International Journal of Modern Physics D

General relativity successfully describes space–times at scales that we can observe and probe today, but it cannot be complete as a consequence of singularity theorems. For a long time, there have been indications that quantum gravity will provide a more complete, non-singular extension which, however, was difficult to verify in the absence of a quantum theory of gravity. By now there are several candidates which show essential hints as to what a quantum theory of gravity may look like. In particular, loop quantum gravity is a non-perturbative formulation which is background independent, two properties which are essentially close to a classical singularity with strong fields and a degenerate metric. In cosmological and black hole settings, one can indeed see explicitly how classical singularities are removed by quantum geometry: there is a well-defined evolution all the way down to, and across, the smallest scales. As for black holes, their horizon dynamics can be studied showing characteristic modifications to the classical behavior. Conceptual and physical issues can also be addressed in this context, providing lessons for quantum gravity in general. Here, we conclude with some comments on the uniqueness issue often linked to quantum gravity in some form or another.

In this talk I summarize some recent progress in string theory in understanding the entropy of a class of black holes including corrections to the Bekenstein–Hawking formula. The quantum corrected entropy is in precise numerical agreement with the logarithm of the number of microstates once quantum corrections are correctly taken into account.

Amal Kumar Raychaudhuri died on June 18, 2005. This essay follows the lecture which was given in honor of this great Indian scientist and teacher on December 26, 2005 in Puri, India.

The description of 4D BPS black holes in terms of branes wrapped on various cycles in a Calabi–Yau space gives us the opportunity to study various issues in quantum gravity in a definite way by means of the worldvolume theory of the branes. In the particular example discussed here, there is a simple worldvolume description in terms of 2D Yang–Mills theory. The latter is an exactly solvable system of free fermions in one dimension. The exact answer for the free energy of this system can be written in a way that suggests an interpretation in terms of contributions from multiple (baby) universes.

Interactions between outgoing Hawking particles and ingoing matter are determined by gravitational forces and Standard Model interactions. In particular, the gravitational interactions are responsible for the unitarity of the scattering against the horizon, as dictated by the holographic principle, but the Standard Model interactions also contribute, and understanding their effects is an important first step towards a complete understanding of the horizon's dynamics. The relation between in- and outgoing states is described in terms of an operator algebra. In this contribution, in which earlier results are rederived and elaborated upon, we first describe the algebra induced on the horizon by U(1) vector fields and scalar fields, including the case of an Englert–Brout–Higgs mechanism, and a more careful consideration of the transverse vector field components.

We demonstrate that, unlike classical black holes, the quantized black hole has on its horizon an imprint of its (recent) past history, i.e., quantum hair. The relation between in- and outgoing states depends on this imprint. As a first step towards the inclusion of non-Abelian interactions, we then compute the effects of magnetic monopoles both in the in-states and in the out-states. They completely modify, and indeed simplify, our algebra.

We discuss the explicit dictionary between general stationary four- and five-dimensional supersymmetric solutions in N = 2 supergravity theories with cubic prepotentials. All these solutions are completely determined in terms of the same set of harmonic functions and attractor equations. We discuss various examples like black holes and black rings in Taub-NUT space–time. Then we consider corrections to the four-dimensional solutions associated with more general prepotentials and comment on analogous corrections on the 5D side.

The maximal rank hyperbolic Kac–Moody algebra 𝔢₁₀ has been conjectured to play a prominent role in the unification of duality symmetries in string and M-theory. We review some recent developments supporting this conjecture.

We begin with the simplest possible introduction to supergravity, and then discuss its spin-3/2 stress tensor. Next, we discuss boundary conditions on fields and boundary actions for N = 1 supergravity. Finally, we discuss new boundary contributions to the mass and central charge of monopoles in N = 4 super Yang–Mills theory. All models are in (3+1) dimensions.

A general paradigm for describing classical (and semiclassical) gravity is presented. This approach brings to the center-stage a holographic relationship between the bulk and surface terms in a general class of action functionals and provides a deeper insight into several aspects of classical gravity which have no explanation in the conventional approach. After highlighting a series of unresolved issues in the conventional approach to gravity, we show that (i) principle of equivalence, (ii) general covariance and (iii) a reasonable condition on the variation of the action functional, suggest a generic Lagrangian for semiclassical gravity of the form L = Q_a^bcdR^a_bcd with ∇_b Q_a^bcd = 0. The expansion of Q_a^bcd in terms of the derivatives of the metric tensor determines the structure of the theory uniquely. The zeroth order term gives the Einstein–Hilbert action and the first order correction is given by the Gauss–Bonnet action. Any such Lagrangian can be decomposed into surface and bulk terms which are related holographically. The equations of motion can be obtained purely from a surface term in the gravity sector. Hence the field equations are invariant under the transformation T_ab → T_ab + λg_ab and gravity does not respond to the changes in the bulk vacuum energy density. The cosmological constant arises as an integration constant in this approach. The implications are discussed.

In the first part of this paper, we explain what empirical evidence points to the need for having an effective grand unification-like symmetry possessing the symmetry SU(4)-color in 4D. If one assumes the premises of a future predictive theory including gravity — be it string/M-theory or a reincarnation — this evidence then suggests that such a theory should lead to an effective grand unification-like symmetry as above in 4D, near the string-GUT-scale, rather than the standard model symmetry. Advantages of an effective supersymmetric G(224) = SU(2)_L × SU(2)_R × SU(4)^c or SO(10) symmetry in 4D in explaining (i) observed neutrino oscillations, (ii) baryogenesis via leptogenesis, and (iii) certain fermion mass-relations are noted. And certain distinguishing tests of a SUSY G(224) or SO(10)-framework involving CP and flavor violations (as in μ → eγ, τ → μγ, edm's of the neutron and the electron) as well as proton decay are briefly mentioned.

Recalling some of the successes we have had in our understanding of nature so far, and the current difficulties of string/M-theory as regards the large multiplicity of string vacua, some comments are made on the traditional goal of understanding vis a vis the recently evolved view of landscape and anthropism.

We apply the "consistent discretization" technique to the Regge action for (Euclidean and Lorentzian) general relativity in arbitrary number of dimensions. The result is a well-defined canonical theory that is free of constraints and where the dynamics is implemented as a canonical transformation. In the Lorentzian case, the framework appears to be naturally free of the "spikes" that plague traditional formulations. It also provides a well-defined recipe for determining the integration measure for quantum Regge calculus.

Loop quantum cosmology provides a new paradigm on the genesis of our universe in which the classical expanding branch is joined via a quantum geometric bridge to a classical contracting branch. The evolution between two phases of our universe is non-singular and deterministic, which is a direct manifestation of incorporating non-perturbative quantum geometric features of loop quantum gravity. Using analytical and numerical techniques, details of the quantum nature of big bang can be quantified and reliable physical predictions can be made. The quantum description can also be well approximated by an effective theory which leads to ρ² modifications to the Friedmann equation in the Planck regime.

Observational cosmology has indeed made a very rapid progress in recent years. The ability to quantify the universe has largely improved due to observational constraints coming from structure formation measurements of CMB anisotropy and, more recently, polarization has played a very important role. Besides precise determination of various parameters of the "standard" cosmological model, observations have also established some important basic tenets that underlie models of cosmology and structure formation in the universe — "acausally" correlated initial perturbations in a flat, statistically isotropic universe, adiabatic nature of primordial density perturbations. These are consistent with the expectation of the paradigm of inflation and the generic prediction of the simplest realization of inflationary scenario in the early universe. Further, gravitational instability is the established mechanism for structure formation from these initial perturbations. In the next decade, future experiments promise to strengthen these deductions and uncover the remaining crucial signature of inflation — the primordial gravitational wave background.

In this article, we review some illustrative results in the study of two related toy models for quantum gravity, namely cylindrical waves (which are cylindrically symmetric gravitational fields)and parametrized field theory (which is just free scalar field theory on a flat space–time in generally covariant disguise). In the former, we focus on the phenomenon of unexpected large quantum gravity effects in regions of weak classical gravitational fields and on an analysis of causality in a quantum geometry. In the latter, we focus on Dirac quantization, argue that this is related to the unitary implementability of free scalar field evolution along curved foliations of the flat space–time and review the relevant results for unitary implementability.