Elias C. Vagenas

Universality of quantum gravity corrections.

We show that the existence of a minimum measurable length and the related generalized uncertainty principle (GUP), predicted by theories of quantum gravity, influence all quantum Hamiltonians. Thus, they predict quantum gravity corrections to various quantum phenomena. We compute such corrections to the Lamb shift, the Landau levels, and the tunneling current in a scanning tunneling microscope. We show that these corrections can be interpreted in two ways: (a) either that they are exceedingly small, beyond the reach of current experiments, or (b) that they predict upper bounds on the quantum gravity parameter in the GUP, compatible with experiments at the electroweak scale. Thus, more accurate measurements in the future should either be able to test these predictions, or further tighten the above bounds and predict an intermediate length scale between the electroweak and the Planck scale.

Discreteness of space from the generalized uncertainty principle

Various approaches to Quantum Gravity (such as String Theory and Doubly Special Relativity), as well as black hole physics predict a minimum measurable length, or a maximum observable momentum, and related modifications of the Heisenberg Uncertainty Principle to a so-called Generalized Uncertainty Principle (GUP). We propose a GUP consistent with String Theory, Doubly Special Relativity and black hole physics, and show that this modifies all quantum mechanical Hamiltonians. When applied to an elementary particle, it implies that the space which confines it must be quantized. This suggests that space itself is discrete, and that all measurable lengths are quantized in units of a fundamental length (which can be the Planck length). On the one hand, this signals the breakdown of the spacetime continuum picture near that scale, and on the other hand, it can predict an upper bound on the quantum gravity parameter in the GUP, from current observations. Furthermore, such fundamental discreteness of space may have observable consequences at length scales much larger than the Planck scale.

When conceptual worlds collide: The generalized uncertainty principle and the Bekenstein-Hawking entropy

Recently, there has been much attention devoted to resolving the quantum corrections to the Bekenstein–Hawking (black hole) entropy. In particular, many researchers have expressed a vested interest in fixing the coefficient of the sub-leading logarithmic term. In the current paper, we are able to make some substantial progress in this direction by utilizing the generalized uncertainty principle (GUP). Notably, the GUP reduces to the conventional Heisenberg relation in situations of weak gravity but transcends it when gravitational effects can no longer be ignored. Ultimately, we formulate the quantum-corrected entropy in terms of an expansion that is consistent with all previous findings. Moreover, we demonstrate that the logarithmic prefactor (indeed, any coefficient of the expansion) can be expressed in terms of a single parameter that should be determinable via the fundamental theory.

Hawking radiation as tunneling through the quantum horizon

Planck-scale corrections to the black-hole radiation spectrum in the Parikh-Wilczek tunneling framework are calculated. The corrective terms arise from modifications in the expression of the surface gravity in terms of the mass-energy of the black hole-emitted particle system. The form of the new spectrum is discussed together with the possible consequences for the fate of black holes in the late stages of evaporation.

A proposal for testing quantum gravity in the lab

Attempts to formulate a quantum theory of gravitation are collectively known as quantum gravity. Various approaches to quantum gravity such as string theory and loop quantum gravity, as well as black hole physics and doubly special relativity theories predict a minimum measurable length, or a maximum observable momentum, and related modifications of the Heisenberg Uncertainty Principle to a so-called generalized uncertainty principle (GUP). We have proposed a GUP consistent with string theory, black hole physics, and doubly special relativity theories and have showed that this modifies all quantum mechanical Hamiltonians. When applied to an elementary particle, it suggests that the space that confines it must be quantized, and in fact that all measurable lengths are quantized in units of a fundamental length (which can be the Planck length). On the one hand, this may signal the breakdown of the spacetime continuum picture near that scale, and on the other hand, it can predict an upper bound on the quantum gravity parameter in the GUP, from current observations. Furthermore, such fundamental discreteness of space may have observable consequences at length scales much larger than the Planck scale. Because this influences all the quantum Hamiltonians in an universal way, it predicts quantum gravity corrections to various quantum phenomena. Therefore, in the present work we compute these corrections to the Lamb shift, simple harmonic oscillator, Landau levels, and the tunneling current in a scanning tunneling microscope.

On Hawking Radiation as Tunneling with Back-Reaction

Recently, Angheben et al.1 have presented a refined method for calculating the (tree-level) black hole temperature by way of the tunneling paradigm. Here, we demonstrate how their formalism can be suitably adapted to accommodate the (higher-order) effects of the gravitational back-reaction.

Generalization of the KKW analysis for black hole radiation

Abstract An extension of the Keski-Vakkuri, Kraus and Wilczek (KKW) analysis to black hole spacetimes which are not Schwarzschild-type is presented. Preserving the regularity at the horizon and stationarity of the metric in order to deal with the across-horizon physics, a more general coordinate transformation is introduced. In this analysis the Hawking radiation is viewed as a tunnelling process which emanates from the non-Schwarzschild-type black hole. Expressions for the temperature and entropy of these non-Schwarzschild-type black holes are extracted. As a paradigm, in the context of this generalization, we consider the Garfinkle–Horowitz–Strominger (GHS) black hole as a dynamical background and we derive the modified temperature and entropy of GHS black hole. Deviations are eliminated and corresponding standard results are recovered to the lowest order in the emitted shell of energy. The extremal GHS black hole is found to be non-“frozen” since it is characterized by a constant non-zero temperature. Furthermore, the modified extremality condition forbids naked singularities to form from the collapse of the GHS black hole.

Semiclassical Corrections to the Bekenstein-Hawking entropy of the BTZ Black Hole via Self-Gravitation

Abstract Hawking radiation is viewed as a tunnelling process. In this way the effect of self-gravitation gives rise to semiclassical corrections to the entropy of the (2+1) BTZ black hole. The modified entropy, due to specific modelling of the self-gravitation effect, of the (2+1) BTZ black hole is evaluated. To first order inxa0 ω which is a shell of energy radiated outwards the event horizon of the BTZ black hole, modified entropy is proportional to the horizon. In this semiclassical analysis, corrections to the Bekenstein–Hawking formula S BH = A H /4l P 2 are found to be negative and the proportionality factor connecting the modified entropy, S bh , of the (2+1) BTZ black hole to the Bekenstein–Hawking entropy, S BH , is evaluated to first order inxa0 ω .

Are extremal 2D black holes really frozen

Abstract In the standard methodology for evaluating the Hawking radiation emanating from a black hole, the background geometry is fixed. Trying to be more realistic we consider a dynamical geometry for a two-dimensional charged black hole and we evaluate the Hawking radiation as a tunneling process. This modification to the geometry gives rise to a nonthermal part in the radiation spectrum. We explore the consequences of this new term for the extremal case.

Area spectrum of rotating black holes via the new interpretation of quasinormal modes

Motivated by the recent work on a new physical interpretation of quasinormal modes by Maggiore, we utilize this new proposal to the interesting case of Kerr black hole. In particular, by modifying Hods idea, the resulting black hole horizon area is quantized and the resulting area quantum is in full agreement with Bekensteins result. Furthermore, in an attempt to show that the area spectrum is equally spaced, we follow Kunstatters method. We propose a new interpretation as a result of Maggiores idea, for the frequency that appears in the adiabatic invariant of a black hole. The derived area spectrum is similar to that of the quantum-corrected Kerr black hole but it is not equally spaced.