Order Curvature Corrections Research Articles

Higher order curvature corrections and holographic renormalization group flow

We study the holographic renormalization group (RG) flow in the presence of higher-order curvature corrections to the $(d+1)$-dimensional Einstein-Hilbert (EH) action for an arbitrary interacting scalar matter field by using the superpotential approach. We find the critical points of the RG flow near the local minima and maxima of the potential and show the existence of the bounce solutions. In contrast to the EH gravity, regarding the values of couplings of the bulk theory, superpotential may have both upper and lower bounds. Moreover, the behavior of the RG flow controls by singular curves. This study may shed some light on how a c-function can exist in the presence of these corrections.

Application of the renormalization group theory for critical asymmetry to surface criticality of one-component fluids

It is well-known that the Tolman length which characterizes the first order curvature corrections to surface tension is associated with the asymmetry in fluid phase coexistence. Recently, we have developed a global renormalization group (GRG) method for describing such asymmetry both near to and far from the critical point. In this work, we use the GRG method and an approximate thermodynamic relation to calculate Tolman lengths of one-component simple fluids in a wide temperature range including the critical vicinity where the density functional theory and the square-gradient theory is inapplicable. Far from the critical point, the accuracy of this work is comparable to the density functional theory and the square-gradient theory. Near the critical point, the GRG method yields the scaling behavior consistent with the prediction of complete scaling theory. We also obtain an accurate method for calculating the near-critical surface tensions.

Higher order curvature corrections to the field emission current density

A simple expression for the Gamow factor is obtained using a second-order curvature-corrected tunneling potential. Our results show that it approximates accurately the “exact-WKB” transmission coefficient obtained by numerically integrating over the tunneling region to obtain the Gamow factor. The average difference in current density using the respective transmission coefficients is about 1.5%, across a range of work functions ϕ∈[3−5.5] eV, Fermi energy EF∈[5−10] eV, local electric fields El∈[3−9] V/nm, and radius of curvature R≥5 nm. An easy-to-use correction factor λP is also provided to approximately map the “exact-WKB” current density to the “exact” current density in terms of EF/ϕ. The average error on using λP is found to be around 3.5%. This is a vast improvement over the average error of 15% when λP=1. Finally, an analytical expression for the curvature-corrected current density is obtained using the Gamow factor. It is found to compare well with the “exact-WKB” current density even at small values of local electric field and the radius of curvature.

Generalised radiating fields in Einstein\u2013Gauss\u2013Bonnet gravity

A five-dimensional spherically symmetric generalised radiating field is studied in Einstein–Gauss–Bonnet gravity. We assume the matter distribution is an extended Vaidya-like source and the resulting Einstein–Gauss–Bonnet field equations are solved for the matter variables and mass function. The evolution of the mass, energy density and pressure are then studied within the spacetime manifold. The effects of the higher order curvature corrections of Einstein–Gauss–Bonnet gravity are prevalent in the analysis of the mass function when compared to general relativity. The effects of diffusive transport are then considered and we derive the specific equation for which diffusive behaviour is possible. Gravitational collapse is then considered and we show that collapse ends with a weak and conical singularity for the generalised source, which is not the case in Einstein gravity.

Global asymptotic dynamics of cosmological Einsteinian cubic gravity

In this paper we investigate the cosmological dynamics of an up to cubic curvature correction to General Relativity (GR) known as Cosmological Einsteinian Cubic Gravity (CECG), whose vacuum spectrum consists of the graviton exclusively and its cosmology is well-posed as an initial value problem. We are able to uncover the global asymptotic structure of the phase space of this theory. It is revealed that an inflationary matter-dominated bigbang is the global past attractor which means that inflation is the starting point of any physically meaningful cosmic history. Given that higher order curvature corrections to GR are assumed to influence the cosmological dynamics at early times -- high energies/large curvature limit -- the late-time inflation can not be a consequence of the up to cubic order curvature modifications. We confirm this assumption by showing that late-time acceleration of the expansion in the CECG model is possible only if add a cosmological constant term.

Possible high-energy negative temperature states after fine-tuning

With the steady-state assumption we approximately solve the simplified reaction-diffusion equation together with isothermal boundary conditions via the boundary perturbation approach and obtain the possible negative (dimensionless) temperatures (around the order of magnitude of \(10^{14}\)) for some selection of fine-tuned physical parameters and a fixed geometric parameter (considering a wavy-rough microannuli). Our numerical evidences will be useful to the understanding of two possible scenarios (i) spontaneous symmetry breaking with negative temperature and broken Lorentz symmetry occurs due to higher order curvature corrections similar to the beginning of the universe in a lattice (ii) dark energy in cosmology (in which a negative-pressure state is necessary to explain the accelerating expansion of the universe) as well as the application for a laboratory dark energy analogue.

Higher-dimensional radiating black holes in Einstein-Gauss-Bonnet gravity

The higher order curvature corrections in Einstein-Gauss-Bonnet gravity play a significant role in the dynamics of gravitational collapse. We extend the gravitational collapse of radiating shells of matter in Einstein-Gauss-Bonnet gravity to higher dimensions, in the context of the cosmic censorship conjecture. In five dimensions the final collapse terminates with the formation of an extended and weak conical, naked singularity in the central region. For dimensions $Ng5$, we determine that collapse terminates with a strong curvature singularity which may or may not be naked. Cosmic censorship is affected by higher-order curvature corrections. A comparison with the higher-dimensional general relativity counterpart is also given, where the dynamics are affected by the higher dimensions.

A High-Precision Resistor-Less CMOS Compensated Bandgap Reference Based on Successive Voltage-Step Compensation

A curvature-compensated resistor-less bandgap reference (BGR), which is fabricated in 0.5- $\mu \text{m}$ CMOS process, is proposed in this paper. The BGR utilizes successive voltage-step compensation to produce a temperature-insensitive voltage reference (VR), including one $\Delta V_{\text {GS}}$ step for first-order compensation and another one for higher order curvature correction. Moreover, a supply noise bypassing technique is adopted to achieve good power supply rejection performance up to high frequency. Experimental results demonstrate that this BGR is able to produce a VR of 1.196 V with a temperature coefficient of 3.98 ppm/°C at 3.6-V supply voltage. A power-supply noise attenuation of −84 dB@100 Hz and −37 dB@100 kHz are easily achieved, and the line regulation is better than 0.19 mV/V when supply voltage varies from 2.1 to 5 V. The proposed reference occupies an active area of $356 \,\,\mu \text {m} \times 150 \,\,\mu \text{m}$ and consumes a quiescent current of $38~\mu \text{A}$ .

Theoretical prediction of crystallization kinetics of a supercooled Lennard-Jones fluid.

The first order curvature correction to the crystal-liquid interfacial free energy is calculated using a theoretical model based on the interfacial excess thermodynamic properties. The correction parameter (δ), which is analogous to the Tolman length at a liquid-vapor interface, is found to be 0.48 ± 0.05 for a Lennard-Jones (LJ) fluid. We show that this curvature correction is crucial in predicting the nucleation barrier when the size of the crystal nucleus is small. The thermodynamic driving force (Δμ) corresponding to available simulated nucleation conditions is also calculated by combining the simulated data with a classical density functional theory. In this paper, we show that the classical nucleation theory is capable of predicting the nucleation barrier with excellent agreement to the simulated results when the curvature correction to the interfacial free energy is accounted for.

Criticality in third order lovelock gravity and butterfly effect

We study third order Lovelock Gravity in D=7 at the critical point which three (A)dS vacua degenerate into one. We see there is not propagating graviton at the critical point. And also we compute the butterfly velocity for this theory at the critical point by considering the shock wave solutions near horizon, this is important to note that although there is no propagating graviton at the critical point, due to boundary gravitons the butterfly velocity is non-zero. Finally we observe that the butterfly velocity for third order Lovelock Gravity at the critical point in D=7 is less than the butterfly velocity for Einstein–Gauss–Bonnet Gravity at the critical point in D=7 which is less than the butterfly velocity in D = 7 for Einstein Gravity, v_{B}^{E.H}>v_{B}^{E.G.B}>v_{B}^{3rd,,Lovelock} . Maybe we can conclude that by adding higher order curvature corrections to Einstein Gravity the butterfly velocity decreases.

A Low Power Bandgap Voltage Reference with Nonlinear Voltage Curvature Compensation

The reference voltage source is the main part both in the analog and mixed-signal integrated circuits. A good reference voltage source can provide a stable voltage for the circuit, so that the system can work stable accurately. This paper describes a low power bandgap voltage reference with second order compensated, which utilizes a Kujik bandgap reference as the first order curvature correction and adding second order non-linear voltage compensation. The presented circuit is implemented in a 0.18μm CMOS technology, and the voltage supply (VDD) is 1.8V. Piecewise curvature compensation is employed to reduce the temperature coefficient of the bandgap reference from 465ppm/°C to 5.5ppm/°C, with a temperature range –45~85°C. The circuit works under the condition of 27 °C, the output of the reference voltage is 1.207 V. The total current consumption of the whole bandgap is 11.69μA, the total area of the layout is 0.10132mm2 and the power supply rejection ratio is -63dB.

Spontaneous Symmetry Breaking in the Early Universe with a Negative Temperature and a Broken Lorentz Symmetry

In this paper we show that, in the early universe, higher order curvature corrections induce spontaneous symmetry breaking with negative temperature and broken Lorentz symmetry when the gravitational coupling constant and the cosmological constant both vary with respect to the quantum expectation value of the scalar curvature. The early universe exists on a two-state system with two different values of the effective gravitational coupling constant and the effective cosmological constant with opposite signs which are merged today into one value each.

Inflation from gravitino condensates

We review work on the formation of gravitino condensates via the super-Higgs effect in the early Universe. This is a scenario for both inflating the early universe and breaking local supersymmetry(supergravity), entirely independent of any coupling to external matter. The goldstino mode associated with the breaking of (global) supersymmetry is “eaten” by the gravitino field, which becomes massive (via its own vacuum condensation) and breaks supergravity dynamically. The most natural association of gravitino condensates with inflation proceeds in an indirect way, via a Starobinsky-type inflation, in the massive gravitino phase. This inflationary phase is associated with scalar modes hidden in the higher order curvature corrections of the effective action arising from integrating out massive gravitino degrees of freedom. The scenario is in agreement with Planck data phenomenology in a natural and phenomenologically-relevant range of parameters, namely Grand-Unified-Theory values for the supersymmetry breaking energy scale and dynamically-induced gravitino mass. A hill-top inflation, on the other hand, which could also occur in the model, whereby the role of the inflaton field is played by the gravitino condensate itself, would require significant fine tuning in the inflaton's wave function renormalisation and thus may be discarded on naturalness grounds.

Asymptotically safe Starobinsky inflation

We revisit Starobinsky inflation in a quantum gravitational context, by means of the exact Renormalisation Group (RG). We calculate the non-perturbative beta functions for Newton's `constant' G and the dimensionless R^2 coupling, and show that there exists an attractive UV fixed point where the latter one vanishes but not the former one, and we provide the corresponding beta functions. The smallness of the R^2 coupling, required for agreement with inflationary observables, is naturally ensured by its vanishing at the UV fixed point, ensuring the smallness of the primordial fluctuations, as well as providing a theoretical motivation for the initial conditions needed for successful inflation in this context. We discuss the corresponding RG dynamics, showing both how inflationary and classical observations define the renormalisation conditions for the couplings, and also how the UV regime is connected with lower energies along the RG flow. Finally, we discuss the consistency of our results when higher order curvature corrections are included, and show that they are robust to the inclusion of R^3 corrections.

Impact of extended Starobinsky model on evolution ofanisotropic, vorticity-free axially symmetric sources

We study the implications of Rn extension of Starobinsky model on dynamical instability of Vorticity-free axially symmetric gravitating body. The matter distribution is considered to be anisotropic for which modified field equations are formed in context of f(R) gravity. In order to achieve the collapse equation, we make use of the dynamical equations, extracted from linearly perturbed contracted Bianchi identities. The collapse equation carries adiabatic index Γ in terms of usual and dark source components, defining the range of stability/insatbility in Newtonian (N) and post-Newtonian (pN) eras. It is found that supersymmetric supergravity f(R) model represents the more practical substitute of higher order curvature corrections.

Effectively four-dimensional spacetimes emerging from d = 5 Einstein–Gauss–Bonnet gravity

Einstein–Gauss–Bonnet gravity in five-dimensional spacetime provides an excellent example of a theory that, while including higher order curvature corrections to general relativity, still shares many of its features, such as second-order field equations for the metric. We focus on the largely unexplored case where the coupling constants of the theory are such that no constant-curvature solution is allowed, leaving open the question of what the vacuum state should then be. We find that even a slight deviation from the anti-de Sitter Chern–Simons theory, where the vacuum state is five-dimensional AdS spacetime, leads to a complete symmetry breakdown, with the fifth dimension either being compactified into a small circle or shrinking away exponentially with time. A complete family of solutions, including duality relations among them, is uncovered and shown to be unique within a certain class. This dynamical dimensional reduction scenario seems particularly attractive as a means for higher dimensional theories to make contact with our four-dimensional world.

Discrete geometry of a small causal diamond

We study the discrete causal set geometry of a small causal diamond in a curved spacetime using the average abundance of k-element chains or total orders in the underlying causal set C. We begin by obtaining the first order curvature corrections to the flat spacetime expression for the abundance using Riemann normal coordinates. For fixed spacetime dimension this allows us to find a new expression for the discrete scalar curvature of C as well as the time-time component of its Ricci tensor in terms of the abundances of k-chains. We also find a new dimension estimator for C which replaces the flat spacetime Myrheim-Meyer estimator in generic curved spacetimes.

Choptuik’s critical phenomenon in Einstein-Gauss-Bonnet gravity

We investigate the effects of higher order curvature corrections to Einstein's Gravity on the critical phenomenon near the black hole threshold, namely the Choptuik phenomenon. We simulate numerically a five dimensional spherically symmetric gravitational collapse of massless scalar field in Einstein-Gauss-Bonnet gravity towards a black hole formation threshold. When the curvature is sufficiently large the additional higher order terms, affect the evolution of the whole system. Since high curvature characterizes the region when the critical behavior takes place this critical behavior is destroyed. Both the self similarity and the mass scaling relation disappear. Instead we find a different behavior near the black hole threshold, which depends on the coupling constant of the higher order terms. The new features include a change of the sign of the Ricci scalar on the origin which indicates changes in the local geometry of space-time, and never occurs in classical general relativity collapse, and oscillations with a constant rather than with a diminishing length scale.

Type N spacetimes as solutions of extended new massive gravity

We study algebraic type N spacetimes in the extended new massive gravity (NMG), considering both the Born-Infeld model (BI-NMG) and the model of NMG with any finite order curvature corrections. We show that for these spacetimes, the field equations of BI-NMG take the form of the massive (tensorial) Klein–Gordon type equation, just as it happens for ordinary NMG. This fact enables us to obtain the type N solution to BI-NMG, utilizing the general type N solution of NMG, earlier found in our work. We also obtain type N solutions to NMG with all finite order curvature corrections and show that, in contrast to BI-NMG, this model admits the critical point solutions, which are counterparts of “logarithmic” AdS pp-waves solutions of NMG.

A Bandgap Reference Circuit with 2nd Order Curvature Correction

Abstract A second-order compensated bandgap reference (BGR) based on a temperature dependent resistor ratio was proposed, and the temperature characteristic of the BGR was optimized. A simulation based on NEC 2 μm BiCMOS process library shows that a temperature coefficient (TC) of 7.14 ppm/oC with a range from 50 to 130 oC and a reference output of 1.167 V at 25 oC and 5 V power supply were obtained. The power supply rejection ratio (PSRR) was 92 Db at low frequency in this circuit With power supply varying between from 3 to 12 V, the variation of the reference output was less than 2.4 mV.