Classical and Quantum Approaches to Black Holes (original) (raw)
Related papers
Acoustic black holes: horizons, ergospheres and Hawking radiation
Classical and Quantum Gravity, 1998
It is a deceptively simple question to ask how acoustic disturbances propagate in a non-homogeneous flowing fluid. Subject to suitable restrictions, this question can be answered by invoking the language of Lorentzian differential geometry. This paper begins with a pedagogical derivation of the following result: if the fluid is barotropic and inviscid, and the flow is irrotational (though possibly time dependent), then the equation of motion for the velocity potential describing a sound wave is identical to that for a minimally coupled massless scalar field propagating in a (3 + 1)-dimensional Lorentzian geometry ψ ≡ 1 √ −g ∂ µ √ −g g µν ∂ ν ψ = 0. The acoustic metric g µν (t, x) governing the propagation of sound depends algebraically on the density, flow velocity, and local speed of sound. Even though the underlying fluid dynamics is Newtonian, non-relativistic, and takes place in flat space plus time, the fluctuations (sound waves) are governed by an effective (3 + 1)-dimensional Lorentzian spacetime geometry. This rather simple physical system exhibits a remarkable connection between classical Newtonian physics and the differential geometry of curved (3 + 1)-dimensional Lorentzian spacetimes, and is the basis underlying a deep and fruitful analogy between the black holes of Einstein gravity and supersonic fluid flows. Many results and definitions can be carried over directly from one system to another. For example, it will be shown how to define the ergosphere, trapped regions, acoustic apparent horizon, and acoustic event horizon for a supersonic fluid flow, and the close relationship between the acoustic metric for the fluid flow surrounding a point sink and the Painlevé-Gullstrand form of the Schwarzschild metric for a black hole will be exhibited. This analysis can be used either to provide a concrete non-relativistic analogy for black-hole physics, or to provide a framework for attacking acoustics problems with the full power of Lorentzian differential geometry.
To be published in the proceedings of, 1998
Acoustic propagation in a moving fluid provides a conceptually clean and powerful analogy for understanding black hole physics. As a teaching tool, the analogy is useful for introducing students to both General Relativity and fluid mechanics. As a research tool, the analogy helps clarify what aspects of the physics are kinematics and what aspects are dynamics. In particular, Hawking radiation is a purely kinematical effect, whereas black hole entropy is intrinsically dynamical. Finally, I discuss the fact that with present technology acoustic Hawking radiation is almost experimentally testable.
Acoustic analogues of black hole singularities
Physical Review D, 2005
We search for acoustic analogues of a spherical symmetric black hole with a pointlike source. We show that the gravitational system has a dynamical counterpart in the constrained, steady motion of a fluid with a planar source. The equations governing the dynamics of the gravitational system can be exactly mapped in those governing the motion of the fluid. The different meaning that singularities and sources have in fluid dynamics and in general relativity is also discussed. Whereas in the latter a pointlike source is always associated with a (curvature) singularity in the former the presence of sources does not necessarily imply divergences of the fields. * Electronic address: mariano.cadoni@ca.infn.it † Electronic address: smignemi@vaxca1.unica.it
New theoretical approaches to black holes
New Astronomy Reviews, 2008
Quite recently, some new mathematical approaches to black holes have appeared in the literature. They do not rely on the classical concept of event horizon—which is very global, but on the local concept of hypersurfaces foliated by trapped surfaces. After a brief introduction to these new horizons, we focus on a viscous fluid analogy that can be developed to describe their dynamics, in a fashion similar to the membrane paradigm introduced for event horizons in the seventies, but with a significant change of sign of the bulk viscosity.
Black holes in the classical and quantum world
arXiv (Cornell University), 2023
These are the lecture notes for an introductory course on black holes and some aspects of their interaction with the classical and quantum world. The focus is on phenomena of "fundamental physics" in the immediate surroundings of the black hole (classical and quantum fields, with little astrophysics). We aim more at qualitative, intuitive understanding than at quantitative rigor or detail. Accordingly, we only assume previous exposure to a conventional introduction to the elements of General Relativity and a glancing acquaintance with the Schwarzschild solution, but not more. We use many figures for illustrations and provide a set of carefully guided exercises. Topics: (1) The black hole as a tale of light and darkness. (2) The black hole that vibrates. (3) The black hole that rotates. (4) The black hole that evaporates.
The Interior Enviroment of a Black Hole.
We consider the case of constantly accelerated frames and rotating frames in the Special Theory of Relativity. We find that both cases have surfaces homologous to an event horizon at the point where the velocity of the non-inertial reference frame, , with respect to an arbitrary but fixed global inertial frame, , becomes and space variables become time-like and the time variable becomes space-like. We conjecture that this is impossible and that one must transfer to another reference frame which becomes non-rigid at least slightly before reaching the event horizon and where space variables are globally space-like and never null or time-like and time variables are globally time-like, never null or space-like. We conjecture, moreover, that in relativity any rigid non-inertial reference frame must have an event horizon somewhere; we also conjecture that this is not a reference frame that could occur in nature and whose space and time variables could be used for meaningful physical analysis. In that case, one must transfer to another reference frame which is non-rigid and in which no event horizon occurs. Mathematical
Scalar exact solutions and phononic Hawking radiation in acoustic black holes
Using the same procedure adopted to study the influence of the gravi\-tation\-al field produced by astrophysical black hole on scalar fields, we obtain exact solutions of the radial part of massless Klein-Gordon equation in the spacetime of both three dimensional rotating and four dimensional canonical acoustic black holes, which are given in terms of the confluent Heun functions. We investigate the solutions in regions near and far from the acoustic event horizon. From the radial solution, we obtain the exact wave solutions near the acoustic horizon. From these, we show that both three dimensional rotating and four dimensional canonical acoustic black holes are the exact analogous to the Kerr and Schwarzschild spacetimes, respectively, and discuss the analogue Hawking radiation of massless scalar particles. Hawking temperature of both rotating and canonical acoustic black holes are derived.
Black Holes: a Different Perspective
International Journal of Advanced Engineering Research and Science (IJAERS), 2019
In this paper we propose a full revised version of a simple model, which allows a formal derivation of an infinite set of Schwarzschild-Like solutions (non-rotating and non-charged "black holes"), without resorting to General Relativity. A new meaning is assigned to the usual Schwarzschild-Like solutions (Hilbert, Droste, Brillouin, Schwarzschild), as well as to the very concepts of "black hole" and "event horizon". We hypothesize a closed Universe, homogeneous and isotropic, characterized by a further spatial dimension. Although the Universe is postulated as belonging to the so-called oscillatory class (in detail, we consider a simple-harmonically oscillating Universe), the metric variation of distances is not thought to be a real phenomenon (otherwise, we would not be able to derive any static solution): on this subject, the cosmological redshift is regarded as being caused by a variation over time of the Planck "constant". Time is considered as being absolute. The influence of matter/energy on space is analysed by the superposition of three three-dimensional scenarios. A short section is dedicated to the so-called gravitational redshift which, once having imposed the conservation of energy, may be ascribable to a local variability of the Planck "constant".