Quantum Ergosphere Research Articles

Quantum ergosphere and brick wall entropy

We revisit the “brick wall” model for black hole entropy taking into account backreaction effects on the horizon structure. We do so by adopting an evaporating metric in the quasi-static approximation in which departures from the standard Schwarzschild metric are governed by a small luminosity factor. One of the effects of the backreaction is to create an ergosphere-like region which naturally tames the usual divergence in the calculation of the partition function of the field. The black hole luminosity sets the width of such ‘quantum ergosphere’. We find a finite horizon contribution to the entropy which, for the luminosity associated to the Hawking flux, reproduces remarkably well the Bekenstein-Hawking entropy-area law.

What gravity waves are telling about quantum spacetime

We discuss various modified dispersion relations motivated by quantum gravity which might affect the propagation of the recently observed gravitational-wave signal of the event GW150914. We find that the bounds set by the data on the characteristic quantum-gravity mass scale $M$ are too weak to constrain these scenarios and, in general, much weaker than the expected $M> 10^4\,\text{eV}$ for a correction to the dispersion relation linear in $1/M$. We illustrate this issue by giving lower bounds on $M$, plus an upper bound coming from constraints on the size of a quantum ergosphere. We also show that a phenomenological dispersion relation $\omega^2 = k^2(1+\alpha k^n/M^n)$ is compatible with observations and, at the same time, has a phenomenologically viable mass $M>10\,\text{TeV}$ only in the quite restrictive range $0<n<0.68$. Remarkably, this is the domain of multiscale spacetimes but not of known quantum-gravity models.

FROM BRICKS TO QUASINORMAL MODES: A NEW PERSPECTIVE ON BLACK HOLE ENTROPY

Calculations of black hole entropy based on the counting of modes of a quantum field propagating in a Schwarzschild background need to be regularized in the vicinity of the horizon. To obtain the Bekenstein–Hawking result, the short distance cut-off needs to be fixed by hand. In this note, we give an argument for obtaining this cut-off in a natural fashion. We do this by modeling the black hole by its set of quasinormal modes (QNMs). The horizon then becomes a extended region: the quantum ergosphere. The interaction of the quantum ergosphere and the quantum field provides a natural regularization mechanism. The width of the quantum ergosphere provides the right cut-off for the entropy calculation. We arrive at a dual picture of black hole entropy. The entropy of the black hole is given both by the entropy of the quantum field in the bulk and the dynamical degrees of freedom on the horizon.

Discussion on event horizon and quantum ergosphere of dynamic rotating black holes in a tunneling framework

According to the Parikh—Wilczek tunneling framework, the locations of the local horizons of dynamic rotating black holes can be worked out. The calculations show that the quantum ergosphere of the black hole is identical with the tunneling potential barrier set by particle's tunneling across the relevant horizon. Then, some discussions on the origin of the Hawking radiation will be shown.

DISCUSSION ON EVENT HORIZON AND QUANTUM ERGOSPHERE OF DYNAMIC DE SITTER BLACK HOLES

In the paper, the tunneling framework is applied to calculate the local horizons of Vaidya–de Sitter black holes and Vaidya–Bonner–de Sitter black holes. The researches show that the quantum ergosphere of a spherically symmetric black hole is identical with the potential barrier set by the tunneling process. The calculations also indicate that both the apparent horizons of the dynamic de Sitter black hole produce Hawking radiation. The conclusions can be applicable to either the charged or uncharged particles' Hawking radiation.

Discussion on event horizon and quantum ergosphere of evaporating black holes in a tunnelling framework

In this paper, with the Parikh-Wilczek tunnelling framework the positions of the event horizon of the Vaidya black hole and the Vaidya-Bonner black hole are calculated respectively. We find that the event horizon and the apparent horizon of these two black holes correspond respectively to the two turning points of the Hawking radiation tunnelling barrier. That is, the quantum ergosphere coincides with the tunnelling barrier. Our calculation also implies that the Hawking radiation comes from the apparent horizon.

Spacetime structure of an evaporating black hole in quantum gravity

The impact of the leading quantum gravity effects on the dynamics of the Hawking evaporation process of a black hole is investigated. Its spacetime structure is described by a renormalization group improved Vaidya metric. Its event horizon, apparent horizon, and timelike limit surface are obtained by taking the scale dependence of Newton's constant into account. The emergence of a quantum ergosphere is discussed. The final state of the evaporation process is a cold, Planck size remnant.

Black hole entropy, log corrections and quantum ergosphere

Quantum gravity corrections to the probability of emission of a particle from a black hole in the Parikh–Wilczek tunneling framework are studied. We consider the effects of zero-point quantum fluctuations of the metric on the emission probability for a tunneling shell. Quantum properties of the geometry are responsible for the formation of a “quantum ergosphere” whose effects on the emission probability can be related to the emergence of a logarithmic correction to the Bekenstein–Hawking entropy–area formula.

NON-EXISTENCE OF NEW QUANTUM ERGOSPHERE EFFECT OF A VAIDYA-TYPE BLACK HOLE

Hawking evaporation of Dirac particles and scalar fields in a Vaidya-type black hole is investigated by the method of generalized tortoise coordinate transformation. It is shown that Hawking radiation of Dirac particles does not exist for P1, Q2 components but for P2, Q1 components in any Vaidya-type black holes. Both the location and the temperature of the event horizon change with time. The thermal radiation spectrum of Dirac particles is the same as that of Klein–Gordon particles. We demonstrate that there is no new quantum ergosphere effect in the thermal radiation of Dirac particles in any spherically symmetry black holes.

QUANTUM ERGOSPHERE AND HAWKING PROCESS

We study both spherically symmetric and rotating (Kerr) nonstationary black holes and discuss the radiation of these black holes via the Hawking process. We find that the thermal radiation spectrum of a nonstationary black hole is obviously dependent on the spin state of a particle and is different from the case of a stationary black hole. This effect originates from the quantum ergosphere. We also find that the field equations of spin s=0,1/2,1 and 2 can combine into a generalized Teukolsky-type master equation with sources for any spherically symmetric black hole.

QUANTUM ERGOSPHERE EFFECT OF SPHERICALLY SYMMETRIC NON-STATIC BLACK HOLE

By means of the Newman-Penrose formalism,the gravitational,electromagnetic, scalar and Dirac fields in spherically symmetric non-static space-times are discussed.It is shown that the quantum ergosphere can influence the radiative mechanism of a non-static black hole.The character of the effect is that the radiative mechanism is obviously dependent on the spin state,which differs from the classical effects due to the Kerr ergosphere and the electromagnetic potential.

Dynamical origin of black-hole radiance

An explanation of the thermal quantum radiance of black holes discovered by Hawking is offered in terms of a black-hole metric undergoing quantum zero-point fluctuations of zero mean in its gravitational quasinormal modes. It is shown that such zero-temperature fluctuations, governed by the uncertainty principle, lead to the formation of a quantum ergosphere that enables matter of all species to tunnel out of the hole. The results confirm that a black hole cannot be in equilibrium at zero temperature. A dynamical temperature is calculated by equating the mean irreducible mass associated with the quantum ergosphere to the mean thermal energy of a quantum oscillator with the lowest quasinormal frequency. The result agrees with the Hawking temperature to within two per cent. The nature of the dynamical equilibrium and the higher modes are discussed, and it is calculated that the thermal excitations of the resonant modes have the canonical distribution to within several per cent. A calculation of the black-hole entropy using the statistical mechanics of the quasinormal modes yields a value $(0.27654){\ensuremath{\hbar}}^{\ensuremath{-}1}(16\ensuremath{\pi}{M}^{2})$, which is near the value usually assumed, $(0.25){\ensuremath{\hbar}}^{\ensuremath{-}1}(16\ensuremath{\pi}{M}^{2})$. Characteristic fluctuation scales are derived. The rms energy fluctuation of the physical (dressed) event horizon is about ${10}^{17}$ GeV, independent of $M$. The physical metric fluctuations near the hole are of order unity when the hole has mass \ensuremath{\approx} (0.15) (Planck mass) \ensuremath{\approx} 1.8\ifmmode\times\else\texttimes\fi{}${10}^{18}$ GeV.