Gabor Kunstatter

d-dimensional black hole entropy spectrum from quasinormal modes

Starting from recent observations about quasinormal modes, we use semiclassical arguments to derive the Bekenstein-Hawking entropy spectrum for d-dimensional spherically symmetric black holes. We find that, as first suggested by Bekenstein, the entropy spectrum is equally spaced: S(BH)=kln((m(0))n, where m(0) is a fixed integer that must be derived from the microscopic theory. As shown in O. Dreyer, gr-qc/0211076, 4D loop quantum gravity yields precisely such a spectrum with m(0)=3 providing the Immirzi parameter is chosen appropriately. For d-dimensional black holes of radius R(H)(M), our analysis predicts the existence of a unique quasinormal mode frequency in the large damping limit omega((d))(M)=alpha((d))c/R(H)(M) with coefficient [formula: see text], where m(0) is an integer.

Exact Dirac quantization of all 2D dilaton gravity theories

Abstract The most general dilaton gravity theory in 2 spacetime dimensions is considered. A Hamiltonian analysis is performed and the reduced phase space, which is two dimensional, is explicitly constructed in a suitable parametrization of the fields. The theory is then quantized via the Dirac method in a functional Schrodinger representation. The quantum constraints are solved exactly to yield the (spatial) diffeomorphism invariant physical wave functionals for all theories considered. These wave functionals depend explicitly on the single configuration space coordinate as well as on the imbedding of space into spacetime (i.e. on the choice of time).

Spectrum of charged black holes—the big fix mechanism revisited

Following an earlier suggestion of the authors (Barvinsky A and Kunstatter G 1997 Mass spectrum for black holes in generic 2-D dilaton gravity Proc. 2nd International A D Sakharov Conference on Physics ed I M Dremin and A M Seminkhatov (Singapore: World Scientific) pp 210–15), we use some basic properties of Euclidean black hole thermodynamics and the quantum mechanics of systems with periodic phase space coordinate to derive the discrete two-parameter area spectrum of generic charged spherically symmetric black holes in any dimension. For the Reissner–Nordstrom black hole we get A/4G = π(2n + p + 1), where the integer p = 0, 1, 2,... gives the charge spectrum, with Q = ± √ p. The quantity π(2n + 1), n = 0, 1,..., gives a measure of the excess of the mass/energy over the critical minimum (i.e. extremal) value allowed for a given fixed charge Q. The classical critical bound cannot be saturated due to vacuum fluctuations of the horizon, so that generically extremal black holes do not appear in the physical spectrum. Consistency also requires the black hole charge to be an integer multiple of any fundamental elementary particle charge: Q = ±me, m = 0, 1, 2,.... As a by-product this yields a relation between the fine structure constant and integer parameters of the black hole—a kind of the Coleman big fix mechanism induced by black holes. In four dimensions, this relationship is e2/ = p/m2 and requires the fine structure constant to be a rational number. Finally, we prove that the horizon area is an adiabatic invariant, as has been conjectured previously.

Quantum mechanics of charged black holes

Abstract We quantize the spherically symmetric sector of generic charged black holes. Thermal properties are incorporated by imposing periodicity in Euclidean time, with period equal to the inverse Hawking temperature of the black hole. This leads to an exact quantization of the area ( A ) and charge ( Q ) operators. For the Reissner–Nordstrom black hole, A =4 πG ℏ(2 n + p +1) and Q = me , for integers n , p , m . Consistency requires the fine structure constant to be quantized: e 2 /ℏ= p / m 2 . Remarkably, vacuum fluctuations exclude extremal black holes from the spectrum, while near extremal black holes are highly quantum objects. We also prove that horizon area is an adiabatic invariant.

2PI effective action and gauge dependence identities

The problem of maintaining gauge invariance when truncating the two particle irreducible (2PI) effective action has been studied recently by several authors. Here we give a simple and very general derivation of the gauge dependence identities for the off-shell 2PI effective action. We consider the case where the gauge is fixed by an arbitrary function of the quantum gauge field, subject only to the restriction that the Faddeev-Popov matrix is invertable. We also study the background field gauge. We address the role that these identies play in solving gauge invariance problems associated with physical quantities calculated using a truncated on-shell 2PI effective action.

One-loop corrected thermodynamics of the extremal and nonextremal spinning Banados-Teitelboim-Zanelli black hole

We consider the one-loop corrected geometry and thermodynamics of a rotating BTZ black hole by way of a dimensionally reduced dilaton model. The analysis begins with a comprehensive study of the non-extremal solution after which two different methods are invoked to study the extremal case. The first approach considers the extremal limit of the non-extremal calculations, whereas the second treatment is based on the following conjecture: extremal and non-extremal black holes are qualitatively distinct entities. We show that only the latter method yields regularity and consistency at the one-loop level. This is suggestive of a generalized third law of thermodynamics that forbids continuous evolution from non-extremal to extremal black hole geometries.

Quantum corrections to the thermodynamics of charged 2D black holes

We consider one-loop quantum corrections to the thermodynamics of a black hole in generic two-dimensional dilaton gravity. The classical action is the most general diffeomorphism invariant action in 1+1 space-time dimensions that contains a metric, dilaton, and Abelian gauge field, and having at most second derivatives of the fields. Quantum corrections are introduced by considering the effect of matter fields conformally coupled to the metric and nonminimally coupled to the dilaton. Back reaction of the matter fields (via nonvanishing trace conformal anomaly) leads to quantum corrections to the black hole geometry. Quantum corrections also lead to modifications in the gravitational action and hence in expressions for thermodynamic quantities. One-loop corrections to both geometry and thermodynamics (energy, entropy) are calculated for the generic theory. The formalism is then applied to a charged black hole in spherically symmetric gravity and to a rotating Ba\~nados-Teitelboim-Zanelli black hole.

Discrete spectra of charged black holes

Bekenstein proposed that the spectrum of horizon area of quantized black holes must be discrete and uniformly spaced. We examine this proposal in the context of spherically symmetric charged black holes in a general class of gravity theories. By imposing suitable boundary conditions on the reduced phase space of the theory to incorporate the thermodynamic properties of these black holes and then performing a simplifying canonical transformation, we are able to quantize the system exactly. The resulting spectra of horizon area, as well as that of charge are indeed discrete. Within this quantization scheme, near-extremal black holes (of any mass) turn out to be highly quantum objects, whereas extremal black holes do not appear in the spectrum, a result that is consistent with the postulated third law of black hole thermodynamics.

The Vilkovisky-DeWitt effective action for quantum gravity

The Vilkovisky-DeWitt effective action for gauge theories is reviewed and then discussed in the context of N-dimensional quantum gravity and quantum Kaluza-Klein theory. The formalism gives an effective action which is gauge-independent and gauge and field-parametrization invariant. These features are illustrated for the vacuum energy of N-dimensional gravity. The Bunch-Parker local momentum space approach is used to calculate also the induced Ricci scalar term in the expansion of the effective action in powers of the curvature. The effective field equations are applied to the self-consistent dimensional reduction of five-dimensional Kaluza-Klein theory. A solution exists, but is found to be physically unacceptable.

On energy in 5-dimensional gravity and the mass of the Kaluza-Klein monopole

Abstract We discuss the concept of energy in higher-dimensional gravity, with special attention given to the problem of the choice of a background. Three different approaches to the calculation of energy for solutions of the 5-dimensional Einstein equation are considered. They are then shown to be equivalent and applied to the calculation of the mass of the Kaluza-Klein monopole. The question of the reduction of a 5-dimensional theory to an effective 4-dimensional one in the presence of a Killing vector field along the compact dimension is then discussed, in particular with regard to the conformal ambiguity in the definition of the metric in the reduced theory. We show that there exists an essentially unique choice of reduction for which the 4-dimensional energy has the usual general relativistic form, and that for the Kaluza-Klein monopole this is the reduction that will make the “naive” 4-dimensional energy additive.