P-v criticality and heat engine efficiency for Bardeen Einstein-Gauss-Bonnet AdS black hole

In this paper,we discuss the P-v criticality and the heat engine efficiency in the Bardeen EinsteinGauss-Bonnet (EGB) AdS black hole space-time.From the P-v plane in the extended phase space,we find that the Bardeen EGB-AdS black hole conforms to Van der Waals (VdW) liquid-gas systems in the extended phase space,and P_cv_/T_c=0.369 of the Bardeen EGB-AdS black hole system is between 0.3333 of the Gauss-Bonnet AdS black hole system and 0.375 of the VdW gas system in the 5-dimensions.Then we construct a heat engine by taking the Bardeen EGB-AdS black hole as the working substance,and consider a rectangle heat cycle in the P-v plane.We find that two cases with different Bardeen parameter e and Gauss-Bonnet parameter a both have the same situation,i.e.as the entropy difference between small black hole and large black hole S2 increases,the heat engine efficiency will increase.Furthermore,as the Bardeen parameter e increases,the efficiency will decrease.However,for the Gauss-Bonnet parameter a,the result is contrary.By comparing with the well-know Carnot heat engine efficiency,we have found the efficiency ratioη/η_c versus entropy S_2 is bounded below l,so it is coincided with the thermodynamical second law.     

Modified entropic gravity revisited

Inspired by Verlinde’s idea,some modified versions of entropic gravity have been suggested.Extending them in a unified formalism,herein we derive the generalized gravitational equations accordingly.From gravitational equations,the energy-momentum conservation law and cosmological equations are investigated.The covariant conservation law of energy-momentum tensor severely constrains viable modifications of entropic gravity.A discrepancy arises when two independent methods are applied to the homogeneous isotropic universe,posing a serious challenge to modified models of entropic gravity.     

Thermodynamics of 4D dS/AdS Gauss–Bonnet black holes according to consistent gravity theory in the presence of a cloud of strings

By looking at the Lovelock theorem one can infer that the gravity model given by [1] cannot be applicable for all types of 4D Einstein–Gauss–Bonnet (EGB) curved space-time. The reason for this is that in 4D space-time, the Gauss–Bonnet invariant is a total derivative and hence it does not contribute to gravitational dynamics. Hence, the authors of [2] presented an alternative consistent EGB gravity model instead of [1] by applying a break-of-diffeomorphism property. In this work, we use the alternative model to produce a de Sitter (dS)/Anti-de Sitter (AdS) black hole metric and then investigate its thermodynamic behavior in the presence of a cloud of Nambu–Goto strings. Mathematical derivations show that the resulting diagrams of pressure vs specific volume at a constant temperature are similar to that for a van der Waals gas/fluid in an ordinary thermodynamic system in the dS sector but not in the AdS background. From this, we infer that the black hole participates in the small-to-large black hole phase transition in the dS background, while it exhibits a Hawking–Page phase transition in the AdS background. In the latter case, an evaporating black hole eventually reaches an AdS vacuum space because of its instability.     

The principle of equivalence and theories of gravity

We construct classical theories of gravity on the basis of special relativity and the Einstein-Infeld accelerating-elevator thought experiment. The resulting theories share most of the main features of general relativity, namely the nonlinear character of the theory, the metrical significance of the gravitational potentials and the geodesic equation of particle motion. They differ from general relativity in at most nonlinear terms in the gravitational constant G in their equations of particle motion and field equations.     

The microstructure and Ruppeiner geometry of charged anti-de Sitter black holes in Gauss–Bonnet gravity: from the critical point to the triple point

Ruppeiner geometry has been successfully applied in the study of the black hole microstructure by combining with the small–large black hole phase transition, and the potential interactions among the molecular-like constituent degrees of freedom are uncovered. In this paper, we will extend the study to the triple point, where three black hole phases coexist acting as a typical feature of black hole systems quite different from the small–large black hole phase transition. For the six-dimensional charged Gauss–Bonnet anti-de Sitter black hole, we thoroughly investigate the swallow tail behaviors of the Gibbs free energy and the equal area laws. After obtaining the black hole triple point in a complete parameter space, we exhibit its phase structures both in the pressure–temperature and temperature–horizon radius diagrams. Quite different from the liquid–vapor phase transition, a double peak behavior is present in the temperature–horizon radius phase diagram. Then we construct the Ruppeiner geometry and calculate the corresponding normalized curvature scalar. Near the triple point, we observe multiple negatively divergent behaviors. Positive curvature scalar is observed for the small black hole with high temperature, which indicates that the repulsive interaction dominates among the microstructure. Furthermore, we consider the variation of the curvature scalar along the coexisting intermediate and large black hole curves. Combining with the observation for different fluids, the result suggests that this black hole system behaves more like the argon or methane. Our study provides a first and preliminary step towards understanding black hole microstructure near the triple point, as well as uncovering the particular properties of the Gauss–Bonnet gravity.     

Charged AdS black holes with finite electrodynamics in 4D Einstein-Gauss-Bonnet gravity

Using a modified expression for the electric potential in the context of T-duality [Gaete and Nicolini, Phys. Lett. B, 2022], we obtained an exact charged solution within the 4D Einstein-Gauss-Bonnet (4D EGB) theory of gravity in the presence of a cosmological constant. We show that the solution also exists in the regularized 4D EGB theory. Moreover, we point out a correspondence between the black hole solution in the 4D EGB theory and the solution in the non-relativistic Horava–Lifshitz theory. The black hole solution is regular and free from singularity. As a special case, we derive a class of well known solutions in the literature.     

Quantization of reimannian gravity: Heisenberg representation

The system of equations recently proposed for a massive graviton, together with an associated spin-zero Kemmer or Proca field ofx-dependent rest mass, define, in a Riemannian covariant form, the Heisenberg representation of the interaction of these two quantized fields. The Einstein curvature of the manifold used in thisx picture is equated to the expectation value of the total energy-momentum density. The dimensionless coupling constant is the exceedingly small numberl ² k ²,l denoting Planck's length andk/c the graviton's rest mass.     

Quantization of reimannian gravity: interaction representation

A Riemann-covariant expression of Schwinger's procedure, leading from a Heisenberg to an interaction representation, completes here our quantization of the coupling of a massive graviton field and a spin-zero Kemmer field.     

A laboratory test of Mach's principle and strong-field relativistic gravity

A laboratory experiment that tests the validity of Mach's principle — the relativity and gravitational induction of inertia — and relativistic gravity in strong-field circumstances is described. It consists of looking for a stationary shift in the apparent weight of an object when a transient mass fluctuation is induced in one of its parts, that part then being subjected to a pulsed thrust. The transient mass fluctuation induced is of the order of a few tens of milligrams, and the stationary weight shift observed is several milligrams. Details of the apparatus used (capable of detecting an effect at the level of about a tenth of a milligram) are presented. Procedural protocols are laid out. The results obtained — signals some 10 to 15 times the standard error in magnitude — confirm to better than order of magnitude that the predicted effect is indeed present. The consequences of this confirmation of Mach's principle and relativistic gravity are briefly addressed. In particular, it is pointed out that in light of these results radical timelessness seems to be the correct way to understand reality and, from the practical point-of-view, it may prove possible to make traversable wormholes whenever we choose to devote sufficient resources to that end.     

Entropy of higher-dimensional charged Gauss–Bonnet black hole in de Sitter space

The fundamental equation of the thermodynamic system gives the relation between the internal energy, entropy and volume of two adjacent equilibrium states. Taking a higher-dimensional charged Gauss–Bonnet black hole in de Sitter space as a thermodynamic system, the state parameters have to meet the fundamental equation of thermodynamics. We introduce the effective thermodynamic quantities to describe the black hole in de Sitter space. Considering that in the lukewarm case the temperature of the black hole horizon is equal to that of the cosmological horizon, we conjecture that the effective temperature has the same value. In this way, we can obtain the entropy formula of spacetime by solving the differential equation. We find that the total entropy contains an extra term besides the sum of the entropies of the two horizons. The corrected term of the entropy is a function of the ratio of the black hole horizon radius to the cosmological horizon radius, and is independent of the charge of the spacetime.     

The gravitational energy‐momentum pseudo‐tensor of higher‐order theories of gravity

We derive the gravitational energy momentum tensor for a general Lagrangian of any order and in particular for a Lagrangian such as . We prove that this tensor, in general, is not covariant but only affine, then it is a pseudo‐tensor. Furthermore, the pseudo‐tensor is calculated in the weak field limit up to a first non‐vanishing term of order h² where h is the metric perturbation. The average value of the pseudo‐tensor over a suitable spacetime domain is obtained. Finally we calculate the power per unit solid angle Ω carried by a gravitational wave in a direction for a fixed wave number under a suitable gauge. These results are useful in view of searching for further modes of gravitational radiation beyond the standard two modes of General Relativity and to deal with nonlocal theories of gravity where terms involving are present. The general aim of the approach is to deal with theories of any order under the same standard of Landau pseudo‐tensor.     

The Raychaudhuri equations: A brief review

We present a brief review on the Raychaudhuri equations. Beginning with a summary of the essential features of the original article by Raychaudhuri and subsequent work of numerous authors, we move on to a discussion of the equations in the context of alternate non-Riemannian spacetimes as well as other theories of gravity, with a special mention on the equations in spacetimes with torsion (Einstein-Cartan-Sciama-Kibble theory). Finally, we give an overview of some recent applications of these equations in general relativity, quantum field theory, string theory and the theory of relativisitic membranes. We conclude with a summary and provide our own perspectives on directions of future research.      

Kinematics in matrix gravity

We develop the kinematics in Matrix Gravity, which is a modified theory of gravity obtained by a non-commutative deformation of General Relativity. In this model the usual interpretation of gravity as Riemannian geometry is replaced by a new kind of geometry, which is equivalent to a collection of Finsler geometries with several Finsler metrics depending both on the position and on the velocity. As a result the Riemannian geodesic flow is replaced by a collection of Finsler flows. This naturally leads to a model in which a particle is described by several mass parameters. If these mass parameters are different then the equivalence principle is violated. In the non-relativistic limit this also leads to corrections to the Newton’s gravitational potential. We find the first and second order corrections to the usual Riemannian geodesic flow and evaluate the anomalous nongeodesic acceleration in a particular case of static spherically symmetric background.     

A Vaidya-type radiating solution in Einstein-Gauss-Bonnet gravity and its application to braneworld

We consider a Vaidya-type radiating spacetime in Einstein gravity with the Gauss-Bonnet combination of quadratic curvature terms. Simply generalizing the known static black hole solutions in Einstein-Gauss-Bonnet gravity, we present an exact solution in arbitrary dimensions with the energy-momentum tensor given by a null fluid form. As an application, we derive an evolution equation for the “dark radiation” in the Gauss-Bonnet braneworld.     

Collisional Penrose process of 4D rotational Einstein-Gauss-Bonnet black holes

The collisional Penrose process of massive spinning particles in a rotational Einstein-Gauss-Bonnet (EGB) black hole background is studied. By numerically solving the equations of motion for spinning particles, we find that the energy extraction efficiency increases monotonically with the decrease of the EGB coupling parameter \begin{document}$ \alpha$\end{document} . Moreover, the efficiency \begin{document}$ \eta$\end{document} increases as the particle spin s grows. We also find that the energy extraction efficiency increases with the decrease of the EGB coupling parameter \begin{document}$ \alpha$\end{document} . When the EGB coupling constant \begin{document}$ \alpha=0$\end{document} , our results reduce to the Kerr case, which has been investigated previously.     

A new metric for rotating black holes in Gauss-Bonnet gravity

This paper presents a new metric and studies slowly rotating Gauss-Bonnet black holes with a nonvanishing angular momentum in five dimensional anti-de Sitter spaces.Taking the angular momentum parameter a up to second order,the slowly rotating black hole solutions are obtained by working directly in the action.In addition,it also finds that this method is applicable in higher order Lovelock gravity.     

Charged black holes in the infinite derivative theory of gravity

The infinite derivative theory of gravity is a generalization of Einstein gravity with many interesting properties,but the black hole solutions in this theory are still not fully understood.In the paper,we concentrate on studying the charged black holes in such a theory.Adding the electromagnetic field part to the effective action,we show how the black hole solutions around the Reissner-Nordstrom metric can be solved perturbatively and iteratively.We further calculate the corresponding temperature,entropy and electrostatic potential of the black holes and verify the first law of thermodynamics.     

Can the Pioneer Anomaly be of Gravitational Origin? A Phenomenological Answer

In order to satisfy the equivalence principle, any non-conventional mechanism proposed to gravitationally explain the Pioneer anomaly, in the form in which it is presently known from the so-far analyzed Pioneer 10/11 data, cannot leave out of consideration its impact on the motion of the planets of the Solar System as well, especially those orbiting in the regions in which the anomalous behavior of the Pioneer probes manifested itself. In this paper we, first, discuss the residuals of the right ascension α and declination δ of Uranus, Neptune and Pluto obtained by processing various data sets with different, well-established dynamical theories (JPL DE, IAA EPM, VSOP). Second, we use the latest determinations of the perihelion secular precessions of some planets in order to put on the test two gravitational mechanisms recently proposed to accommodate the Pioneer anomaly based on two models of modified gravity. Finally, we adopt the ranging data to Voyager 2 when it encountered Uranus and Neptune to perform a further, independent test of the hypothesis that a Pioneer-like acceleration can also affect the motion of the outer planets of the Solar System. The obtained answers are negative.      

The strong coupling constant: Its theoretical derivation from a geometric approach to hadron structure

Since more than a decade, abi-scale, unified approach to strong and gravitational interactions has been proposed, that uses the geometrical methods of general relativity, and yielded results similar to strong gravity theory's. We fix our attention, in this note, on hadron structure, and show that also the strong interaction strength _S, ordinarily called the (perturbative) coupling-constant square, can be evaluated within our theory, and found to decrease (increase) as the distancer decreases (increases). This yields both the confinement of the hadron constituents (for large values ofr) and their asymptotic freedom (for small values ofr inside the hadron): in qualitative agreement with the experimental evidence. In other words, our approach leads us, on a purely theoretical ground, to a dependence of _S onr which had been previously found only on phenomenological and heuristic grounds. We expect the above agreement to be also quantitative, on the basis of a few checks performed in this paper, and of further work of ours on calculating meson mass spectra.     

量子引力的曲率两点真空相关

以平坦的Minkowski时空为背景，得到了任意坐标系和谐和坐标系中，n维GR引力和高导数引力的引力子自由传播子，求得了四种可能的曲率两点真空相关函数的首项.用微扰计算证明了曲率的两点真空相关函数在GR引力中为零，而在高导数引力中不为零.讨论了高导数引力与GR的引力子传播子、曲率相关函数的关系. 关键词： GR 高导数引力 引力子自由传播子 曲率真空相关函数 平移传播子