Quantum Black Hole Entropy Research Articles

A possible quantum gravity hint in binary black hole merger

We present a semi-rigorous justification of Bekenstein's Generalized Second Law of Thermodynamics applicable to a universe with black holes present, based on a generic quantum gravity formulation of a black hole spacetime, where the bulk Hamiltonian constraint plays a central role. Specializing to Loop Quantum Gravity, and considering the inspiral and post-ringdown stages of binary black hole merger into a remnant black hole, we show that the Generalized Second Law implies a lower bound on the non-perturbative LQG correction to the Bekenstein-Hawking area law for black hole entropy. This lower bound itself is expressed as a function of the Bekenstein-Hawking area formula for entropy. Results of the analyses of LIGO-VIRGO-KAGRA data recently performed to verify the Hawking Area Theorem for binary black hole merger are shown to be entirely consistent with this Loop Quantum Gravity-induced inequality. However, the consistency is independent of the magnitude of the LQG corrections to black hole entropy, depending only on the negative algebraic sign of the quantum correction. We argue that results of alternative quantum gravity computations of quantum black hole entropy, where the quantum entropy exceeds the Bekenstein-Hawking value, may not share this consistency.

Slow-Goldstone mode generated by order from quantum disorder and its experimental detection

The order from quantum disorders (OFQD) phenomenon is well-known and ubiquitous in particle physics and frustrated magnetic systems. Typically, OFQD transfers a spurious Goldstone mode into a pseudo-Goldstone mode with a tiny gap. Here, we report an opposite phenomenon: OFQD transfers a spurious quadratic mode into a true linear Goldstone mode with a very small velocity (named slow-Goldstone mode). This new phenomenon is demonstrated in an interacting bosonic system subjected to an Abelian flux. We develop a new and systematic OFQD analysis to determine the true quantum ground state and the whole excitation spectrum. In the weak-coupling limit, the superfluid ground state has a 4-sublattice 90° coplanar spin structure, which supports 4 linear Goldstone modes with 3 different velocities. One of which is generated by the OFQD is much softer than the other 3 Goldstone modes, so it can be easily detected in the cold atom or photonic experiments. In the strong-coupling limit, the ferromagnetic Mott ground state with a true quadratic Goldstone mode. We speculate that there could be some topological phases intervening between the two symmetry broken states. These novel phenomena may be observed in the current cold-atom or photonic experiments subjected to an Abelian flux at the weak coupling limit where the heatings may be well under control. Possible connections to Coleman-Weinberg potential in particle physics, 1/N expansion of Sachdev-Ye-Kitaev models and zero temperature quantum black hole entropy are outlined.

Holographic bound on area of a compact binary merger remnant

Using concomitantly the generalized second law of black hole thermodynamics and the holographic Bekenstein entropy bound embellished by loop quantum gravity corrections to quantum black hole entropy, we show that the boundary cross sectional area of the postmerger remnant formed from the compact binary merger in gravitational wave detection experiments like GW150914 et seq., by the LIGO-VIRGO collaboration, is bounded from below. This lower bound is more general than the bound obtained from application of Hawking's classical area theorem for black holes, since it does not depend on whether the inspiralling compact binary pair or the postmerger remnant consists of black holes or other exotic compact objects. The derivation of the bound entails an estimate of the entropy of the gravitational waves emitted during the binary merger, which adapts to gravitational waves an extant formalism proposed originally for particle ensembles. The results for the minimal cross sectional area of the merger remnant due to binary compact mergers observed recently by the LIGO-VIRGO collaboration are discussed. While accurate measurement of the mass of the remnant for the binary neutron star merger GW170817 remains a challenge, we provide a proof of principle that for binary neutron star mergers our lower bound on the cross sectional area of the remnant provides an alternative approach to probe the validity of neutron star equations of state, independent of the tidal deformabilities of the components.

Quantum BTZ black hole

We study a holographic construction of quantum rotating BTZ black holes that incorporates the exact backreaction from strongly coupled quantum conformal fields. It is based on an exact four-dimensional solution for a black hole localized on a brane in AdS4, first discussed some years ago but never fully investigated in this manner. Besides quantum CFT effects and their backreaction, we also investigate the role of higher-curvature corrections in the effective three-dimensional theory. We obtain the quantum-corrected geometry and the renormalized stress tensor. We show that the quantum black hole entropy, which includes the entanglement of the fields outside the horizon, satisfies the first law of thermodynamics exactly, even in the presence of backreaction and with higher-curvature corrections, while the Bekenstein-Hawking-Wald entropy does not. This result, which involves a rather non-trivial bulk calculation, shows the consistency of the holographic interpretation of braneworlds. We compare our renormalized stress tensor to results derived for free conformal fields, and for a previous holographic construction without backreaction effects, which is shown to be a limit of the solutions in this article.

Quantum black hole entropy from 4d supersymmetric Cardy formula

We study supersymmetric index of 4d $SU(N)$ $\mathcal{N}=4$ super Yang-Mills theory on $S^1 \times M_3$. We compute asymptotic behavior of the index in the limit of shrinking $S^1$ for arbitrary $N$ by a refinement of supersymmetric Cardy formula. The asymptotic behavior for the superconformal index case ($M_3 =S^3$) at large $N$ agrees with the Bekenstein-Hawking entropy of rotating electrically charged BPS black hole in $AdS_5$ via a Legendre transformation as recently shown in literature. We also find that the agreement formally persists for finite $N$ if we slightly modify the AdS/CFT dictionary between Newton constant and $N$. This implies an existence of non-renormalization property of the quantum black hole entropy. We also study the cases with other gauge groups and additional matters, and the orbifold $\mathcal{N}=4$ super Yang-Mills theory. It turns out that the entropies of all the CFT examples in this paper are given by $2\pi \sqrt{Q_1 Q_2 +Q_1 Q_3 +Q_2 Q_3 -2c(J_1 +J_2 )} $ with charges $Q_{1,2,3}$, angular momenta $J_{1,2}$ and central charge $c$. The results for other $M_3$ make predictions to the gravity side.

Functional determinants, index theorems, and exact quantum black hole entropy

The exact quantum entropy of BPS black holes can be evaluated using localization in supergravity. An important ingredient in this program, that has been lacking so far, is the one-loop effect arising from the quadratic fluctuations of the exact deformation (the $Q\mathcal{V}$ operator). We compute the fluctuation determinant for vector multiplets and hyper multiplets around $Q$-invariant off-shell configurations in four-dimensional $\mathcal{N}=2$ supergravity with $AdS_{2} \times S^{2}$ boundary conditions, using the Atiyah-Bott fixed-point index theorem and a subsequent zeta function regularization. Our results extend the large-charge on-shell entropy computations in the literature to a regime of finite charges. Based on our results, we present an exact formula for the quantum entropy of BPS black holes in $\mathcal{N}=2$ supergravity. We explain cancellations concerning $\frac18$-BPS black holes in $\mathcal{N}=8$ supergravity that were observed in arXiv:1111.1161. We also make comments about the interpretation of a logarithmic term in the topological string partition function in the low energy supergravity theory.

Quantum black hole entropy and the holomorphic prepotential of $ \mathcal{N}=2 $ supergravity

Abstract Supersymmetric terms in the effective action of $ \mathcal{N}=2 $ supergravity in four dimensions are generically classified into chiral-superspace integrals and full-superspace integrals. For a theory of $ \mathcal{N}=2 $ vector multiplets coupled to supergravity, a special class of couplings is given by chiral-superspace integrals that are governed by a holomorphic prepotential function. The quantum entropy of BPS black holes in such theories depends on the prepotential according to a known integral formula. We show, using techniques of localization, that a large class of full-superspace integrals in the effective action of $ \mathcal{N}=2 $ supergravity do not contribute to the quantum entropy of BPS black holes at any level in the derivative expansion. Our work extends similar results for semi-classical supersymmetric black hole entropy, and goes towards providing an explanation of why the prepotential terms capture the exact microscopic quantum black hole entropy.

Generalized mirror symmetry and quantum black hole entropy

We find general relations between the on-shell gravitational trace anomaly AN, and the logarithmic correction ΔSN to the entropy of “large” BPS extremal black holes in N⩾2 supergravity theories in D=4 space–time dimensions (recently computed by Sen, 2011 [1]). For (generalized) self-mirror theories (all having AN=0), we obtain the result ΔSN=−ΔS8−N=2−N/2, whereas for generic theories the trace anomaly A˜N of the fully dualized theory turns out to coincide with 2ΔSN, up to a model-independent shift: A˜N=2ΔSN−1. We also speculate on N=1 theories displaying “large” extremal black hole solutions.