声学时空中的大质量粒子的涌现惯性和被动引力
Massive particles in acoustic space-times emergent inertia and passive gravity
摘要：
我表明，在一个理想流体的势流上的弱，球形，外部扰动，可以模拟粒子动力学。有效拉格朗日量的形式为mc^2 L（U^2/c^2），其中U是粒子相对于流体的速度，c是声速。这可以作为一个模型的涌现相对论性惯性的一个马赫原理与m扮演的角色惯性质量，也模拟重力，它也是被动的引力质量。m取决于粒子类型和内在结构，而L是普适的：对于D维粒子，L与超几何函数F（1，1/2;D/2;U^2/c^2）成正比。粒子在模拟引力场中以相同的方式下落，与其内部结构无关，因此满足弱等效原理。当D小于或等于5时，它们都有一个相对论极限，当U接近c时，获得的能量和动量发散。对于D小于或等于7，标准声学度量的零测地线解出我们的运动方程。有趣的是，对于D=4，动力学非常接近洛伦兹。粒子可以说是遵循芬斯勒类型的广义声学度量的测地线，该广义声学度量与标准声学度量共享零测地线。在旋涡几何学中，能层自动地是静态极限。正如在现实世界中一样，在"黑洞“几何中，圆形轨道在视界外的某个半径以下不存在。反粒子有一个自然的定义;我描述了一个模拟粒子真空，在其上下文中可以讨论，例如，事件视界附近的粒子霍金辐射。
英文摘要：
I show that massive-particle dynamics can be simulated by a weak, spherical, external perturbation on a potential flow in an ideal fluid. The effective Lagrangian is of the form mc^2L(U^2/c^2), where U is the velocity of the particle relative to the fluid and c the speed of sound. This can serve as a model for emergent relativistic inertia a la Mach's principle with m playing the role of inertial mass, and also of analog gravity where it is also the passive gravitational mass. m depends on the particle type and intrinsic structure, while L is universal: For D dimensional particles L is proportional to the hypergeometric function F(1,1/2;D/2;U^2/c^2). Particles fall in the same way in the analog gravitational field independent of their internal structure, thus satisfying the weak equivalence principle. For D less or equal 5 they all have a relativistic limit with the acquired energy and momentum diverging as U approaches c. For D less or equal 7 the null geodesics of the standard acoustic metric solve our equation of motion. Interestingly, for D=4 the dynamics is very nearly Lorentzian. The particles can be said to follow the geodesics of a generalized acoustic metric of a Finslerian type that shares the null geodesics with the standard acoustic metric. In vortex geometries, the ergosphere is automatically the static limit. As in the real world, in ``black hole'' geometries circular orbits do not exist below a certain radius that occurs outside the horizon. There is a natural definition of antiparticles; and I describe a mock particle vacuum in whose context one can discuss, e.g., particle Hawking radiation near event horizons.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
