hole, Reissner-Nordström-Taub-NUT black hole, Kerr-Taub-NUT black hole and Kerr-Newman-Taub-NUT b…

Lindblad resonance torques in relativistic discs: II. Computation of resonance strengths

We present a fully relativistic computation of the torques due to Lindblad resonances from perturbers on circular, equatorial orbits on discs around Schwarzschild and Kerr black holes. The computation proceeds by establishing a relation between the Lindblad torques and the gravitational waveforms emitted by the perturber and a test particle in a slightly eccentric orbit at the radius of the Lindblad resonance. We show that our result reduces to the usual formula when taking the nonrelativistic limit. Discs around a black hole possess an m=1 inner Lindblad resonance with no Newtonian Keplerian …

Area (or entropy) products for Newman-Unti-Tamburino class of Black Holes

We compute area (or entropy) product formula for Newman-Unti-Tamburino (NUT) class of black holes. Specifically, we derive the area product of outer horizon and inner horizon (${ \mathcal{H}}^{\pm }$) for Taub-NUT, Euclidean Taub-NUT black hole, Reissner-Nordström--Taub-NUT black hole, Kerr-Taub-NUT black hole and Kerr-Newman-Taub-NUT black hole under the formalism developed very recently by Wu et al. \cite{wu} [PRD 100, 101501(R) (2019)]. The formalism is that a generic four dimensional Taub-NUT spacetime should be described completely in terms of three or four different types of thermodynami…

Thermodynamics of the Schwarzschild-AdS black hole with a minimal length

Using the mass-smeared scheme of black holes, we study the thermodynamics of black holes. Two interesting models are considered. One is the self-regular Schwarzschild-AdS black hole whose mass density is given by the analogue to probability densities of quantum hydrogen atoms. The other model is the same black hole but whose mass density is chosen to be a rational fractional function of radial coordinates. Both mass densities are in fact analytic expressions of the $δ$-function. We analyze the phase structures of the two models by investigating the heat capacity at constant pressure and the Gi…

AdS空间中NUT类黑洞的Bekenstein-Hawking熵积

Bekenstein-Hawking Entropy Products for NUT class of Black Holes in AdS Space

本文推导了Taub-NUT-de Sitter和Taub-NUT-anti-de Sitter黑洞的与质量无关的熵积规则，并基于新形式揭示了其普适性源于与Kerr类角动量相似的新守恒荷J_{N}=MN。