Entropic Origin of Hawking Radiation

A Note on Temperature and Energy of 4-dimensional Black Holes from Entropic Force

We investigate the temperature and energy on holographic screens for 4-dimensional black holes with the entropic force idea proposed by Verlinde. We find that the "Unruh-Verlinde temperature" is equal to the Hawking temperature on the horizon and can be considered as a generalized Hawking temperature on the holographic screen outside the horizons. The energy on the holographic screen is not the black hole mass $M$ but the reduced mass $M_0$, which is related to the black hole parameters. With the replacement of the black hole mass $M$ by the reduced mass $M_0$, the entropic force can be writte…

Entropic Entanglement: Information Prison Break

We argue certain nonviolent local quantum field theory (LQFT) modification considered at the global horizon ($r=2M$) of a static spherically-symmetric black hole can lead to adiabatic leakage of quantum information in the form of Hawking particles. The source of the modification is (i) smooth at $r=2M$ and (ii) rapidly vanishing at $r\gg2M$. Furthermore, we restore the unitary evolution by introducing extra quanta which departs slightly from the generic Hawking emission without changing the experience of an infalling observer (no drama). Also, we suggest that a possible interpretation of the B…

Entropic uncertainty relation in Garfinkle-Horowitz-Strominger dilation black hole

Heisenberg's uncertainty principle is a fundamental element in quantum mechanics. It sets a bound on our ability to predict the measurement outcomes of two incompatible observables simultaneously. In quantum information theory, the uncertainty principle can be expressed using entropic measures. The entropic uncertainty relation can be improved by considering an additional particle as a memory particle. The presence of quantum correlation between the memory particle and the measured particle reduces the uncertainty. In a curved space-time, the presence of the Hawking radiation can reduce quantu…

Schwarzschild-de Sitter black hole from entropic viewpoint

In a Schwarzschild-de Sitter space, we consider an equipotential surface which consists of two holographic screens. Adapting the Bousso-Hawking's reference point of vanishing force, we divide the space into two regions, which are from the reference point to each holographic screen. These two regions can be treated as independent thermodynamical systems, because the Bousso-Hawking reference point with zero temperature behaves like a thermally insulating wall. The entropy obtained in this way agrees with the conventional results; i) when the holographic screens lie at the black hole and cosmolog…

Entropic Principles

We discuss the evolution of radiation and Bekenstein-Hawking entropies in expanding isotropic universes. We establish a general relation which shows why it is inevitable that there is currently a huge difference in the numerical values of these two entropies. Some anthropic constraints on their values are given and other aspects of the cosmological 'entropy gap' problem are discussed. The coincidence of the classical and quantum entropies for black holes with Hawking lifetime equal to the age of the universe, and hence of radius equal to the proton size, is shown to be identical to the conditi…

Machian Origin of the Entropic Gravity and Cosmic Acceleration

We discuss the emergence of relativistic effects in the Machian universe with a global preferred frame and use thermodynamic considerations to clarify the origin of gravity as an entropic force and the origin of dark energy/cosmic acceleration as related to the Hawking-Unruh temperature at the universe's horizon.

Evaporating Black Holes And An Entropic Scale-Hierarchy

It is argued that a characteristic length may be associated with the entropic state of a spherically symmetric black hole in the cosmological context. This length is much smaller than the Schwarzschild-radius of a black hole and may act as a regulator of arbitrarily high frequencies apparently entering the usual derivation of Hawking's radiation.

Thermodynamically consistent entropic-force cosmology

We analyze the thermodynamical consistency of entropic-force cosmological models. Our analysis is based on a generalized entropy scaling with an arbitrary power of the Hubble radius. The Bekenstein-Hawking entropy, proportional to the area, and the nonadditive $S_{δ=3/2}$-entropy, proportional to the volume, are particular cases. One of the points to be solved by entropic-force cosmology for being taken as a serious alternative to mainstream cosmology is to provide a physical principle that points out what entropy and temperature have to be used. We determine the temperature of the universe ho…

Entropic force in black hole binaries and its Newtonian limits

We give an exact solution for the static force between two black holes at the turning points in their binary motion. The results are derived by Gibbs' principle and the Bekenstein-Hawking entropy applied to the apparent horizon surfaces in time-symmetric initial data. New power laws are derived for the entropy jump in mergers, while Newton's law is shown to derive from a new adiabatic variational principle for the Hilbert action in the presence of apparent horizon surfaces. In this approach, entropy is strictly monotonic such that gravity is attractive for all separations including mergers, an…

引力彩虹中的超熵黑洞及彩虹函数约束的确定

Super-entropic black holes in gravity's rainbow and determining constraints on rainbow functions

本文针对引力彩虹框架下的d维能量依赖黑洞，计算其扩展与非扩展相空间的热力学量，结合逆等周不等式确定彩虹函数约束，并证明满足约束时黑洞符合超熵条件。

Microscopic Origin of the Bekenstein-Hawking Entropy

The Bekenstein-Hawking area-entropy relation $S_{BH}=A/4$ is derived for a class of five-dimensional extremal black holes in string theory by counting the degeneracy of BPS soliton bound states.

`Thermodynamics' of Minimal Surfaces and Entropic Origin of Gravity

Deformations of minimal surfaces lying in constant time slices in static space-times are studied. An exact and universal formula for a change of the area of a minimal surface under shifts of nearby point-like particles is found. It allows one to introduce a local temperature on the surface and represent variations of its area in a thermodynamical form by assuming that the entropy in the Planck units equals the quarter of the area. These results provide a strong support to a recent hypothesis that gravity has an entropic origin, the minimal surfaces being a sort of holographic screens. The grav…

Some new insights on the statistical origin of the Bekenstein-Hawking entropy I: Some heuristic arguments

Now that the Bekenstein-Hawking entropy has been found within the traditional theory, its physical interpretation should hide in quantum field theory in curved spacetime (only its quantum corrections require a detailed knowledge of quantum gravity). However, to interpret the statistical origin of the Bekenstein-Hawking entropy, there have developed many microscopic pictures, some of them are based on the theories that themselves remain to be experimentally verified, while some cite the Hawking temperature formula and actually argue in circle (and then they have not provided more information th…

Newtonian black holes: Particle production, "Hawking" temperature, entropies and entropy field equations

Newtonian gravitation with some slight modifications, along with some highly simplified ideas from quantum field theory allow us to reproduce, at least at the level of back-of-the-envelope calculations, many results of black hole physics. We consider particle production by a black hole, the Newtonian equivalent of the Hawking temperature, and the Bekenstein entropy. Also, we are able to deduce Newtonian field equations from entropy. We finally study higher-order Newtonian theories under the same assumptions used for ordinary Newtonian theory. In a companion article we will look at entropic for…

Origin of Hawking Radiation: Firewall or Atmosphere?

The Unruh vacuum not admitting any outgoing flux at the horizon implies that the origin of the outgoing Hawking radiation is the atmosphere of a near-horizon quantum region without resort to the firewall; however, the existence of the firewall of superplanckian excitations at the horizon can be supported by the infinite Tolman temperature at the horizon. In an exactly soluble model, we explicitly show that the firewall necessarily emerges out of the Unruh vacuum so that the Tolman temperature in the Unruh vacuum is divergent in essence due to the infinitely blueshifted negative ingoing flux cr…

Comment on "Empty Black Holes, Firewalls, and the Origin of Bekenstein-Hawking Entropy"

Saravani, Afshordi and Mann \cite{SAM} considered a surface fluid with vanishing energy density on the stretched horizon of a black hole, taken as the new boundary of spacetime. We show that their entropy per unit area of the fluid does not correspond to the Bekenstein-Hawking entropy, both for a Schwarzschild black hole and for a Kerr-Newman black hole. Due to the lack of a horizon, we argue that the Unruh effect could not be taken into account and the concept of local thermodynamic equilibrium is not sustained because of the $θ$-dependence of the temperature.

On the Origin of Entropic Gravity and Inertia

It was recently suggested that quantum field theory is not fundamental but emerges from the loss of phase space information about matter crossing causal horizons. Possible connections between this formalism and Verlinde's entropic gravity and Jacobson's thermodynamic gravity are proposed. The holographic screen in Verlinde's formalism can be identified as local Rindler horizons and its entropy as that of the bulk fields beyond the horizons. This naturally resolves some issues on entropic gravity. The quantum fluctuation of the fields is the origin of the thermodynamic nature of entropic gravit…

Hawking temperature in the tunneling picture

We examine Hawking radiation from a Schwarzschild black hole in several reference frames using the quasi-classical tunneling picture. It is shown that when one uses, $Γ\propto \exp(Im [\oint p dr])$, rather than, $Γ\propto \exp(2 Im [\int p dr])$, for the tunneling probability/decay rate one obtains twice the original Hawking temperature. The former expression for $Γ$ is argued to be correct since $\oint p dr$ is invariant under canonical transformations, while $\int p dr$ is not. Thus, either the tunneling methods of calculating Hawking radiation are suspect or the Hawking temperature is twic…

Bell粒子的隧穿、Page曲线与黑洞信息

Tunneling of Bell Particles, Page Curve and Black Hole Information

提出黑洞视界下方的Bell粒子薄壳解释Bekenstein-Hawking熵，利用隧穿效应导出Page曲线，证明黑洞信息通过Hawking辐射完全返回外部，并关联岛与量子极值面。

A Microscopic Description of Thermodynamic Volume in Extended Black Hole Thermodynamics

Using the fact that theories of gravity with asymptotically three-dimensional anti-de Sitter geometries have dual descriptions as two-dimensional conformal field theories (CFTs), we present the first study in field theory of the thermodynamic volume of various black hole solutions. We explain in general two-dimensional CFT terms why the presence of a thermodynamic volume can render certain black hole solutions "super-entropic". Super-entropicity simply results from the fact that the Cardy formula, which gives the gravitational Bekenstein-Hawking entropy, can over-count the CFT entropy. The exa…

Holevo Bound of Entropic Uncertainty in Schwarzschild Spacetime

For a pair of incompatible quantum measurements, the total uncertainty can be bounded by a state-independent constant. However, such a bound can be violated if the quantum system is entangled with another quantum system (called memory); the quantum correlation between the systems can reduce the measurement uncertainty. On the other hand, in a curved spacetime, the presence of the Hawking radiation can increase the uncertainty in quantum measurement. The interplay of quantum correlation in the curved spacetime has become an interesting arena for studying quantum uncertainty relations. Here we d…

On the Black Hole's Thermodynamics and the Entropic Origin of Gravity

The Schwarzschild's black hole dynamics in presence of gravity is described on using the thermodynamic equations of state for contractile materials. Its entropy and temperature, obtained by using classical principles, reproduce the results derived from quantum field theories and statistical mechanics. The given results show that, by using the gravitational dynamics to reproduce the thermodynamic equation TdS/dx = Fgravity, there is no way to establish the entropic origin of gravity, because the results can be seen the other way around.

广义熵不确定性关系与Schwarzschild黑洞中的非经典性

Generalized entropic uncertainty relation and non-classicality in Schwarzschild black hole

本研究提出广义熵不确定性关系，揭示了Schwarzschild黑洞中量子相干性与纠缠的等价性，并展示了霍金温度对量子相干性的影响。

A Note on Vacuum Polarisation and Hawking Radiation

We re-examine vacuum polarisation of a scalar field in a quasi-local volume including the horizon. We find that Hawking radiation rate is derived as a pure decay of vacuum due to scalar field interaction with classical gravity exactly in the same way as the origin of vacuum polarisation effect in Electrodynamics.

Hawking Radiation -- Revisited

In this paper we revisited Hawking radiation in the light of the original calculations of Hawking and Wald and found that some additional insights can be gained. We review a "derivation" of the field theory Hilbert space from the space of solutions, followed by the calculation of Bogoliubov coefficients in a collapsed spacetime from first principles. We show that these calculations can be generalized to the case of local Killing horizons and also to asymptotically non-flat spaces.

Einstein gravity with Gauss-Bonnet entropic corrections

A toy model of Einstein gravity with a Gauss-Bonnet classically "entropic" term mimicking a quantum correction is considered. The static black hole solution due to Tomozawa is found and generalized with the inclusion of non trivial horizon topology, and its entropy evaluated deriving the first law by equations of motion. As a result the Bekenstein-Hawking area law turns to be corrected by a logarithmic area term. A Misner-Sharp expression for the mass of black hole is found. Within a Friedmann-Lemaître-Robertson-Walker (FLRW) cosmological setting, the model is used in order to derive modified …

Comments on the entropic gravity proposal

Explicit tests are presented of the conjectured entropic origin of the gravitational force. The gravitational force on a test particle in the vicinity of the horizon of a large Schwarzschild black hole in arbitrary spacetime dimensions is obtained as entropic force. The same conclusion can be reached for the cases of a large electrically charged black hole and a large slowly rotating Kerr black hole. The generalization along the same lines to a test mass in the field of an arbitrary spherical star is also studied and found not to be possible. Our results thus reinforce the argument that the en…

Subtleties in the quasi-classical calculation of Hawking radiation

he quasi-classical method of deriving Hawking radiation is investigated. In order to recover the original Hawking temperature one must take into account a previously ignored contribution coming from the temporal part of the action. This contribution plus a contribution coming from the spatial part of the action gives the correct temperature.

The spectrum of Hawking radiation in Tsallis statistical mechanics

Hawking radiation is one of the cores in modern gratitational theory. Several articles have calculated the spectrum of Hawking radiation in Boltzmann-Gibbs statistical mechanics. However, based on recent researches, gravitational systems cannot be studied by the standard statistical mechanics. In this article, we calculate the modification to the spectrum of Hawking radiation in Tsallis statistical mechanics. We obtain the modified Stefan-Boltzmann's law and modified power of Hawking radiation. We confirm the conclusion proposed by Giddings, namely, the radiation should originate from the effe…

Hawking Radiation and Tunneling Mechanism for a New Class of Black Holes in Einstein-Gauss-Bonnet Gravity

We study the Hawking radiation in a new class of black hole solutions in the Einstein-Gauss-Bonnet theory. The black hole has been argued to have vanishing mass and entropy, but finite Hawking temperature. To check if it really emits radiation, we analyse the Hawking radiation using the original method of quantization of scalar field in the black hole background and the quantum tunneling method, and confirm that it emits radiation at the Hawking temperature. A general formula is derived for the Hawking temperature and backreaction in the tunneling approach. Physical implications of these resul…

The Hawking paradox and the Bekenstein resolution in higher-dimensional spacetimes

The black-hole information puzzle has attracted much attention over the years from both physicists and mathematicians. One of the most intriguing suggestions to resolve the information paradox is due to Bekenstein, who has stressed the fact that the low-energy part of the semi-classical black-hole emission spectrum is partly blocked by the curvature potential that surrounds the black hole. As explicitly shown by Bekenstein, this fact implies that the grey-body emission spectrum of a (3+1)-dimensional black hole is considerably less entropic than the corresponding radiation spectrum of a perfec…

Einstein Equations and MOND Theory from Debye Entropic Gravity

Verlinde's proposal on the entropic origin of gravity is based strongly on the assumption that the equipartition law of energy holds on the holographic screen induced by the mass distribution of the system. However, from the theory of statistical mechanics we know that the equipartition law of energy does not hold in the limit of very low temperature. Inspired by the Debye model for the equipartition law of energy in statistical thermodynamics and adopting the viewpoint that gravitational systems can be regarded as a thermodynamical system, we modify Einstein field equations. We also perform t…

利用引力反常研究稳态黑洞的霍金辐射

Hawking radiation from stationary black holes using gravitational anomaly

本文将Robinson-Wilczek引力反常方法推广到微扰偏离广义相对论的引力理论中的稳态轴对称黑洞，利用近视界几何简化与黑洞力学第零定律说明霍金能流如何抵消反常并恢复量子协变性。

推导悖论：Hawking辐射的原始推导

Deriving the paradox: original derivation of Hawking radiation

本文以教学方式重现Hawking辐射的原始推导，聚焦恒星球对称坍缩成黑洞，并梳理相关假设、物理意义、影响与局限。

Hawking radiation as tunneling from squashed Kaluza-Klein black hole

We discuss Hawking radiation from a five-dimensional squashed Kaluza-Klein black hole on the basis of the tunneling mechanism. A simple manner, which was recently suggested by Umetsu, is possible to extend the original derivation by Parikh and Wilczek to various black holes. That is, we use the two-dimensional effective metric, which is obtained by the dimensional reduction near the horizon, as the background metric. By using same manner, we derive both the desired result of the Hawking temperature and the effect of the back reaction associated with the radiation in the squashed Kaluza-Klein b…

On the thermodynamic origin of the Hawking entropy and a measurement of the Hawking temperature

In the spherically symmetric case the Einstein field equations take on their simplest form for a matter-density rho = 1 / (8 pi r^2), from which a radial metric coefficient g_{rr} \propto r follows. The boundary of an object with such an interior matter-density is situated slightly outside of its gravitational radius. Its surface-redshift scales with z \propto \sqrt{r}, so that any such large object is practically indistinguishable from a black hole, as seen from exterior space-time. The interior matter has a well defined temperature, T \propto 1 / \sqrt{r}. Under the assumption, that the inte…

Back Reaction of Hawking Radiation on Black Hole Geometry

We propose a model for the geometry of a dynamical spherical shell in which the metric is asymptotically Schwarzschild, but deviates from Ricci-flatness in a finite neighbourhood of the shell. Hence, the geometry corresponds to a `hairy' black hole, with the hair originating on the shell. The metric is regular for an infalling shell, but it bifurcates, leading to two disconnected Schwarzschild-like spacetime geometries. The shell is interpreted as either collapsing matter or as Hawking radiation, depending on whether or not the shell is infalling or outgoing. In this model, the Hawking radiati…

Hawking-Moss transition with a black hole seed

We extend the the concept of Hawking-Moss, or up-tunnelling, transitions in the early universe to include black hole seeds. The black hole greatly enhances the decay amplitude, however, order to have physically consistent results, we need to impose a new condition (automatically satisfied for the original Hawking-Moss instanton) that the cosmological horizon area should not increase during tunnelling. We motivate this conjecture physically in two ways. First, we look at the energetics of the process, using the formalism of extended black hole thermodynamics; secondly, we extend the stochastic …

Time Dependence of Hawking Radiation Entropy

If a black hole starts in a pure quantum state and evaporates completely by a unitary process, the von Neumann entropy of the Hawking radiation initially increases and then decreases back to zero when the black hole has disappeared. Here numerical results are given for an approximation to the time dependence of the radiation entropy under an assumption of fast scrambling, for large nonrotating black holes that emit essentially only photons and gravitons. The maximum of the von Neumann entropy then occurs after about 53.81% of the evaporation time, when the black hole has lost about 40.25% of i…

Hawking Radiation and Unitary evolution

We find a family of exact solutions to the semi-classical equations (including back-reaction) of two-dimensional dilaton gravity, describing infalling null matter that becomes outgoing and returns to infinity without forming a black hole. When a black hole almost forms, the radiation reaching infinity in advance of the original outgoing null matter has the properties of Hawking radiation. The radiation reaching infinity after the null matter consists of a brief burst of negative energy that preserves unitarity and transfers information faster than the theoretical bound for positive energy.

Hawking radiation, the Stefan-Boltzmann law, and unitarization

Where does Hawking radiation originate? A common picture is that it arises from excitations very near or at the horizon, and this viewpoint has supported the "firewall" argument and arguments for a key role for the UV-dependent entanglement entropy in describing the quantum mechanics of black holes. However, closer investigation of both the total emission rate and the stress tensor of Hawking radiation supports the statement that its source is a near-horizon quantum region, or "atmosphere," whose radial extent is set by the horizon radius scale. This is potentially important, since Hawking rad…

Entropic corrected Newton's law of gravitation and the Loop Quantum Black Hole gravitational atom

One proposal by Verlinde \cite{Verlinde:2010hp} is that gravity is not a fundamental, but an entropic force. In this way, Verlinde has provide us with a way to derive the Newton's law of gravitation from the Bekenstein-Hawking entropy-area formula. On the other hand, since it has been demonstrated that this formula is susceptible to quantum gravity corrections, one may hope that these corrections could be inherited by the Newton's law. In this way, the entropic interpretation of Newton's law could be a prolific way in order to get verifiable or falsifiable quantum corrections to ordinary gravi…

Hawking radiation of a vector field and gravitational anomalies

Recently, the relation between Hawking radiation and gravitational anomalies has been used to estimate the flux of Hawking radiation for a large class of black objects. In this paper, we extend the formalism, originally proposed by Robinson and Wilczek, to the Hawking radiation of vector particles (photons). It is explicitly shown, with Hamiltonian formalism, that the theory of an electromagnetic field on d-dimensional spherical black holes reduces to one of an infinite number of massive complex scalar fields on 2-dimensional spacetime, for which the usual anomaly-cancellation method is availa…

Schrödinger evolution of the Hawking state

A Schrödinger-picture description of the evolving quantum state of Hawking radiation is given, based on an ADM decomposition using time slicings that smoothly cross the horizon. This treatment avoids requiring a role for trans-planckian modes, which can be viewed as artifacts of Hawking's original calculation, and also supports arguments that radiation from black holes is produced in a "quantum atmosphere" with thickness comparable to the horizon size, rather than microscopically far from it. Particularly explicit formulas are given for the two-dimensional analog of the Schwarzschild geometry.…

Entropy of a self-gravitating electrically charged thin shell and the black hole limit

A static self-gravitating electrically charged spherical thin shell embedded in a (3+1)-dimensional spacetime is used to study the thermodynamic and entropic properties of the corresponding spacetime. Inside the shell, the spacetime is flat, outside it is Reissner-Nordström, and this establishes the energy density, the pressure, and the electric charge in the shell. Imposing that the shell is at a given local temperature and that the first law of thermodynamics holds on the shell one can find the integrability conditions for the temperature and for the thermodynamic electric potential, the the…

Empty Black Holes, Firewalls, and the Origin of Bekenstein-Hawking Entropy

We propose a novel solution for the endpoint of gravitational collapse, in which spacetime ends (and is orbifolded) at a microscopic distance from black hole event horizons. This model is motivated by the emergence of singular event horizons in the gravitational aether theory, a semi-classical solution to the cosmological constant problem(s), and thus suggests a catastrophic breakdown of general relativity close to black hole event horizons. A similar picture emerges in fuzzball models of black holes in string theory, as well as the recent firewall proposal to resolve the information paradox. …

The entropy of Hawking radiation and the generalized second law

We derive an approximate expression for the entropy of Hawking radiation filling a spherical box in stable thermodynamic equilibrium with the Schwarzschild black hole that produced the said radiation. The Bekenstein entropy bound is satisfied but the generalized second law might not be always guaranteed. We briefly discuss the possible origin of this unexpected result.

（2+1）引力中贝肯斯坦-霍金熵的微观起源：热场动力学方法

Microscopic Origin of Bekenstein-Hawking Entropy in $(2+1)$ Gravity: A Thermo Field Dynamics Approach

通过热场动力学方法，研究（2+1）引力中黑洞的纠缠熵与贝肯斯坦-霍金熵的微观起源。

引力坍缩的互补性（I）贝肯斯坦-霍金熵的起源

Complementarity of Gravitational Collapse (I) Origin of the Bekenstein-Hawking Entropy

通过两个精确解家族和自由参数的一一对应，展示出在Schwarzschild时间定义下接近实现视界的坍缩者与在Lemaître时间定义下经历所有可能模式的过振固球构成黑洞引力坍缩内结构的互补描述，并通过计算坍缩物质波函数的退化性证明贝肯斯坦-霍金熵面积公式。

On the origin of the particles in black hole evaporation

We present an analytic derivation of Hawking radiation for an arbitrary (spatial) dispersion relation $ω(k)$ as a model for ultra-high energy deviations from general covariance. It turns out that the Hawking temperature is proportional to the product of the group $dω/dk$ and phase $ω/k$ velocities evaluated at the frequency $ω$ of the outgoing radiation far away, which suggests that Hawking radiation is basically a low-energy phenomenon. Nevertheless, a group velocity growing too fast at ultra-short distances would generate Hawking radiation at ultra-high energies (``ultra-violet catastrophe''…

Hawking Radiation as Tunnelling in Static Black Holes

Hawking radiation can usefully be viewed as a semi-classical tunnelling process that originates at the black hole horizon. The conservation of energy implies the effect of self-gravitation. For a static black hole, a generalized Painleve coordinate system is introduced, and Hawking radiation as tunnelling under the effect of self-gravitation is investigated. The corrected radiation is consistent with the underlying unitary theory.

Discrete Black-Hole Radiation and the Information Loss Paradox

Hawking's black hole information puzzle highlights the incompatibility between our present understanding of gravity and quantum physics. However, Hawking's prediction of black-hole evaporation is at a semiclassical level. One therefore suspects some modifications of the character of the radiation when quantum properties of the {\it black hole itself} are properly taken into account. In fact, during the last three decades evidence has been mounting that, in a quantum theory of gravity black holes may have a discrete mass spectrum, with concomitant {\it discrete} line emission. A direct conseque…

The theory of Hawking radiation in laboratory analogues

Hawking radiation, despite being known to theoretical physics for nearly forty years, remains elusive and undetected. It also suffers, in its original context of gravitational black holes, from practical and conceptual difficulties. Of particular note is the trans-Planckian problem, which is concerned with the apparent origin of the radiation in absurdly high frequencies. In order to gain better theoretical understanding and, it is hoped, experimental verification of Hawking radiation, much study is being devoted to laboratory systems which use moving media to model the spacetime geometry of b…

Hawking Radiation in Dispersive Media

Hawking radiation, despite its presence in theoretical physics for over thirty years, remains elusive and undetected. It also suffers, in its original context of gravitational black holes, from conceptual difficulties. Of particular note is the trans-Planckian problem, which is concerned with the apparent origin of the radiation in absurdly high frequencies. In order to gain better theoretical understanding and, it is hoped, experimental verification of Hawking radiation, much study is being devoted to systems which model the spacetime geometry of black holes, and which, by analogy, are also t…