Distributions of extremal black holes in Calabi-Yau compactifications

We study non-supersymmetric extremal black hole excitations of 4d $$ \mathcal{N} $$ N = 2 supersymmetric string vacua arising from compactification on Calabi-Yau threefolds. The values of the (vector multiplet) moduli at the black hole horizon are governed by the attractor mechanism. This raises natural questions, such as “what is the distribution of attractor points on moduli space?” and “how many attractor black holes are there with horizon area up to a certain size?” We employ tools developed by Denef and Douglas [1] to answer these questions.

Hawking-Moss transition with a black hole seed

We extend 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 inflationary formalism to include primordial black holes. Both of these methods give a physical substantiation of our conjecture.

Properties of a recent quantum extension of the Kruskal geometry

Recently, it was shown that, in an effective description motivated by loop quantum gravity, singularities of the Kruskal spacetime are naturally resolved [A. Ashtekar, J. Olmedo and P. Singh, Phys. Rev. Lett. 121 (2018) 241301; A. Ashtekar, J. Olmedo and P. Singh, Phys. Rev. D 98 (2018) 126003]. In this paper, we explore a few properties of this quantum corrected effective metric. In particular, we (i) calculate the Hawking temperature associated with the horizon of the effective geometry and show that the quantum correction to the temperature is completely negligible for macroscopic black holes, just as one would hope; (ii) discuss the subtleties associated with the asymptotic properties of the spacetime metric, and show that the metric is asymptotically flat in a precise sense; (iii) analyze the asymptotic fall-off of curvature; and, (iv) show that the ADM energy is well defined (and agrees with that determined by the horizon area), even though the curvature falls off less rapidly than in the standard asymptotically flat context.

Black Hole Entropy: A Closer Look

In many papers in the literature, author(s) express their perplexity concerning the fact that the ( 3 + 1 ) black-hole ‘thermodynamical’ entropy appears to be proportional to its area and not to its volume, and would therefore seemingly be nonextensive, or, to be more precise, subextensive. To discuss this question on more clear terms, a non-Boltzmannian entropic functional noted S δ was applied [Tsallis and Cirto, Eur. Phys. J. C 73, 2487 (2013)] to this complex system which exhibits the so-called area-law. However, some nontrivial physical points still remain open, which we revisit now. This discussion is also based on the fact that the well known Bekenstein-Hawking entropy can be expressed as being proportional to the event horizon area divided by the square of the Planck length.

Tunnelling radiation of charged particles from a Hořava–Lifshitz gravity black hole

The Hawking radiation of charged particles from black holes in the Hořava–Lifshitz (HL) gravity is investigated by using the Parikh–Wilczek (PW) method, and the emission rate is calculated. The emission spectrum is not purely thermal and is consistent with an underlying unitary theory. Some other characteristics exist for a HL gravity black hole. Assuming the conventional tunnelling rate associated with the change of entropy, the entropy of the HL gravity black hole is obtained. The entropy is not proportional to the horizon area because a logarithmic term exists. However, it complies with the first law of thermodynamics and is in accord with earlier results.

Distorted vacuum black holes in the canonical ensemble

We consider a vacuum static spacetime in a finite size cavity. On the boundary, we specify a metric and a finite constant local temperature [Formula: see text]. No spherical or any other spatial symmetry is assumed. We show that (i) inside a cavity, only a black hole or flat spacetime are possible, whereas a curved horizonless regular spacetime is excluded, (ii) in the limit when the horizon area shrinks, the Hawking temperature diverges, (iii) for the existence of a black hole, [Formula: see text] should be high enough. When [Formula: see text], a black hole phase is favorable thermodynamically. Our consideration essentially uses the coordinate system introduced by Israel in his famous proof of the uniqueness theorem.

Thermal fluctuations and correlations among hairs of a stable quantum black hole: Some examples

We have already derived the criteria for thermal stability of charged rotating quantum black holes, for horizon areas that are large relative to the Planck area. The derivation is done by using results of loop quantum gravity and equilibrium statistical mechanics of the grand canonical ensemble. We have also showed that in four-dimensional spacetime, quantum AdS Kerr–Newman black hole and asymptotically AdS dyonic black hole with electric and magnetic charge are thermally stable within certain range of its parameters. In this paper, the expectation values of fluctuations and correlations among horizon area, electric charge and angular momentum (magnetic charge) of these black holes are calculated within their range of stability. Interestingly, it is found that leading order fluctuations of electric charge and angular momentum (magnetic charge), in large horizon area limit, are independent of the values of electric charge and angular momentum (magnetic charge) at equilibrium.

Maxwell–Boltzmann type Hawking radiation

Twenty years ago, Rovelli proposed that the degeneracy of black hole (i.e. the exponential of the Bekenstein–Hawking entropy) is given by the number of ways the black hole horizon area can be expressed as a sum of unit areas. However, when counting the sum, one should treat the area quanta on the black hole horizon as distinguishable. This distinguishability of area quanta is noted in Rovelli’s paper. Building on this idea, we derive that the Hawking radiation spectrum is not given by Planck radiation spectrum (i.e. Bose–Einstein distribution) but given by Maxwell–Boltzmann distribution.