We demonstrate the power of the black hole mass gap as a novel probe of fundamental physics. New light particles that couple to the Standard Model can act as an additional source of energy loss in the cores of population-III stars, dramatically altering their evolution. We investigate the effects of two paradigmatic weakly coupled, low-mass particles, axions and hidden photons, and find that the pulsational pair instability, which causes a substantial amount of mass loss, is suppressed. As a result, it is possible to form black holes of $72\msun$ or heavier, deep inside the black hole mass gap predicted by the Standard Model. The upper edge of the mass gap is raised to $>130{\rm M}_\odot$, implying that heavier black holes, anticipated to be observed after LIGO's sensitivity is upgraded, would also be impacted. In contrast, thermally produced heavy particles would remain in the core, leading to the tantalizing possibility that they drive a new instability akin to the electron-positron pair instability. We investigate this effect analytically and find that stars that avoid the electron-positron pair instability could experience this new instability. We discuss our results in light of current and upcoming gravitational wave interferometer detections of binary black hole mergers.
We pioneer the black hole mass gap as a powerful new tool for constraining new particles. A new particle that couples to the Standard Model---such as an axion---acts as an additional source of loss in the cores of population-III stars, suppressing mass lost due to winds and quenching the pair-instability. This results in heavier astrophysical black holes. As an example, using stellar simulations we show that the solar axion explanation of the recent XENON1T excess implies astrophysical black holes of ~ 56 MS, squarely within the black hole mass gap predicted by the Standard Model.
Black holes could be produced at the Large Hadron Collider in TeV-scale gravity scenarios. We discuss missing energy mechanisms in black hole production and decay in large extra-dimensional models. In particular, we examine how graviton emission into the bulk could give the black hole enough recoil to leave the brane. Such a perturbation would cause an abrupt termination in Hawking emission and result in large missing-energy signatures.
In the semiclassical treatment of gravity, an external observer can measure only the mean (not the exact) mass of the black hole (BH). By contrast, in fully quantum gravity the exact (not only mean) BH mass is measurable by the external observer. This additional information (missing in the semiclassical treatment) available to the external observer significantly helps to understand how information leaks out during the BH evaporation.
The rotation of a black hole splits its spectrum in two, yet only one sector is known in the highly-damped regime. We find the second, at least partly oblate sector, with quasinormal modes approaching the total reflection frequencies ω(n>>1) ~ mΩ- 2πiT(n-s), where Ωand T are the horizon angular velocity and temperature, s is the field spin, and m is an azimuthal eigenvalue. Some physical implications are discussed.
There are few observed high-mass X-ray binaries (HMXBs) that harbor massive black holes, and none are likely to result in a binary black hole (BBH) that merges within a Hubble time; however, we know that massive merging BBHs exist from gravitational-wave observations. We investigate the role that X-ray and gravitational-wave observational selection effects play in determining the properties of their respective detected binary populations. We find that, as a result of selection effects, detectable HMXBs and detectable BBHs form at different redshifts and metallicities, with detectable HMXBs for…
Gravitational waves are expected to be radiated by supermassive black hole binaries formed during galaxy mergers. A stochastic superposition of gravitational waves from all such binary systems will modulate the arrival times of pulses from radio pulsars. Using observations of millisecond pulsars obtained with the Parkes radio telescope, we constrain the characteristic amplitude of this background, $A_{\rm c,yr}$, to be < $1.0\times10^{-15}$ with 95% confidence. This limit excludes predicted ranges for $A_{\rm c,yr}$ from current models with 91-99.7% probability. We conclude that binary evoluti…
The Hamiltonian formulation of conformally invariant Weyl-squared higher derivative theory teaches us that conformal symmetry is expressed through particular first class constraints related to the absence of the three-metric determinant and the trace of the extrinsic curvature from the theory. Any term depending on them which is added to this theory breaks conformal invariance and turns these constraints into second class ones. Such second class constraints are missing in the standard canonical formulation of the conformally non-invariant Einstein-Hilbert theory. It is demonstrated that such c…
The early literature on black hole thermodynamics ignored the $P$-$V$ term associated with the existence of a fundamental physical constant in the black hole solution. The inclusion of this constant in the first law becomes inconsistent with the Smarr relation. Once the missing $P$-$V$ term introduced is, it becomes customary to introduce it only in problems where there is a negative cosmological constant. This practice is inherited from cosmological approaches which consider the quantity $-Λ/8π$ as the constant pressure due to a cosmological fluid. However, the notions of pressure and thermod…
We investigate the consequences of superkicks on the population of supermassive black holes (SMBHs) in the Universe residing in brightest cluster galaxies (BCGs). There is strong observational evidence that BCGs grew prominently at late times (up to a factor 2-4 in mass from z=1), mainly through mergers with satellite galaxies from the cluster, and they are known to host the most massive SMBHs ever observed. Those SMBHs are also expected to grow hierarchically, experiencing a series of mergers with other SMBHs brought in by merging satellites. Because of the net linear momentum taken away from…
We revisit the Hawking radiation by comparing the effective actions in the in-out formalism, and advance an interpretation of the vacuum polarization and the Hawking radiation. The equivalence exists between the spinor QED effective action in a constant electric field and the nonperturbative effective action of a massless boson on the horizon of a Schwarzschild black hole.
The gravitational-wave astronomical revolution began in 2015 with LIGO's observation of the coalescence of two stellar-mass black holes. Over the coming decades, ground-based detectors like LIGO will extend their reach, discovering thousands of stellar-mass binaries. In the 2030s, the space-based LISA will enable gravitational-wave observations of the massive black holes in galactic centres. Between LISA and ground-based observatories lies the unexplored decihertz gravitational-wave frequency band. Here, we propose a Decihertz Observatory to cover this band, and complement observations made by…
The Jackiw-Teitelboim (JT) model arises from the dimensional reduction of charged black holes. Motivated by the holographic complexity conjecture, we calculate the late-time rate of change of action of a Wheeler-DeWitt patch in the JT theory. Surprisingly, the rate vanishes. This is puzzling because it contradicts both holographic expectations for the rate of complexification and also action calculations for charged black holes. We trace the discrepancy to an improper treatment of boundary terms when naively doing the dimensional reduction. Once the boundary term is corrected, we find exact ag…
The membrane paradigm approach to black holes fixes in the vicinity of the event horizon a fictitious surface, the stretched horizon, so that the spacetime outside remains unchanged and the spacetime inside is vacuum. Using this powerful method, several black hole properties have been found and settled, such as the horizon's viscosity, electrical conductivity, resistivity, as well as other properties. On the other hand the Euclidean action approach to black hole spacetimes has been very fruitful in understanding black hole entropy. Combining both the Euclidean action and membrane paradigm appr…
The destructive interference of the neighbouring field configurations with infinite classical action in the gravitational path integral approach serves as a dynamical mechanism resolving the black hole singularity problem. It also provides an isotropic and homogeneous early universe without the need of inflation. In this work, we elaborate on the finite action in the framework of Horava-Lifshitz gravity -- a ghost-free QFT. Assuming the mixmaster chaotic solutions in the projectable H-L theory, we show that the beginning of the universe is homogeneous and isotropic. Furthermore, we show that t…
In the context of (2+1)--dimensional Chern-Simons SL(N,R)\times SL(N,R) gauge fields and spin N black holes we compute the on-shell action and show that it generates sensible and consistent thermodynamics. In particular, the Chern-Simons action solves the integrability conditions recently considered in the literature.
Carlip has shown that the entropy of the three-dimensional black hole has its origin in the statistical mechanics of microscopic states living at the horizon. Beginning with a certain orthonormal frame action, and applying similar methods, I show that an analogous result extends to the (Euclidean) black hole in any spacetime dimension. However, this approach still faces many interesting challenges, both technical and conceptual.
Action-angle coordinates are a tool commonly used in celestial mechanics to systematically parametrize and store general solutions of the equations of motion of astrophysical bodies. I perturbatively construct action-angle coordinates for bound test particle motion in static, spherically symmetric space-times using a post-circular expansion. Then I specialise the expressions to the motion in the gravitational fields of Schwarzschild black holes and give explicit formulas for the Hamiltonian to the 10th power in the radial action (20th power in eccentricity), and the transformation to angle coo…
The Hamiltonian actions for extreme and non-extreme black holes are compared and contrasted and a simple derivation of the lack of entropy of extreme black holes is given. In the non-extreme case the wave function of the black hole depends on horizon degrees of freedom which give rise to the entropy. Those additional degrees of freedom are absent in the extreme case.
Several different but equivalent forms of the spherical black hole (Schwarzschild) are known, as well as several derivations. Here a novel form is derived through the power of the action formalism. The method generalizes to any spherical black hole or brane, and the charged hole case (Reissner-Nordstrom) is worked out in detail.
According to the conjecture "complexity equals action," the complexity of a holographic state is equal to the action of a Wheeler-DeWitt (WDW) patch of black holes in anti-de Sitter space. In this paper we calculate the action growth of charged black holes with a single horizon, paying attention to the contribution from a spacelike singularity inside the horizon. We consider two kinds of such charged black holes: one is a charged dilaton black hole, and the other is a Born-Infeld black hole with $β^2 Q^2<1/4$. In both cases, although an electric charge appears in the black hole solutions, the …
The vivid debate concerning the paradox of information being lost when objects are swallowed by a black hole is shown to be void. We argue that no information is ever missing for any observer neither located above, nor falling beneath the event horizon. The information is preserved in a classical scenario of eternal black holes and semi-classical one allowing Hawking radiation.
It is shown that Zaslavskii's misunderstanding of our published proof of the irrelevance of all extremal black hole configurations (whether with equal charge and mass or not) rests on his refusal to see the essential difference between the correct inequality governing extremal and non-extremal actions and his incorrect version.
We adapt the complexity as action prescription (CA) to a semi-classical model of two-dimensional dilaton gravity and determine the rate of increase of holographic complexity for an evaporating black hole. The results are consistent with our previous numerical results for semi-classical black hole complexity using a volume prescription (CV) in the same model, but the CA calculation is fully analytic and provides a non-trivial positive test for the holographic representation of the black hole interior.
We suggest a way to study possible conformal symmetries on black hole horizons. We do this by carrying out a Kaluza-Klein like reduction of the Einstein-Hilbert action along the ignorable coordinates of stationary and axisymmetric black holes. Rigid diffeomorphism invariance of the $m$-ignorable coordinates then becomes a global $SL(m,R)$ gauge symmetry of the reduced action. Related to each non-vanishing angular velocity there is a particular $SL(2,R)$ subgroup, which can be extended to the Witt algebra on the black hole horizons. The classical Einstein-Hilbert action thus has $k$-copies of i…
The membrane paradigm is the remarkable view that, to an external observer, a black hole appears to behave exactly like a dynamical fluid membrane, obeying such pre-relativistic equations as Ohm's law and the Navier-Stokes equation. It has traditionally been derived by manipulating the equations of motion. Here we provide an action formulation of this picture, clarifying what underlies the paradigm, and simplifying the derivations. Within this framework, we derive previous membrane results, and extend them to dyonic black hole solutions. We discuss how it is that an action can produce dissipat…
We compare the canonical quantization and the effective action method to derive expectation values of the stress energy tensor for scalar fields conformally coupled to a 2D Schwarzschild black hole spacetime. Particular attention is devoted to the thermal equilibrium Hartle-Hawking state where the striking disagreement of the results may be reconduced to the incomplete knowledge of the effective action. We show how to reconcile the two procedures and find physically meaningful analytical approximate expressions for the stress tensor in the Hartle-Hawking state.
Among many modified gravity theories, the Chern-Simons modified gravity stands out as one of the few examples whose Dirichlet boundary problem has been well studied. Known solutions to this theory include the Schwarzschild black hole and a slowly rotating black hole. Making use of the Dirichlet boundary term of this theory, we calculate the late-time action growth rates of the Wheeler-DeWitt patch for the Schwarzschild and the slowly rotating solutions. In light of the conjecture of complexity/action duality, the result has implications on the quantum complexity of a state in the dual field th…
In the Euclidean path integral approach, we calculate the actions and the entropies for the Reissner-Nordström-de Sitter solutions. When the temperatures of black hole and cosmological horizons are equal, the entropy is the sum of one-quarter areas of black hole and cosmological horizons; when the inner and outer black hole horizons coincide, the entropy is only one-quarter area of cosmological horizon; and the entropy vanishes when the two black hole horizons and cosmological horizon coincide. We also calculate the Euler numbers of the corresponding Euclidean manifolds, and discuss the relati…
The problem of merging in black holes the rotation and a massless scalar field is treated. It is argued in the comment that the Kerr-like and Demianski-like metrics in General Relativity with a free massless scalar field or in the free Brans-Dicke theory, claimed so far in the literature as an application of the Newman-Janis algorithm, prove to be invalid. Finding the missing stationary axisymmetric scalar-vacuum solution(s), containing the Kerr one, is still urgent.
Since 2015 the gravitational-wave observations of LIGO and Virgo have transformed our understanding of compact-object binaries. In the years to come, ground-based gravitational-wave observatories such as LIGO, Virgo, and their successors will increase in sensitivity, discovering thousands of stellar-mass binaries. In the 2030s, the space-based LISA will provide gravitational-wave observations of massive black holes binaries. Between the $\sim 10$-$10^3~\mathrm{Hz}$ band of ground-based observatories and the $\sim10^{-4}$-$10^{-1}~\mathrm{Hz}$ band of LISA lies the uncharted decihertz gravitati…
Using the Wald's relation between the Noether charge of diffeomorphisms and the entropy for a generic spacetime possessing a bifurcation surface, we introduce a method to obtain a family of higher order derivatives effective actions from the entropy of black holes. Our point of view is to consider fundamental the black hole entropy and the action an emerged object. We then specialize to a particular class of effective theories: the f(R) theories. We apply the idea, using a simple mind ansatz, to loop quantum gravity and to a general class of log-corrected entropy formulas.
Our earlier paper "Complexity Equals Action" conjectured that the quantum computational complexity of a holographic state is given by the classical action of a region in the bulk (the "Wheeler-DeWitt" patch). We provide calculations for the results quoted in that paper, explain how it fits into a broader (tensor) network of ideas, and elaborate on the hypothesis that black holes are the fastest computers in nature.
Quadratic Curvature Correction to the Euclidean Action of Rotating AdS Black Holes in General Dimensions
The International Joint Institute of Tianjin University, Fuzhou, Tianjin University（天津大学福州国际联合学院）；Center for Joint Quantum Studies, Department of Physics, School of Science, Tianjin University（天津大学理学院物理系联合量子研究中心）
Probing missing physics from inspiralling compact binaries via time-frequency tracks
Fudan University（复旦大学）；Université Catholique de Louvain（天主教鲁汶大学）；Royal Observatory of Belgium（比利时皇家天文台）；Indian Institute of Technology Gandhinagar（甘地纳加尔印度理工学院）；New Uzbekistan University（新乌兹别克斯坦大学）
If the situation of quantum gravity nowadays is nearly the same as that of the quantum mechanics in it's early time of Bohr and Sommerfeld, then a first step study of the quantum gravity from Sommerfeld's quantum condition of action might be helpful. In this short paper the spectra of Schwarzschild black hole(SBH) in quasi-classical approach of quantum mechanics is given. We find the quantum of area, the quantum of entropy and the Hawking evaporation will cease as the black hole reaches its ground state.
We consider the behaviour of a quantum scalar field on three-dimensional Euclidean backgrounds: Anti-de Sitter space, the regular BTZ black hole instanton and the BTZ instanton with a conical singularity at the horizon. The corresponding heat kernel and effective action are calculated explicitly for both rotating and non-rotating holes. The quantum entropy of the BTZ black hole is calculated by differentiating the effective action with respect to the angular deficit at the conical singularity. The renormalization of the UV-divergent terms in the action and entropy is considered. The structure …
As observed recently in arXiv:1212.2922, the action of General Relativity (GR) in finite spacetime regions has an imaginary part that resembles the Bekenstein entropy. In this paper, we expand on that argument, with attention to different causal types of boundaries. This property of the GR action may open a new approach to the puzzles of gravitational entropy. In particular, the imaginary action can be evaluated for non-stationary finite regions, where the notion of entropy is not fully understood. As a first step in constructing the precise relationship between the imaginary action and entrop…
We perform Bayesian analysis of gravitational-wave signals from non-spinning, intermediate-mass black-hole binaries (IMBHBs) with observed total mass, $M_{\mathrm{obs}}$, from $50\mathrm{M}_{\odot}$ to $500\mathrm{M}_{\odot}$ and mass ratio $1\mbox{--}4$ using advanced LIGO and Virgo detectors. We employ inspiral-merger-ringdown waveform models based on the effective-one-body formalism and include subleading modes of radiation beyond the leading $(2,2)$ mode. The presence of subleading modes increases signal power for inclined binaries and allows for improved accuracy and precision in measurem…
Black hole perturbation theory is useful for studying the stability of black holes and calculating ringdown gravitational waves after the collision of two black holes. Most previous calculations were carried out at the level of the field equations instead of the action. In this work, we compute the Einstein-Hilbert action to quadratic order in linear metric perturbations about a spherically symmetric vacuum background in Regge-Wheeler gauge. Using a 2+2 splitting of spacetime, we expand the metric perturbations into a sum over scalar, vector, and tensor spherical harmonics, and dimensionally r…
With the help of the Bohr--Sommerfeld quantization rule, the area spectrum of a charged, spherically symmetric spacetime is obtained by studying an adiabatic invariant action variable. The period of the Einstein-Maxwell system, which is related to the surface gravity of a given spacetime, is determined by the Kruskal--like coordinates. It is shown that the area spectrum of the Reissner-Nordström black hole is evenly spaced and the spacing is the same as that of a Schwarzschild black hole, which indicates that the area spectrum of a black hole is independent of its parameters. In contrast to th…
Microscopic black holes are sensitive to higher dimension operators in the gravitational action. We compute the influence of these operators on the Schwarzschild solution using perturbation theory. All (time reversal invariant) operators of dimension six are included (dimension four operators don't alter the Schwarzschild solution). Corrections to the relation between the Hawking temperature and the black hole mass are found. The entropy is calculated using the Gibbons-Hawking prescription for the Euclidean path integral and using naive thermodynamic reasoning. These two methods agree, however…
A black hole-like solution to a toy model scalar field action for the pion is presented. It has a "horizon" that traps pion field information (it cannot escape in finite time) and is thermal, with a finite and calculable temperature, $T=\sqrt{2}/(πα)$, with $α$ a coupling parameter. The action is a scalar DBI action (D-brane action), coupled to a particular fixed source term. The DBI action by itself has "catenoid" solutions that have horizons with infinite temperature and trap only high energy information. It is also proven that the unique scalar action that admits thermal horizons is of DBI …
The paper deals with the extension of the Weak Isolated Horizon (WIH) formulation to the non- minimally coupled Holst action. In the first part of the paper, we introduce the non- minimal scalar coupling of the Holst action and construct the covariant phase space of the theory. Using the covariant phase space, we prove the laws of black hole mechanics and show that with a gauge fixing, the symplectic structure on the horizon reduces to that of a U(1) Chern-Simons theory. The level of the Chern- Simons theory is shown to depend on the non-minimally coupled scalar field.
We elaborate on the role of higher-derivative curvature invariants as a quantum selection mechanism of regular spacetimes in the framework of the Lorentzian path integral approach to quantum gravity. We show that for a large class of black hole metrics prominently regular there are higher-derivative curvature invariants which are singular. If such terms are included in the action, according to the finite action principle applied to a higher-derivative gravity model, not only singular spacetimes but also some of the regular ones do not seem to contribute to the path integral.
We continue the study of the non-metric theory of gravity introduced in hep-th/0611182 and gr-qc/0703002 and obtain its general spherically symmetric vacuum solution. It respects the analog of the Birkhoff theorem, i.e., the vacuum spherically symmetric solution is necessarily static. As in general relativity, the spherically symmetric solution is seen to describe a black hole. The exterior geometry is essentially the same as in the Schwarzschild case, with power-law corrections to the Newtonian potential. The behavior inside the black-hole region is different from the Schwarzschild case in th…
The negative mode of the Schwarzschild black hole is central to Euclidean quantum gravity around hot flat space and for the Gregory-Laflamme black string instability. Numerous gauges were employed in the past to analyze it. Here _the_ analytic derivation is found, based on postponing the gauge fixing, on the power of the action and on decoupling of non-dynamic fields. A broad-range generalization to perturbations around arbitrary co-homogeneity 1 geometries is discussed.
A frame dependent effective action motivated by the postulates of three-space general coordinate invariance and Weyl scaling invariance exactly mimics a cosmological constant in Robertson-Walker spacetimes. However, in a static spherically symmetric Schwarzschild-like geometry it modifies the black hole horizon structure within microscopic distances of the nominal horizon, in such a way that $g_{00}$ never vanishes. This could have important implications for the black hole "information paradox".
We compute the on-shell Euclidean action of Schwarzschild-de Sitter black holes, and take their contributions in the gravitational path integral into account using the formalism of constrained instantons. Although Euclidean de Sitter black hole geometries have conical singularities for generic masses, their on-shell action is finite and is shown to be independent of the Euclidean time periodicity and equal to minus the sum of the black hole and cosmological horizon entropy. We apply this result to compute the probability for a nonrotating, neutral arbitrary mass black hole to nucleate spontane…
We propose a set of boundary terms for higher spin theories in AdS$_3$ that lead to a well-defined variational principle compatible with Dirichlet boundary conditions for the metric and higher spin fields. These boundary terms are valid for higher spin theories in the Fefferman-Graham gauge and they allow us to compute the canonical free energy of higher spin black holes directly from the Euclidean, covariant, on-shell action. Using these results we reproduce the thermodynamics of the higher spin black hole of Ammon, Gutperle, Kraus, and Perlmutter and comment on the corresponding theory of in…
In the action-complexity proposal there are two different methods to regularize the gravitational on-shell action, which are equivalent in the framework of AdS/CFT. In this paper, we want to study the equivalence of them for a pure BTZ black hole microstate. The microstate is obtained from a two-sided BTZ black hole truncated by a dynamical timelike ETW brane. Moreover, it is dual to a finite energy pure state in a two-dimensional CFT. We show that if one includes the timelike counterterms inspired by holographic renormalization as well as the Gibbons-Hawking-York term on the timelike boundary…
The authors have recently proposed a ``microcanonical functional integral" representation of the density of quantum states of the gravitational field. The phase of this real--time functional integral is determined by a ``microcanonical" or Jacobi action, the extrema of which are classical solutions at fixed total energy, not at fixed total time interval as in Hamilton's action. This approach is fully general but is especially well suited to gravitating systems because for them the total energy can be fixed simply as a boundary condition on the gravitational field. In this paper we describe how…
Gauss-Bonnet gravity provides one of the most promising frameworks to study curvature corrections to the Einstein action in supersymmetric string theories, while avoiding ghosts and keeping second order field equations. Although Schwarzschild-type solutions for Gauss-Bonnet black holes have been known for long, the Kerr-Gauss-Bonnet metric is missing. In this paper, a five dimensional Gauss-Bonnet approximation is analytically derived for spinning black holes and the related thermodynamical properties are briefly outlined.
We study the phenomenological implications stemming from the dependence of the tidal charge on the brane thickness $L$ for the evaporation and decay of microscopic black holes. In general, the larger $L$, the longer are the black hole life-times and the greater their maximum mass for those cases in which the black hole can grow. In particular, we again find that tidal-charged black holes might live long enough to escape the detectors and even the gravitational field of the Earth, thus resulting in large amounts of missing energy. However, under no circumstances could TeV-scale black holes grow…
