Employing the Noether charge technique and Visser's Euclidean approach the entropy of the nonlinear black hole described by the perturbative solution of the system of coupled equations of the quadratic gravity and nonlinear electrodynamics is constructed. The solution is parametrized by the exact location of the event horizon and charge. Special emphasis in put on the extremal configuration. Consequences of the second choice of the boundary conditions, in which the solution is paramerized by the charge and the total mass as seen by a distant observer is briefly examined.
We discuss locally Weyl (scale) covariant generalisation of quadratic curvature gravity theory in three dimensions using Riemann-Cartan-Weyl space-times. We show that this procedure of Weyl gauging yields a consistent generalisation for a particular class of quadratic curvature gravity theories which includes the New Massive Gravity theory.
The quadratic curvature lagrangians having metric field equations with second order trace are constructed relative to an orthonormal coframe. In $n>4$ dimensions, pure quadratic curvature lagrangian having second order trace constructed contains three free parameters in the most general case. The fourth order field equations of some of these models, in arbitrary dimensions, are cast in a particular form using the Schouten tensor. As a consequence, the field equations for the New massive gravity theory are related to those of the Topologically massive gravity. In particular, the conditions unde…
Black hole solutions in pure quadratic theories of gravity are interesting since they allow to formulate a set of scale-invariant thermodynamics laws. Recently, we have proven that static scale-invariant black holes have a well-defined entropy, which characterizes equivalent classes of solutions. In this paper, we generalize these results and explore the thermodynamics of rotating black holes in pure quadratic gravity.
Quadratic curvature gravity equations are projected to a complex null coframe by using the algebra of exterior forms and expressed in terms of the spinor quantities defined originally by Newman and Penrose. As an application, a new family of impulsive gravitational wave solutions propagating in various type D backgrounds is introduced.
For the quadratic theory of gravity with a scalar field, exact solutions are found for gravitational-wave models in Shapovalov~I~type spacetimes, which do not arise in models of the general theory of relativity. The theory of gravity under consideration can effectively describe the early stages of the dynamics of the universe. Type I Shapovalov spaces are the most general form of gravitational-wave Shapovalov spacetimes, whose metric in privileged coordinate systems depends on three variables, including the wave variable. For Einstein vacuum spacetimes, these wave models degenerate into simple…
In this paper, we investigate the generalized covariant entropy bound in the theory where the Einstein gravity is perturbed by the higher-order Lovelock terms. After replacing the Bekenstein-Hawking entropy with the Jacobson-Myers entropy and introducing two reasonable physical assumptions, we showed that the corresponding generalized covariant entropy bound is satisfied under a higher-order approximation of the perturbation from the higher-order Lovelock terms. Our result implies that the Jacobson-Myers entropy strictly obeys the entropy bound under the perturbation level, and the generalized…
We study the entropy spectrum of (2+1) BTZ black holes in massive gravity models. We use the formalism proposed by Jiang and Han where black hole property of adiabaticity and the oscillating velocity of the black hole horizon are used to investigate the quantization of the entropy of such systems. We find that the entropy of the BTZ black holes in massive gravity is quantized with equally spaced spectra.
In this paper, we calculated the entropy of the BTZ black hole in the framework of loop quantum gravity. We got the result that the horizon degrees of freedom can be described by the 2D SO(1,1) punctured BF theory. Finally we got the area law for the entropy of BTZ black hole.
The two gravitomagnetic effects which influence bodies orbiting around a gravitational source are the geodetic effect and the Lense-Thirring effect. The former describes the precession angle of the axis of a spinning gyroscope while in orbit around a nonrotating gravitational source whereas the latter provides a correction for this angle in the case of a spinning source. In this paper we derive the relevant equations in quadratic gravity and relate them to their equivalents in general relativity. Starting with an investigation into Kepler's third law in quadratic gravity with a scalar field, t…
Penrose suggested that issues with the origin of the second law of thermodynamics and the remarkable homogeneous and isotropic nature of the universe on large scales can be resolved with a concept of an entropy for gravitational fields captured by the Weyl curvature tensor. This has led to various proposals for an entropy density for gravity constructed from the Weyl tensor. Most work investigating such entropy densities have been restricted to general relativity and little work has been done to them in modified theories of gravity. To remedy this, we investigate the simplest proposal for an e…
The entropy functional formalism allows one to recover general relativity, modified gravity theories, as well as the Bekenstein-Hawking entropy formula. In most approaches to quantum gravity, the Bekenstein-Hawking's entropy formula acquires a logarithmic correction term. As such terms occur almost universally in most approaches to quantum gravity, we analyze the effect of such terms on the entropy functional formalism. We demonstrate that the leading correction to the micro-canonical entropy in the entropy functional formalism can be used to recover modified theories of gravity already obtain…
Since all Einstein spacetimes are vacuum solutions to quadratic gravity in four dimensions, in this paper we study various aspects of non-Einstein vacuum solutions to this theory. Most such known solutions are of traceless Ricci and Petrov type N with a constant Ricci scalar. Thus we assume the Ricci scalar to be constant which leads to a substantial simplification of the field equations. We prove that a vacuum solution to quadratic gravity with traceless Ricci tensor of type N and aligned Weyl tensor of any Petrov type is necessarily a Kundt spacetime. This will considerably simplify the sear…
In this paper, we study the Casimir effect in a curved spacetime described by gravitational actions quadratic in the curvature. In particular, we consider the dynamics of a massless scalar field confined between two nearby plates and compute the corresponding mean vacuum energy density and pressure in the framework of quadratic theories of gravity. Since we are interested in the weak-field limit, as far as the gravitational sector is concerned we work in the linear regime. Remarkably, corrections to the flat spacetime result due to extended models of gravity (although very small) may appear at…
We present a comparison of the calculation of BTZ black hole entropy in loop quantum gravity and in spin foam models. We see that both give the same answer.
For higher derivative theories of gravity, it is possible to write the action in terms of auxiliary fields. In such case, one can show that the equations of motion for both actions are equivalent and hence the actions themselves. In this paper we show that one can obtain the Wald's entropy from the equivalent action. We use this useful approach to localise a non-local gravitational action and calculate its associated entropy.
A short overview of black hole entropy in alternative gravitational theories is presented. Motivated by the recent attempts to explain the cosmic acceleration without dark energy, we focus on metric and Palatini f(R) gravity and on scalar-tensor theories.
In this paper we obtain the entropy of the Kerr black hole for a number of modified theories of gravity. We show that as long as the deviation from Einstein Hilbert term consists purely of terms involving scalar curvature and Ricci tensor, the entropy is solely given by the area law. However, the area law will be modified by appropriate corrections when we consider terms involving Riemann tensor explicitly.
The paper deals with universal thermodynamics for FRW model of the universe bounded by apparent (or event) horizon. Assuming Hawking temperature on the horizon, the unified first law is examined on the horizon for different gravity theories. The results show that equilibrium configuration is preserved with a modification to Bekenstein entropy on the horizon.
We study the entropy of black holes in the deformed Horava-Lifshitz gravity with coupling constant lambda. For lambda=1, the black hole resembles the Reissner-Norstrom black hole with a geometric parameter acting like the electric charge. Therefore, we obtain some differences in the entropy when comparing with the Schwarzschild black hole. Finally, we study the heat capacity and the thermodynamical stability of this solution.
Using quantum tunneling approach, we are able to derive the entropy with logarithmic term of the static spherically symmetric black hole in semi-classical Einstein equations with conformal anomaly. The results indicate that the logarithmic correction to Bekenstein-Hawking area entropy can be well explained by the self-gravitation.
Motivated by the analogy between the spacetime and the solid with inhomogeneous elasticity modulus, we present an alternative method to obtain the field equation of any diffeomorphism-invariant gravity, by extremizing the constructed entropy function of the displacement vector field of spacetime solid. In general stationary spacetimes, we show that the Wald entropy of horizon arises from the on-shell entropy function of spacetime solid.
Einstein's equation could be interpreted as the first law of thermodynamic near the spherically symmetric horizon. Through recalling the Einstein gravity with a more general static spherical symmetric metric, we find that the entropy would have a correction in Einstein gravity. By using this method, we investigate the Eddington-inspired Born-Infeld (EiBI) gravity. Without matter field, we can also derive the first law in EiBI gravity. With an electromagnetic field, as the field equations have a more general spherically symmetric solution in EiBI gravity, we find that correction of the entropy …
Standard methods for calculating the black hole entropy beyond general relativity are ambiguous when the horizon is non stationary. We fix these ambiguities in all quadratic curvature gravity theories, by demanding that the entropy be increasing at every time, for linear perturbations to a stationary black hole. Our result matches with the entropy formula found previously in holographic entanglement entropy calculations. We explicitly calculate the entropy increase for Vaidya-like solutions in Ricci-tensor gravity to show that (unlike the Wald entropy) the holographic entropy obeys a Second La…
The Israel equations for thin shells in General Relativity are derived directly from the least action principle. The method is elaborated for obtaining the equations for double layers in quadratic gravity from the least action principle.
We give an exact solution of the quadratic gravity in D dimensions. The solution is a plane fronted wave metric with a cosmological constant. This metric solves not only the full quadratic gravity field equations but also the linearized ones which include the linearized equations of the recently found critical gravity. A subset of the solutions change the asymptotic structure of the anti-de Sitter space due to their logarithmic behavior.
We present a simplified formulation of massive gravity where the Higgs fields have quadratic kinetic term. This new formulation allows us to prove in a very explicit way that all massive gravity theories considered so far inevitably have Boulware-Deser ghost in non-trivial fluctuations of background metric.
We generalize the Noether current method proposed by Majhi and Padmanabhan recently to $f(R)$ gravity and conformal gravity and analyze the near horizon symmetry of black holes in these models. It is shown that the entropy obtained with Cardy's formula agrees with Wald entropy.
Perturbative solutions to the fourth-order gravity describing spherically-symmetric, static and electrically charged black hole in an asymptotically de Sitter universe is constructed and discussed. Special emphasis is put on the lukewarm configurations, in which the temperature of the event horizon equals the temperature of the cosmological horizon.
The Hawking radiation of static, spherically symmetric, asymptotically flat solutions in quadratic gravity, is here explored. The emitted fermions are governed by the Dirac equation in the generalized uncertainty principle (GUP) context, that probes the spacetime (quantum) nature. The Hawking thermal spectrum is scrutinized out of the tunnelling method and the WKB procedure. The Hawking flux is shown to vanish for small black holes, for a precise combination of the GUP parameter and the coupling constants that drive the gravitational interaction in quadratic gravity, yielding absolutely stable…
