Higher Curvature Terms Research Articles

Self-gravitating solutions in Yang–Mills–Chern–Simons theory coupled to 3D massive gravity

We study self-gravitating solutions of three-dimensional massive gravity coupled to the Yang–Mills–Chern–Simons gauge theory. Among these, there is a family of asymptotically Warped-Anti de Sitter black holes that come to generalize previous solutions found in the literature and studied in the context of WAdS3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_3$$\\end{document}/CFT2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_2$$\\end{document}. We also present self-gravitating solutions to three-dimensional Einstein–Yang–Mills theory, as well other self-gravitating solutions in the presence of higher-curvature terms.

Quantum backreactions in (A)dS3 massive gravity and logarithmic asymptotic behavior

We study the interplay between higher-curvature terms and the backreaction of quantum fluctuations in three-dimensional massive gravity in asymptotically (anti–)de Sitter space. We focus on the theory at the special point of the parameter space where the two maximally symmetric vacua coincide. In the case of positive cosmological constant, this corresponds to the partially massless point, at which the classical theory admits de Sitter black holes and exhibits an extra conformal symmetry at linear level. We explicitly find the quantum corrected black hole geometry in the semiclassical approximation and show that it induces a relaxation of the standard asymptotic conditions. Nonetheless, the new asymptotic behavior is still preserved by an infinite-dimensional algebra, which, in addition to Virasoro, contains logarithmic supertranslations. Finally, we show that all the results we obtain for the quadratic massive gravity theory can be extended to theories including cubic and quartic terms in the curvature. Published by the American Physical Society 2024

Effectiveness of Weyl gravity in probing quantum corrections to AdS black holes

Computing leading higher curvature contributions to thermodynamic quantities of AdS black hole is drastically simplified once the higher curvature terms are expressed in terms of powers of Weyl tensor by applying proper field redefinitions, avoiding the usual complications caused by higher derivative Gibbons-Hawking-York term or surface counterterms. We establish the method by computing the Euclidean action of general rotating anti–de Sitter (AdS) black holes in five-dimensional quadratic curvature theories with or without supersymmetry and verifying the results numerically. Our result is the state of the art for charged rotating AdS black holes in five-dimensional minimal gauged supergravity including corrections from all three supersymmetric curvature squared terms. Our approach facilitates precision tests in the AdS/CFT correspondence and should be applicable in diverse dimensions. Published by the American Physical Society 2024

Probing Gauss-Bonnet-corrected inflation with gravitational waves

The low energy effective action of quantum gravity may include the higher curvature terms such as the Gauss-Bonnet term.The inflaton dynamics may be affected by the Gauss-Bonnet term if there is an inflaton-Gauss-Bonnet coupling.We show that an inflation model with a simple power law potential is made viable if it is coupled to the Gauss-Bonnet term since the prediction on the scalar spectral index and the tensor-to-scalar ratio are modified.We further point out that such a model predicts huge amount of gravitational waves at the high frequency range around 100 GHz–100 THz through the perturbative inflaton decay into gravitons induced by the Gauss-Bonnet term.Thus the spectrum of high frequency gravitational background is a unique feature of the inflation models with a Gauss-Bonnet correction.

Constraints on Einstein-dilaton Gauss-Bonnet gravity with Taiji

In the 2030s, space-based gravitational-wave (GW) detectors will exhibit unprecedented sensitivity in the millihertz frequency band, greatly expanding the potential for testing theories of gravity compared to ground-based GW detectors. Inspired by effective string theory, Einstein-dilaton Gauss–Bonnet (EdGB) gravity introduces an extra dilaton scalar field that is directly coupled to higher curvature terms. Here, we investigate the capability of Taiji to constrain the parameters of EdGB gravity by analyzing GWs from massive black hole binaries (MBHBs). We utilize the parameterized post-Einsteinian (ppE) waveform with the leading order EdGB corrections for the inspiral phase of MBHBs. The constraints on the coupling constants are obtained by performing Fisher matrix analysis. With different mass ratios and spins χi\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi _i$$\\end{document} at redshifts z=2,3,4,5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$z=2,3,4,5$$\\end{document}, the 1σ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1\\sigma $$\\end{document} bounds on the parameter α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document} have the same order of magnitude: α∼107\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sqrt{\\alpha }\\sim 10^7$$\\end{document} m.

Blandford–Znajek process in Einsteinian cubic gravity

In this paper, we investigate the Blandford–Znajek (BZ) process within the framework of Einsteinian cubic gravity (ECG). To analytically study the BZ process using the split monopole configuration, we construct a slowly rotating black hole in ECG up to cubic order in small spin, considering the leading order in small coupling constant of higher curvature terms. By deriving the magnetosphere solution around the black hole, we determine the BZ power up to the second relative order in spin. The BZ power is modified by the coupling constant compared to Kerr black hole case. Although the general nature of the BZ process in ECG remains unchanged at the leading order in spin, the coupling constant introduces modification at the second relative order in spin. Therefore, we anticipate that it is feasible to discern general relativity from higher derivative gravities by examining the BZ power in rapidly rotating black holes.

Extremal Kerr Black Holes as Amplifiers of New Physics.

We show that extremal Kerr black holes are sensitive probes of new physics. Stringy or quantum corrections to general relativity are expected to generate higher-curvature terms in the gravitational action. We show that in the presence of these terms, asymptotically flat extremal rotating black holes have curvature singularities on their horizon. Furthermore, near-extremal black holes can have large yet finite tidal forces for infalling observers. In addition, we consider five-dimensional extremal charged black holes and show that higher-curvature terms can have a large effect on the horizon geometry.

Partition Function for a Volume of Space.

We consider the quantum gravity partition function that counts the dimension of the Hilbert space of a spatial region with topology of a ball and fixed proper volume, and evaluate it in the leading order saddle point approximation. The result is the exponential of the Bekenstein-Hawking entropy associated with the area of the saddle ball boundary, and is reliable within effective field theory provided the mild curvature singularity at the ball boundary is regulated by higher curvature terms. This generalizes the classic Gibbons-Hawking computation of the de Sitter entropy for the case of positive cosmological constant and unconstrained volume, and hence exhibits the holographic nature of nonperturbative quantum gravity in generic finite volumes of space.

De Sitter potential in six dimensional Einstein–Gauss–Bonnet isotropic fluids

We present a physically reasonable stellar model in 6-dimensional Einstein–Gauss–Bonnet gravity by prescribing the de Sitter temporal metric potential. The model displays the necessary qualitative features of a compact star model with variable density profile. For a specified parameter space, the model is shown to be well-behaved in the sense that the energy density and pressure are both positive and smooth decreasing functions, with the pressure vanishing on a suitable hyper-surface, thus establishing a finite boundary for the isotropic distribution. Additionally, the model is causal, the energy conditions and adiabatic stability index are all satisfied. The exact solution does not contain the Einstein gravity model by switching off the higher curvature coupling. The model in the standard theory is constructed from the field equations, and its own associated parameter space is determined. The Einstein model displays some undesirable traits, which are eliminated when the higher curvature terms are active.

Quasi-topological gravities on general spherically symmetric metric

In this work we study a more restricted class of quasi-topological gravity theories where the higher curvature terms have no contribution to the equation of motion on general static spherically symmetric metric where gttgrr ≠ constant. We construct such theories up to quintic order in Riemann tensor and observe an important property of these theories: the higher order term in the Lagrangian vanishes identically when evaluated on the most general non-stationary spherically symmetric metric ansatz. This not only signals the higher terms could only have non-trivial effects when considering perturbations, but also makes the theories quasi-topological on a much wider range of metrics. As an example of the holographic effects of such theories, we consider a general Einstein-scalar theory and calculate it’s holographic shear viscosity.

What Is the Fate of Hawking Evaporation in Gravity Theories with Higher Curvature Terms?

During the final stages of black hole evaporation, ultraviolet deviations from general relativity eventually become dramatic, potentially affecting the end state. We explore this problem by performing nonlinear simulations of wave packets in Einstein-dilaton-Gauss-Bonnet gravity, the only gravity theory with quadratic curvature terms which can be studied at a fully nonperturbative level. Black holes in this theory have a minimum mass but also a nonvanishing temperature. This poses a puzzle concerning the final fate of Hawking evaporation in the presence of high-curvature nonperturbative effects. By simulating the mass loss induced by evaporation at the classical level using an auxiliary phantom field, we study the nonlinear evolution of black holes past the minimum mass. We observe a runaway shrink of the horizon (a nonperturbative effect forbidden in general relativity) which eventually unveils a high-curvature elliptic region. While this might hint to the formation of a naked singularity (and hence to a violation of the weak cosmic censorship) or of a pathological spacetime region, a different numerical formulation of the initial-value problem in this theory might be required to rule out other possibilities, including the transition from the critical black hole to a stable horizonless remnant. Our Letter is relevant in the context of the information-loss paradox, dark-matter remnants, and for constraints on microscopic primordial black holes.

R2 corrections to the black string instability and the boosted black string

We consider a perturbative Gauss-Bonnet term supplementing the Einstein-Hilbert action, and evaluate its effect on the spectrum of the scalar mode that triggers the Gregory-Laflamme instability of black strings in five dimensional General Relativity. After studying some properties of the static black string, we provide the correction to the Lichnerowicz operator up to $\mathcal{O}(\alpha^2)$. For the scalar mode of the gravitational perturbation, we find a master variable and study its spectrum, providing an analysis of the regime of validity of our scheme. We show that the instability persists under the inclusion of the $R^2$-correction, and that the critical wavelength increases with the value of $\alpha/r_+^2<<1$, providing new evidence of the phenomenon which was already observed in other approaches. We also construct the boosted black strings and compute the correction to the mass, the momentum and the tension due to the higher curvature term. The presence of the dimensionful coupling $\alpha$ spoils the validity of the Smarr relation, which is the gravitational version of the Euler relation which must hold for every homogeneous, thermodynamic system. We show that this identity can be restored by working in an extended thermodynamic setup that includes variations of the Gauss-Bonnet coupling.

First order corrections to the black hole thermodynamics in higher curvature theories of gravity

In modified theories of gravity, higher curvature terms may be added to the Einstein-Hilbert action. Conventionally, the effects of the higher curvature terms on the black hole thermodynamics are rather difficult to obtain. In this paper, we show that, at least at the first order level, the corrections to the thermodynamics of the Schwarzschild black hole can be easily obtained, without solving the modified black hole metric. We examine some specific examples, which produces the known results in the literature, as well as those previously unknown. Furthermore, we find some nonperturbative exact results by generalizing the first-order analysis. In particular, a novel relation between the Euclidean integrals of the Einstein--Hilbert term and the higher curvature terms is found and proved.

An Alternative Study about the Geometry and the First Law of Thermodynamics for AdS Lovelock Gravity, Using the Definition of Conserved Charges.

In this work, we introduce an extension of the study of the first law of thermodynamics of black holes based on the geometry of the extended phase space for AdS Lovelock gravities, which includes changes in scales. As expected, the result obtained coincides with the previously known four-dimensional case. For higher dimensions, the result is the rise of two new contributions to the first law of thermodynamics. The first term corresponds to corrections of the usual definition of thermodynamic volumes at the horizon due to the presence of the higher curvature terms. The second term arises in odd dimensions, comes from the asymptotic region, and corresponds to a scale transformation of the form , with l the AdS radius and ℓ a parameter. A particularly interesting case corresponds to the Chern Simons gravity where the change scale does not generate a contribution at the asymptotic region, likely due to the Chern Simons AdS local symmetry.

Non-trivial time crystal-like ground state for gravitational perturbation in quadratic gravity

We consider gravitational perturbation around maximally symmetric background of a theory of gravity involving quadratic curvature correction. This leads to a decoupled model of the standard transverse, traceless graviton mode and an additional scalar degree of freedom. Evolution of the latter is governed by a Lagrangian, which depends on higher derivative terms, inherited from the quadratic curvature correction in the action. It turns out that stability of the gravitational theory allows the scalar sector to choose between possible lowest energy states (or, ground states), that can sustain periodic form of inhomogeneity, either in space or in time. The latter, with a restricted form of invariance in time translation, is possibly a variant form of the time crystal. Existence of this novel ground state, depicting a time crystal, is solely related to the presence of higher curvature terms in the action. In particular, this non-trivial condensate-like ground state describe the spacetime fabric itself by introducing fundamental scales in the theory. Possible implications are also discussed.

New symmetry in higher curvature spacetimes

New symmetries have been found in Einstein-Maxwell spacetimes. New symmetries have also been found in imperfect fluid curved spacetimes. We will prove in this paper that we can extend these symmetries to spacetimes with higher curvature terms. Higher curvature theories are in many cases associated to dark energy for instance. We provide further justification for these higher curvature formulations through the existence of a new symmetry.

Scalarized black holes

Black holes represent outstanding astrophysical laboratories to test the strong gravity regime, since alternative theories of gravity may predict black hole solutions whose properties may differ distinctly from those of general relativity. When higher curvature terms are included in the gravitational action as, for instance, in the form of the Gauss–Bonnet term coupled to a scalar field, scalarized black holes result. Here we discuss several types of scalarized black holes and some of their properties.

Inflation and supersymmetry breaking in Higgs-R2 supergravity

We propose a new construction of the supergravity inflation as an UV completion of the Higgs-R2 inflation. In the dual description of R2-supergravity, we show that there appear dual chiral superfields containing the scalaron or sigma field in the Starobinsky inflation, which unitarizes the supersymmetric Higgs inflation with a large non-minimal coupling up to the Planck scale. We find that a successful slow-roll inflation is achievable in the Higgs-sigma field space, but under the condition that higher curvature terms are introduced to cure the tachyonic mass problems for spectator singlet scalar fields. We also discuss supersymmetry breaking and its transmission to the visible sector as a result of the couplings of the dual chiral superfields and the non-minimal gravity coupling of the Higgs fields.

Nonstaticity with type II, III, or IV matter field in $$f(R_{\mu \nu \rho \sigma },g^{\mu \nu })$$ gravity

In all $n(\ge 3)$-dimensional gravitation theories whose Lagrangians are functions of the Riemann tensor and metric, we show that static solutions are absent unless the total energy-momentum tensor for matter fields is of type I in the Hawking-Ellis classification. In other words, there is no hypersurface-orthogonal timelike Killing vector in a spacetime region with an energy-momentum tensor of type II, III, or IV. This asserts that, if back-reaction is taken into account to give a self-consistent solution, ultra-dense regions with a semiclassical type-IV matter field cannot be static even with higher-curvature correction terms. As a consequence, a static Planck-mass relic is possible as a final state of an evaporating black hole only if the semiclassical total energy-momentum tensor is of type I.

First law of black hole in the gravitational electromagnetic system

After considering the quantum corrections of Einstein-Maxwell theory, the effective theory will contain some higher-curvature terms and nonminimally coupled electromagnetic fields. In this paper, we study the first law of black holes in the gravitational electromagnetic system with the Lagrangian ℒ(gab, Rabcd, Fab). Firstly, we calculate the Noether charge and the variational identity in this theory, and then generically derive the first law of thermodynamics for an asymptotically flat stationary-axisymmetric symmetric black hole without the requirement that the electromagnetic field is smooth on the bifurcation surface. Our results indicate that the first law of black hole thermodynamics might be valid for the Einstein-Maxwell theory with some quantum corrections in the effective region.